A paper which analyses the motion of a satellite launch vehicle, a rocket, from the moment it is launched till when it is placed into orbit. The paper contains derivations for equations for thrust, mass, mass loss, distance, velocity, burnout time and burnout velocity
Data models are a set of rules and/or constructs used to describe and represent aspects of the real world in a computer. GIS can handle four data models for various applications. This module explains those four.
hiee guyes this is swapnil thaware here i uploaded slide for your knowledge if you want more detail msg me on fb or mail i will help you
thanking you and slideshare.com
This lecture covers the laws of motion governing artificial satellites. It discusses key concepts like orbital mechanics, Kepler's laws, and different types of satellite orbits such as low Earth orbit, medium Earth orbit, and geostationary orbit. The lecture notes that satellites must travel at a minimum horizontal speed of 8000 m/s to achieve stable orbit and not fall back to Earth. It also explains factors that can perturb satellite orbits like non-spherical gravity and atmospheric drag.
The document discusses how mineral identification can be done using various properties. It outlines several key properties including hardness, color, streak, luster, density, cleavage, fracture, chemical activity, and special properties. Minerals can be identified by comparing these observable properties to known mineral samples. The properties allow minerals to be distinguished from one another.
Meteorite Classification and Trajectory ModelingJessie Miller
This document summarizes a student project on meteorite classification and trajectory modeling. It describes the three main types of meteorites - stony, iron, and stony iron. It discusses techniques for analyzing meteorites like thin section microscopy. The document outlines equations of motion and initial conditions used to model meteorite trajectories. Plots of orbital paths are generated and future work is proposed to model meteorite impacts or deflections off Earth.
The document discusses plate tectonics and the structure of the Earth. It describes how seismic waves can reveal layers inside the Earth like the crust, mantle, and core. It explains continental drift and how the theory of plate tectonics developed. Plates move at boundaries where they can spread apart, collide, or slide past each other, causing earthquakes and building landforms.
The International Space Station is the 10th largest engineering project in the world. It was launched in 1998 and took 10 years to build, with contributions from 16 countries. The ISS orbits Earth every 90 minutes at a speed of 17,500 mph and serves as a laboratory for research that benefits life on Earth. It is significantly larger than previous space stations and has over 50 computers controlling its various functions.
Data models are a set of rules and/or constructs used to describe and represent aspects of the real world in a computer. GIS can handle four data models for various applications. This module explains those four.
hiee guyes this is swapnil thaware here i uploaded slide for your knowledge if you want more detail msg me on fb or mail i will help you
thanking you and slideshare.com
This lecture covers the laws of motion governing artificial satellites. It discusses key concepts like orbital mechanics, Kepler's laws, and different types of satellite orbits such as low Earth orbit, medium Earth orbit, and geostationary orbit. The lecture notes that satellites must travel at a minimum horizontal speed of 8000 m/s to achieve stable orbit and not fall back to Earth. It also explains factors that can perturb satellite orbits like non-spherical gravity and atmospheric drag.
The document discusses how mineral identification can be done using various properties. It outlines several key properties including hardness, color, streak, luster, density, cleavage, fracture, chemical activity, and special properties. Minerals can be identified by comparing these observable properties to known mineral samples. The properties allow minerals to be distinguished from one another.
Meteorite Classification and Trajectory ModelingJessie Miller
This document summarizes a student project on meteorite classification and trajectory modeling. It describes the three main types of meteorites - stony, iron, and stony iron. It discusses techniques for analyzing meteorites like thin section microscopy. The document outlines equations of motion and initial conditions used to model meteorite trajectories. Plots of orbital paths are generated and future work is proposed to model meteorite impacts or deflections off Earth.
The document discusses plate tectonics and the structure of the Earth. It describes how seismic waves can reveal layers inside the Earth like the crust, mantle, and core. It explains continental drift and how the theory of plate tectonics developed. Plates move at boundaries where they can spread apart, collide, or slide past each other, causing earthquakes and building landforms.
The International Space Station is the 10th largest engineering project in the world. It was launched in 1998 and took 10 years to build, with contributions from 16 countries. The ISS orbits Earth every 90 minutes at a speed of 17,500 mph and serves as a laboratory for research that benefits life on Earth. It is significantly larger than previous space stations and has over 50 computers controlling its various functions.
The document provides information about India's Mars Orbiter Mission (Mangalyaan). It describes the mission objectives to study the Martian surface, atmosphere, and climate. It details the scientific instruments onboard including cameras and spectrometers. The spacecraft was launched in 2013 aboard a PSLV rocket and entered Mars orbit in 2014. It is controlled from the Spacecraft Control Center in Bangalore and aims to further scientific understanding of the Red Planet through its affordable design.
A Digital Terrain Model (DTM) is a digital file that provides a detailed 3D representation of the topography of the Earth's surface. It consists of terrain elevations at regularly spaced intervals that can be used to create 3D visualizations and analyze slope, aspect, height, and other topographical features. DTMs with draped aerial imagery can help with planning, engineering, and environmental impact assessments by providing accurate 3D models of land surfaces. They are used across a variety of industries and applications.
This document discusses the key elements of geography and maps. It defines geography as the study of the Earth, including natural and human factors. It also outlines several important map essentials, such as symbols, color, lines and boundaries that are used to represent geographic information visually. Specifically, it explains common map elements like compasses, scales, legends, as well as lines of latitude and longitude that are vital to identifying location and orientation on maps.
Thermal remote sensing measures the radiation emitted from surfaces using infrared wavelengths. It is based on the infrared portion of the electromagnetic spectrum, specifically the mid-wave and long-wave infrared. Thermal remote sensing is commonly performed using wavelengths between 8-14 micrometers, which corresponds to an atmospheric window and the peak emissions of most earth surfaces. It obeys fundamental radiation laws including Planck's law, Wein's displacement law, and Stefan-Boltzmann law. Emissivity describes an object's ability to emit radiation and is affected by properties like color, roughness, and moisture. Thermal remote sensing has applications in measuring land and ocean temperatures, detecting fires and monitoring volcanoes.
This document discusses clay minerals and their properties. It begins by defining clay minerals as hydrous aluminium phyllosilicates that occur with varying amounts of calcium, magnesium, iron, sodium and potassium. It notes that clay minerals are ultrafine grained and require special techniques like X-ray diffraction for study. The document then covers the chemical composition, physical properties, optical properties, structures, and classification of different clay minerals - including kaolinite, smectite, illite, and vermiculite. It concludes by discussing the paragenesis, uses, and references.
This document discusses different types of mass movements such as landslides, rock falls, avalanches, mud flows, and debris flows. It describes key concepts related to mass movements including their anatomy, causes, triggers, and classification. Specifically, it discusses how gravity, water, earth materials, slope steepness, vegetation, climate, and time can all contribute to slope instability and mass wasting events. The document also provides examples of different mass movement types including rotational and translational landslides, falls, flows, slides, and subsidence.
GPS uses trilateration to determine location based on distances to at least three satellites. Each satellite transmits its precise location and time of transmission. The GPS receiver uses the speed of light and transmission time to calculate distances, allowing it to determine its position at the intersection of distance spheres from multiple satellites. Accuracy relies on precise timekeeping of satellites and receivers.
This document provides a detailed overview of the stratigraphy, lithology, structure, tectonics, and mineral resources of Meghalaya, India. It discusses the geological formations in the region from the Precambrian basement rocks up through more recent Cretaceous and Tertiary sediments. Key formations include the Shillong Group metasedimentary rocks and Khasi Greenstone volcanic rocks from the Proterozoic, as well as the overlying Khasi, Jaintia, and Garo Groups of sedimentary rocks ranging from the Cretaceous to Tertiary periods. The structure of the Shillong Plateau is influenced by numerous faults and was uplifted starting in the Tert
The document provides an overview of the formation and components of our solar system. It describes how the solar system formed from a large cloud of gas and dust called the solar nebula. It then discusses each planet individually, including their physical characteristics such as size, composition, and orbital properties. It also briefly touches on other objects in our solar system such as comets, asteroids, and dwarf planets like Pluto.
Asteroids are rocky objects that orbit the sun and are smaller than planets. Comets are made of ice and dust with elongated orbits around the sun, forming tails as they near the sun. Meteors enter Earth's atmosphere as meteorites and appear as "shooting stars", transitioning from meteoroid to meteor to meteorite. While both appear as streaks of light, comets remain stationary while meteors quickly streak across the sky.
Vertical exaggeration (VE) refers to how much a cross-sectional profile has been exaggerated compared to the actual terrain. To calculate VE, divide the vertical scale by the horizontal scale. The vertical scale represents the height units per centimeter on the profile, while the horizontal scale is the map scale used to create the profile. The VE number indicates how many times the vertical axis has been stretched compared to the horizontal axis.
Fractures are weaknesses in rock where separation can occur. They form due to stress from tectonic and other geological forces. There are two main types of fractures: faults where adjacent blocks are displaced parallel to the fracture surface from shearing; and joints where blocks move perpendicular with no displacement. Fractures are important for fluid migration, understanding geology and tectonics, and engineering projects. They are classified based on displacement and can be identified through field evidence like offset strata, slickensides and fault rocks.
This document discusses remote sensing and the interactions of electromagnetic radiation with the atmosphere and Earth's surface. It covers three main topics:
1. How EM radiation interacts with particles and gases in the atmosphere through scattering, absorption, and transmission, attenuating the signal. The main types of scattering - Rayleigh, Mie, and non-selective - are described.
2. The three main atmospheric constituents that absorb radiation: ozone, carbon dioxide, and water vapor. Absorption windows where radiation can pass through are identified.
3. How radiation interacts with the Earth's surface through absorption, reflection, and transmission. The spectral reflectance curves of vegetation, soil, water, and rock are examined.
The document summarizes India's Mars Orbiter Mission (MOM), which made India the first nation to successfully reach Mars on its first attempt. MOM was launched aboard a Polar Satellite Launch Vehicle on November 5, 2013. It carried scientific instruments to study the Martian atmosphere and surface. After orbit raising maneuvers, MOM was successfully inserted into Mars' orbit on September 24, 2014, making India the fourth space agency to reach Mars. The mission aims to develop technologies for interplanetary travel and explore the Red Planet's features and atmosphere.
This document outlines the theoretical framework for how data is transformed in a geographic information system (GIS). It discusses four main stages of transformation: (1) data is selected from the real world, (2) input into the GIS, (3) manipulated and stored within the system, and (4) output from the system. Each stage may involve several operations on the data. Understanding how these transformations work forms the theoretical basis for modeling and representing real-world objects and information in a GIS.
The document discusses various types of satellite orbits. It explains that low Earth orbit ranges from 600-1000 km from the Earth's surface. Satellites in these orbits circle the Earth every 90 minutes. Their orbits can be either ascending, moving south to north, or descending, moving north to south, when crossing the equator. Many Earth observation satellites use a sun-synchronous polar orbit, which keeps the satellite in the same position relative to the sun as it circles the Earth 16 times per day.
Cordinate system and map projection.pdfsamuelzewdu3
This document discusses coordinate systems and map projections. It defines projection as representing the curved Earth on a flat surface, which inevitably causes distortions. It describes geographic and projection coordinate systems, and how Universal Transverse Mercator (UTM) divides the world into zones to allow for linear measurements. Datums define precise starting points for coordinate systems and projections.
The document summarizes the Mesozoic Era stratigraphy in three periods: Triassic, Jurassic, and Cretaceous. It describes the lithology and fossil content of formations from these periods found in various regions of India, including the Himalayas, Kashmir, Spiti, and the Indian peninsula. Key points include the marine deposits of the Triassic in Spiti and Kashmir characterized by limestones and shales, and the Jurassic rock units of Spiti, Kashmir, and Kutch divided into named members.
This document summarizes different groups of silicate minerals. It discusses isolated silicates like olivine, single chain silicates like pyroxene, double chain silicates like amphibole, sheet silicates like mica and chlorite, and framework silicates like quartz and feldspar. Each group is characterized by the arrangement and bonding of silicon and oxygen tetrahedra. Key identification features are also provided for common minerals in each group like olivine, pyroxene, amphibole, biotite, muscovite, chlorite, quartz, potassium feldspar and plagioclase feldspar.
This document discusses the four main types of satellite orbits:
1) GEO (geostationary earth orbit) satellites orbit at 36,000 km from Earth and are used for radio, TV, etc. due to their ability to cover large areas with few satellites. However, they require large antennas and transmission power.
2) MEO (medium earth orbit) satellites operate between 5,000-12,000 km and require a moderate number of satellites but higher transmission power and specialized antennas.
3) LEO (low earth orbit) satellites orbit within 1,500 km and require low transmission power but a large number (50-200) of satellites for global coverage and have short lifespans of 5-
This document summarizes a student's analysis of aeroelastic divergence and flutter for a swept wing. In part 1, the student calculates the required stiffness (K) to achieve a specified divergence speed for a given wing configuration. A parametric study shows that increasing flexural rigidity (EI), torsional rigidity (GJ), or stiffness (K) increases divergence speed as expected. With K=0, the student estimates possible forward sweep angles that would achieve the required divergence speed. In part 2, the student considers flutter of the flexible wing and calculates flutter speeds for different configurations.
Aerodynamics aeronautics and flight mechanicsAghilesh V
The document discusses the history of aeronautics and provides an overview of key topics in aerodynamics and aircraft performance. It begins with a brief summary of the Wright Brothers' first controlled, powered flight on December 17, 1903. The document then outlines several chapters that will cover topics like fluid mechanics, lift generation, drag, high-speed aerodynamics, thrust production, aircraft performance, stability and control. It provides the table of contents to guide the discussion of aeronautical science concepts.
The document provides information about India's Mars Orbiter Mission (Mangalyaan). It describes the mission objectives to study the Martian surface, atmosphere, and climate. It details the scientific instruments onboard including cameras and spectrometers. The spacecraft was launched in 2013 aboard a PSLV rocket and entered Mars orbit in 2014. It is controlled from the Spacecraft Control Center in Bangalore and aims to further scientific understanding of the Red Planet through its affordable design.
A Digital Terrain Model (DTM) is a digital file that provides a detailed 3D representation of the topography of the Earth's surface. It consists of terrain elevations at regularly spaced intervals that can be used to create 3D visualizations and analyze slope, aspect, height, and other topographical features. DTMs with draped aerial imagery can help with planning, engineering, and environmental impact assessments by providing accurate 3D models of land surfaces. They are used across a variety of industries and applications.
This document discusses the key elements of geography and maps. It defines geography as the study of the Earth, including natural and human factors. It also outlines several important map essentials, such as symbols, color, lines and boundaries that are used to represent geographic information visually. Specifically, it explains common map elements like compasses, scales, legends, as well as lines of latitude and longitude that are vital to identifying location and orientation on maps.
Thermal remote sensing measures the radiation emitted from surfaces using infrared wavelengths. It is based on the infrared portion of the electromagnetic spectrum, specifically the mid-wave and long-wave infrared. Thermal remote sensing is commonly performed using wavelengths between 8-14 micrometers, which corresponds to an atmospheric window and the peak emissions of most earth surfaces. It obeys fundamental radiation laws including Planck's law, Wein's displacement law, and Stefan-Boltzmann law. Emissivity describes an object's ability to emit radiation and is affected by properties like color, roughness, and moisture. Thermal remote sensing has applications in measuring land and ocean temperatures, detecting fires and monitoring volcanoes.
This document discusses clay minerals and their properties. It begins by defining clay minerals as hydrous aluminium phyllosilicates that occur with varying amounts of calcium, magnesium, iron, sodium and potassium. It notes that clay minerals are ultrafine grained and require special techniques like X-ray diffraction for study. The document then covers the chemical composition, physical properties, optical properties, structures, and classification of different clay minerals - including kaolinite, smectite, illite, and vermiculite. It concludes by discussing the paragenesis, uses, and references.
This document discusses different types of mass movements such as landslides, rock falls, avalanches, mud flows, and debris flows. It describes key concepts related to mass movements including their anatomy, causes, triggers, and classification. Specifically, it discusses how gravity, water, earth materials, slope steepness, vegetation, climate, and time can all contribute to slope instability and mass wasting events. The document also provides examples of different mass movement types including rotational and translational landslides, falls, flows, slides, and subsidence.
GPS uses trilateration to determine location based on distances to at least three satellites. Each satellite transmits its precise location and time of transmission. The GPS receiver uses the speed of light and transmission time to calculate distances, allowing it to determine its position at the intersection of distance spheres from multiple satellites. Accuracy relies on precise timekeeping of satellites and receivers.
This document provides a detailed overview of the stratigraphy, lithology, structure, tectonics, and mineral resources of Meghalaya, India. It discusses the geological formations in the region from the Precambrian basement rocks up through more recent Cretaceous and Tertiary sediments. Key formations include the Shillong Group metasedimentary rocks and Khasi Greenstone volcanic rocks from the Proterozoic, as well as the overlying Khasi, Jaintia, and Garo Groups of sedimentary rocks ranging from the Cretaceous to Tertiary periods. The structure of the Shillong Plateau is influenced by numerous faults and was uplifted starting in the Tert
The document provides an overview of the formation and components of our solar system. It describes how the solar system formed from a large cloud of gas and dust called the solar nebula. It then discusses each planet individually, including their physical characteristics such as size, composition, and orbital properties. It also briefly touches on other objects in our solar system such as comets, asteroids, and dwarf planets like Pluto.
Asteroids are rocky objects that orbit the sun and are smaller than planets. Comets are made of ice and dust with elongated orbits around the sun, forming tails as they near the sun. Meteors enter Earth's atmosphere as meteorites and appear as "shooting stars", transitioning from meteoroid to meteor to meteorite. While both appear as streaks of light, comets remain stationary while meteors quickly streak across the sky.
Vertical exaggeration (VE) refers to how much a cross-sectional profile has been exaggerated compared to the actual terrain. To calculate VE, divide the vertical scale by the horizontal scale. The vertical scale represents the height units per centimeter on the profile, while the horizontal scale is the map scale used to create the profile. The VE number indicates how many times the vertical axis has been stretched compared to the horizontal axis.
Fractures are weaknesses in rock where separation can occur. They form due to stress from tectonic and other geological forces. There are two main types of fractures: faults where adjacent blocks are displaced parallel to the fracture surface from shearing; and joints where blocks move perpendicular with no displacement. Fractures are important for fluid migration, understanding geology and tectonics, and engineering projects. They are classified based on displacement and can be identified through field evidence like offset strata, slickensides and fault rocks.
This document discusses remote sensing and the interactions of electromagnetic radiation with the atmosphere and Earth's surface. It covers three main topics:
1. How EM radiation interacts with particles and gases in the atmosphere through scattering, absorption, and transmission, attenuating the signal. The main types of scattering - Rayleigh, Mie, and non-selective - are described.
2. The three main atmospheric constituents that absorb radiation: ozone, carbon dioxide, and water vapor. Absorption windows where radiation can pass through are identified.
3. How radiation interacts with the Earth's surface through absorption, reflection, and transmission. The spectral reflectance curves of vegetation, soil, water, and rock are examined.
The document summarizes India's Mars Orbiter Mission (MOM), which made India the first nation to successfully reach Mars on its first attempt. MOM was launched aboard a Polar Satellite Launch Vehicle on November 5, 2013. It carried scientific instruments to study the Martian atmosphere and surface. After orbit raising maneuvers, MOM was successfully inserted into Mars' orbit on September 24, 2014, making India the fourth space agency to reach Mars. The mission aims to develop technologies for interplanetary travel and explore the Red Planet's features and atmosphere.
This document outlines the theoretical framework for how data is transformed in a geographic information system (GIS). It discusses four main stages of transformation: (1) data is selected from the real world, (2) input into the GIS, (3) manipulated and stored within the system, and (4) output from the system. Each stage may involve several operations on the data. Understanding how these transformations work forms the theoretical basis for modeling and representing real-world objects and information in a GIS.
The document discusses various types of satellite orbits. It explains that low Earth orbit ranges from 600-1000 km from the Earth's surface. Satellites in these orbits circle the Earth every 90 minutes. Their orbits can be either ascending, moving south to north, or descending, moving north to south, when crossing the equator. Many Earth observation satellites use a sun-synchronous polar orbit, which keeps the satellite in the same position relative to the sun as it circles the Earth 16 times per day.
Cordinate system and map projection.pdfsamuelzewdu3
This document discusses coordinate systems and map projections. It defines projection as representing the curved Earth on a flat surface, which inevitably causes distortions. It describes geographic and projection coordinate systems, and how Universal Transverse Mercator (UTM) divides the world into zones to allow for linear measurements. Datums define precise starting points for coordinate systems and projections.
The document summarizes the Mesozoic Era stratigraphy in three periods: Triassic, Jurassic, and Cretaceous. It describes the lithology and fossil content of formations from these periods found in various regions of India, including the Himalayas, Kashmir, Spiti, and the Indian peninsula. Key points include the marine deposits of the Triassic in Spiti and Kashmir characterized by limestones and shales, and the Jurassic rock units of Spiti, Kashmir, and Kutch divided into named members.
This document summarizes different groups of silicate minerals. It discusses isolated silicates like olivine, single chain silicates like pyroxene, double chain silicates like amphibole, sheet silicates like mica and chlorite, and framework silicates like quartz and feldspar. Each group is characterized by the arrangement and bonding of silicon and oxygen tetrahedra. Key identification features are also provided for common minerals in each group like olivine, pyroxene, amphibole, biotite, muscovite, chlorite, quartz, potassium feldspar and plagioclase feldspar.
This document discusses the four main types of satellite orbits:
1) GEO (geostationary earth orbit) satellites orbit at 36,000 km from Earth and are used for radio, TV, etc. due to their ability to cover large areas with few satellites. However, they require large antennas and transmission power.
2) MEO (medium earth orbit) satellites operate between 5,000-12,000 km and require a moderate number of satellites but higher transmission power and specialized antennas.
3) LEO (low earth orbit) satellites orbit within 1,500 km and require low transmission power but a large number (50-200) of satellites for global coverage and have short lifespans of 5-
This document summarizes a student's analysis of aeroelastic divergence and flutter for a swept wing. In part 1, the student calculates the required stiffness (K) to achieve a specified divergence speed for a given wing configuration. A parametric study shows that increasing flexural rigidity (EI), torsional rigidity (GJ), or stiffness (K) increases divergence speed as expected. With K=0, the student estimates possible forward sweep angles that would achieve the required divergence speed. In part 2, the student considers flutter of the flexible wing and calculates flutter speeds for different configurations.
Aerodynamics aeronautics and flight mechanicsAghilesh V
The document discusses the history of aeronautics and provides an overview of key topics in aerodynamics and aircraft performance. It begins with a brief summary of the Wright Brothers' first controlled, powered flight on December 17, 1903. The document then outlines several chapters that will cover topics like fluid mechanics, lift generation, drag, high-speed aerodynamics, thrust production, aircraft performance, stability and control. It provides the table of contents to guide the discussion of aeronautical science concepts.
Basics of Rocket Propulsion Part 2 The Thrust EquationZack Wanambwa
1) A rocket system can be modeled using Newton's Second Law of Motion. The thrust of a rocket is equal to the rate of change of momentum.
2) For a rocket of initial mass m drifting at velocity V0, the thrust is equal to the rate at which exhaust gases are ejected multiplied by the exhaust velocity.
3) The thrust equation relates the thrust of a rocket to the mass flow rate and exhaust velocity, where thrust equals the mass flow rate times exhaust velocity.
This document is a translation of a Russian text on the aerodynamics and flight dynamics of turbojet aircraft. It covers topics such as compressible flow, subsonic and supersonic air flow, shock waves, aerodynamic characteristics of wings and aircraft like lift and drag coefficients, effects of Mach number, high-speed flight characteristics, takeoff and climb performance, and horizontal flight forces. The translation was produced by NASA and is being provided for public use.
Mechanics of Aircraft Structures solution manual C.T. Sun 2nd edDiego Fung
Designed to help students get a solid background in structural mechanics and extensively updated to help professionals get up to speed on recent advances This Second Edition of the bestselling textbook Mechanics of Aircraft Structures combines fundamentals, an overview of new materials, and rigorous analysis tools into an excellent one-semester introductory course in structural mechanics and aerospace engineering. It's also extremely useful to practicing aerospace or mechanical engineers who want to keep abreast of new materials and recent advances. Updated and expanded, this hands-on reference covers: * Introduction to elasticity of anisotropic solids, including mechanics of composite materials and laminated structures * Stress analysis of thin-walled structures with end constraints * Elastic buckling of beam-column, plates, and thin-walled bars * Fracture mechanics as a tool in studying damage tolerance and durability Designed and structured to provide a solid foundation in structural mechanics, Mechanics of Aircraft Structures, Second Edition includes more examples, more details on some of the derivations, and more sample problems to ensure that students develop a thorough understanding of the principles.
The document discusses rocket propulsion, focusing on the launch phase of spaceflight. It describes how rockets use liquid or solid fuel engines to accelerate spacecraft to orbital velocity within 3 minutes. Liquid-fueled engines can control thrust by regulating fuel and oxidizer flow and can be stopped and restarted, while solid-fueled engines are simpler but cannot control thrust or be stopped once ignited. Common rocket fuels include liquid hydrogen and oxygen or kerosene and oxygen for liquid engines and aluminum powder for solid boosters.
This document provides an overview and summary of aerodynamic data for various space vehicles. It begins with a preface describing the history and development of understanding planetary motion from a geocentric to heliocentric model. It then presents aerodynamic data for several types of space vehicles, including capsules, probes, winged vehicles, and airbreathing hypersonic vehicles. The data includes configurational details, coefficients of steady and unsteady aerodynamic forces, and other technical specifications. The intent is to provide graduate students and engineers with reference aerodynamic information to support new space vehicle design projects.
1) The document classifies rocket propulsion systems based on their gas acceleration mechanism, including chemical, nuclear thermal, ion, hall thruster, electrostatic, magneto-plasma dynamics, and pulsed plasma thrusters.
2) It describes different types of chemical propellants including solid (black powder, homogeneous, heterogeneous), liquid (petroleum, cryogenic, hypergolic), and hybrid propellants.
3) Cryogenic propellants like liquid hydrogen and liquid oxygen provide very high performance but are difficult to store, while hypergolic propellants provide easy ignition but are highly toxic.
Rockets propel themselves through the combustion of onboard fuel and ejection of exhaust gases from a nozzle. They produce thrust through Newton's third law of equal and opposite reactions. Rockets come in different propulsion types including chemical, nuclear, and electric and are used to launch missiles, scientific sounding rockets, satellite launch vehicles, and spacecraft thrusters. Key components include multiple staging to increase thrust capacity during launch, and control systems to maintain stability and steer the rocket during flight.
This document discusses different types of rocket propulsion systems. It describes solid, liquid, gas, and hybrid rocket propellants. Solid propellant rockets have the fuel and oxidizer pre-mixed and stored in the rocket casing. Liquid propellant rockets store the fuel and oxidizer separately and pump them into the combustion chamber. Hybrid rockets combine aspects of solid and liquid rockets. The document also discusses factors to consider when selecting rocket fuels such as physical properties, performance, economic factors, and health and safety issues.
Automatic control of aircraft and missiles 2nd ed john h. blakelockMaRwa Hamed
This document is the preface to the second edition of the book "Automatic Control of Aircraft and Missiles" by John H. Blakelock. The preface outlines the changes and additions made to the material in the second edition, including expanded coverage of topics like missile guidance systems, multivariable control systems, and modeling of human pilots. It also thanks those who provided assistance in preparing the second edition.
Jet propulsion systems use gas turbines for aircraft propulsion. Gas turbines are light, compact, and have a high power-to-weight ratio. They operate on an open cycle where air is compressed, mixed with fuel and combusted, and the hot gases are expanded to produce thrust. Common jet propulsion systems include turbojets, turbofans, and turboprops which partially or fully expand combustion gases in a turbine before exiting through a nozzle.
study of jet engines & how they works
1.History of jet engine 2. Introduction 3. Parts of jet engine 4. How a get engine works 5. Types of jet engine (i) Ramjet (ii) Turbojet (iii) Turbofan (iv) Turboprop (v) Turbo shaft 6.Comparison of Turbo Jet 7.Jet engines Vs Rockets 8.Difficulties 9.Suggestion for improvement 10. Merit and Demerits 11. Jet engine uses 12.Conclusion 13.Future vision
PHYS 220A30 November 2015Endeavour Space ShuttleThe visit .docxrandymartin91030
PHYS 220A
30 November 2015
Endeavour Space Shuttle
The visit to Endeavour Space Shuttle in Los Angeles provided me with a deeper insight of how physics principles are applied in real life. Not only did I learn of how the rockets get propelled into space, but also gained a better understanding of how the satellites are injected into orbit after the rocket gets into space. As I strolled into the facility, I was excited since I finally had the chance to get the answers to the several questions that crammed in my mind regarding rockets and satellites. Before the visit, questions such as how does the spacecraft travel with accuracy and know where it’s going? Once it reaches the orbit, what keeps it in motion? Besides, can any place be chosen for the launch of the rockets? Even more importantly, I was fascinated to learn the various structural parts of the rockets and the fuel used in its operation.
The process of rocket propulsion was illustrated to me just like I had learned in my theoretical physics. Essentially, a rocket is propelled forward due to a rearward ejection of burned fuel that was initially in the rocket. Consequently, the forward thrust gained by the rocket is as a result of the back force of the ejected burning fuel. In the end, the rocket propulsion principle confirmed Newton’s third law of motion which states that action and reaction are opposite yet equal forces. Unlike the jet engine that depends on drawing in air to burn the fuel, the rockets utilize the fuel on board which is a mixture of liquid oxygen and hydrogen to cause combustion ensuring that they can operate in space where a vacuum exists. I was also intrigued to learn that the rocket didn’t work on the principle of pushing against the ground, or air but depended solely on the thrust force provided by the burning fuel. I also realized that for a large weight of rockets is dominated by fuel. As such, for massive uplift force to be achieved by the rocket, the fuel has to be burned at a rapid rate. This would ultimately ensure that the rate of change of momentum is huge and therefore causing the propulsion force to be sufficient to cause uplift. Certainly, this principle was in line with Newton’s second law of motion which suggests that the magnitude of force on a moving body is directly proportion to the rate of change of its momentum {F = (v-u)dm/t}.
The second fact that I learned at the science facility is that the earth is shielded from radioactive particles from the sun by an electromagnetic field around it. As such, when the rockets pass through the layer of the earth’s electromagnetic field, it may get charged and risk burning when leaving or entering the earth’s atmosphere from space. Therefore, the rocket’s nose is designed to be curved instead of being sharp pointed in order avoid the concentration of charges that may in the end build an electrical potential difference capable of destroying the rocket. Certainly, this principle reiterated the electrostatic cha.
Optimal trajectory to Saturn in ion-thruster powered spacecraftKristopherKerames
In this document, I derive the equations of motion for an ion-thruster powered spacecraft and use numerical methods to calculate its optimal trajectory to Saturn. I did this work within 48 hours for the University Physics Competition in 2020.
1) The document describes a mathematical model for predicting the reentry and impact of satellites into Earth's atmosphere. It uses Newton's second law of motion and models the forces of gravity and drag.
2) By solving the resulting differential equation numerically, the model can determine the impact time and velocity of a satellite. This allows estimates of the damage caused and time for evacuation if the satellite were to impact a populated area.
3) The document provides an example application of the model to Sputnik 1 and graphs the results, showing a impact time of about 5.5 minutes and velocity of 47 m/s.
This document discusses rotational motion of rigid bodies and satellites. It defines rigid bodies and rotational motion, and describes concepts like moment of inertia, kinetic energy of rotating bodies, and gravitational force. It then discusses different types of satellites like geo-stationary and polar satellites, and their uses which include weather monitoring, remote sensing, communication, and military applications.
Satellites are used for telecommunications including mobile applications like communication with ships, planes, vehicles, and handheld devices as well as TV and radio broadcasting. They provide these services to an assigned region on Earth. Satellites follow Kepler's laws of planetary motion, with their path being an ellipse around the primary body (Earth). Their motion also follows Newton's laws of motion and gravity. Orbital parameters like inclination, eccentricity, and altitude affect satellite orbits and must be maintained through station keeping to prevent orbital decay over time from perturbations. Geostationary satellites orbit at an altitude of 35,786 km, maintaining a fixed position over a location on Earth, while other non-geostationary orbits are also used.
1. The document discusses gravitation and the laws governing it, including Kepler's laws of planetary motion and Newton's universal law of gravitation.
2. It also covers topics like acceleration due to gravity, gravitational potential energy, escape velocity, satellites (both natural and artificial), and different types of satellites like geostationary and polar satellites.
3. The document concludes by explaining weightlessness experienced by astronauts in satellites due to everything being in a state of free fall under the satellite's acceleration due to gravity.
Diane Guo designed a space shuttle for a mission to Mars. The shuttle is cone-shaped to reduce atmospheric resistance. It will be made of titanium, a hard material that can withstand heat. To land, the shuttle will use parachutes at 10km above Earth and a rudder, wheels, and speed brakes. It will carry two astronauts, 400kg of food, oxygen, nitrogen and water produced from fuel cells. The shuttle will use rockets and engines fueled by hydrazine to overcome Earth's gravity and reach Mars after approximately 164 days.
Orbits and space flight, types of orbitsShiva Uppu
This document discusses orbital mechanics including different types of orbits around Earth and other planets. It begins by defining orbital elements like eccentricity, semi-major axis, inclination, and orbital period. It then describes different types of orbits including low Earth orbit, geosynchronous orbit, polar orbit, and Hohmann transfer orbits. Basic orbital equations are provided relating centripetal force, gravitational force, orbital velocity, and orbital radius. Numerical examples are worked through to calculate orbital velocity, orbital radius, and orbital period for satellites orbiting Earth.
This document provides an overview of key concepts in gravitation including: the definition of gravitation; Newton's law of universal gravitation; acceleration due to gravity and how it varies with height and depth; escape velocity; orbital velocity; gravitational potential; time period of satellites; Kepler's laws of planetary motion; and types of satellites. Key points covered include how gravity decreases with height but increases with depth below the Earth's surface, and definitions of geostationary, polar, and binding energy as they relate to satellites orbiting the Earth.
The document summarizes the effects of perturbations on satellite orbits due to the non-spherical shape and inhomogeneous mass distribution of Earth. It describes how Earth can be modeled using spherical harmonics and how the different terms (zonal, sectoral, tesseral) in the expansion affect the orbital elements like inclination, eccentricity, and longitude of satellites. While short-term changes may occur, the average values of semimajor axis and eccentricity remain constant. Long-term effects are seen in the right ascension of the ascending node, argument of perigee, and mean anomaly. The document provides mathematical expressions to describe these perturbations.
The Tsiolkovsky rocket equation describes the motion of rocket vehicles and was derived independently by several scientists in the 19th and early 20th centuries. It states that the change in velocity of a rocket is determined by the exhaust velocity and the ratio of the rocket's initial mass to its final mass. The rocket equation accounts only for thrust and does not include other forces like gravity. It indicates that higher fuel loads require more propellant due to the increased overall mass, illustrating the inefficiency of rocket propulsion.
In physics, gravity (from Latin gravitas 'weight'[1]) is a fundamental interaction which causes mutual attraction between all things that have mass. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the strong interaction, 1036 times weaker than the electromagnetic force and 1029 times weaker than the weak interaction. As a result, it has no significant influence at the level of subatomic particles.[2] However, gravity is the most significant interaction between objects at the macroscopic scale, and it determines the motion of planets, stars, galaxies, and even light.
On Earth, gravity gives weight to physical objects, and the Moon's gravity is responsible for sublunar tides in the oceans (the corresponding antipodal tide is caused by the inertia of the Earth and Moon orbiting one another). Gravity also has many important biological functions, helping to guide the growth of plants through the process of gravitropism and influencing the circulation of fluids in multicellular organisms.
The gravitational attraction between the original gaseous matter in the universe caused it to coalesce and form stars which eventually condensed into galaxies, so gravity is responsible for many of the large-scale structures in the universe. Gravity has an infinite range, although its effects become weaker as objects get farther away.
Gravity is most accurately described by the general theory of relativity (proposed by Albert Einstein in 1915), which describes gravity not as a force, but as the curvature of spacetime, caused by the uneven distribution of mass, and causing masses to move along geodesic lines. The most extreme example of this curvature of spacetime is a black hole, from which nothing—not even light—can escape once past the black hole's event horizon.[3] However, for most applications, gravity is well approximated by Newton's law of universal gravitation, which describes gravity as a force causing any two bodies to be attracted toward each other, with magnitude proportional to the product of their masses and inversely proportional to the square of the distance between them.
Current models of particle physics imply that the earliest instance of gravity in the universe, possibly in the form of quantum gravity, supergravity or a gravitational singularity, along with ordinary space and time, developed during the Planck epoch (up to 10−43 seconds after the birth of the universe), possibly from a primeval state, such as a false vacuum, quantum vacuum or virtual particle, in a currently unknown manner.[4] Scientists are currently working to develop a theory of gravity consistent with quantum mechanics, a quantum gravity theory,[5] which would allow gravity to be united in a common mathematical framework (a theory of everything) with the other three fundamental interactions of physics.
Satellite Communication Unit 1 ppt for ECEssuserb20042
The document provides information about the EC8094 Satellite Communication course offered at an educational institution. The objectives of the course are to understand satellite orbits, satellite and earth segments, link power budget calculations, satellite access and coding technologies, and satellite networks. The outcomes are that students will be able to identify satellite orbits, analyze satellite subsystems, evaluate link power budgets, identify access technologies, and design satellite applications. The course consists of 5 units covering satellite orbits, the space segment, satellite link design, access and coding methods, and satellite applications.
1) The gravitational slingshot effect allows spacecraft to gain kinetic energy from planetary flybys through a process explained by Newtonian physics and relativistic kinematics.
2) Relativistic analysis shows that a spacecraft's kinetic energy increases if it approaches a planet with a smaller exit angle compared to its entrance angle, and decreases if the exit angle is larger.
3) NASA has used the slingshot effect to boost spacecraft to explore the outer solar system, with Voyager gaining assistance from Jupiter and Cassini planned to receive boosts on its journey to Saturn.
This document reviews solar tracking systems which move photovoltaic panels to face the sun throughout the day, improving efficiency over fixed panels. It discusses types of tracking systems including single-axis and dual-axis that track azimuth and altitude angles. While dual-axis tracking is most efficient, single-axis tracking is more cost-effective. The review covers components like sensors, algorithms, controllers and actuators used in tracking systems. It also explains how tracking maximizes the cosine angle of incidence to the sun compared to fixed panels, increasing energy yield.
Gravity is a mysterious force that attracts all objects with mass, even when far apart. Newton discovered that all objects accelerate towards Earth at 9.81 m/s2, and the moon accelerates towards Earth at 2.72 m/s2. Gravity is weak but exists between all objects, causing dust in space to come together to form stars and planets.
This document contains lecture notes on various topics related to gravitation and orbital mechanics:
1. It defines Newton's law of gravitation and the gravitational constant G.
2. It discusses the difference between G and g, the acceleration due to gravity, and derives the relation between the two.
3. It then covers concepts like the critical velocity, time period, binding energy, and escape velocity required for a satellite to orbit or escape the gravitational pull of Earth.
4. Additional topics include weightlessness in satellites, variation of g with altitude and depth, and the definition of latitude.
Immersive Learning That Works: Research Grounding and Paths ForwardLeonel Morgado
We will metaverse into the essence of immersive learning, into its three dimensions and conceptual models. This approach encompasses elements from teaching methodologies to social involvement, through organizational concerns and technologies. Challenging the perception of learning as knowledge transfer, we introduce a 'Uses, Practices & Strategies' model operationalized by the 'Immersive Learning Brain' and ‘Immersion Cube’ frameworks. This approach offers a comprehensive guide through the intricacies of immersive educational experiences and spotlighting research frontiers, along the immersion dimensions of system, narrative, and agency. Our discourse extends to stakeholders beyond the academic sphere, addressing the interests of technologists, instructional designers, and policymakers. We span various contexts, from formal education to organizational transformation to the new horizon of an AI-pervasive society. This keynote aims to unite the iLRN community in a collaborative journey towards a future where immersive learning research and practice coalesce, paving the way for innovative educational research and practice landscapes.
Travis Hills' Endeavors in Minnesota: Fostering Environmental and Economic Pr...Travis Hills MN
Travis Hills of Minnesota developed a method to convert waste into high-value dry fertilizer, significantly enriching soil quality. By providing farmers with a valuable resource derived from waste, Travis Hills helps enhance farm profitability while promoting environmental stewardship. Travis Hills' sustainable practices lead to cost savings and increased revenue for farmers by improving resource efficiency and reducing waste.
Phenomics assisted breeding in crop improvementIshaGoswami9
As the population is increasing and will reach about 9 billion upto 2050. Also due to climate change, it is difficult to meet the food requirement of such a large population. Facing the challenges presented by resource shortages, climate
change, and increasing global population, crop yield and quality need to be improved in a sustainable way over the coming decades. Genetic improvement by breeding is the best way to increase crop productivity. With the rapid progression of functional
genomics, an increasing number of crop genomes have been sequenced and dozens of genes influencing key agronomic traits have been identified. However, current genome sequence information has not been adequately exploited for understanding
the complex characteristics of multiple gene, owing to a lack of crop phenotypic data. Efficient, automatic, and accurate technologies and platforms that can capture phenotypic data that can
be linked to genomics information for crop improvement at all growth stages have become as important as genotyping. Thus,
high-throughput phenotyping has become the major bottleneck restricting crop breeding. Plant phenomics has been defined as the high-throughput, accurate acquisition and analysis of multi-dimensional phenotypes
during crop growing stages at the organism level, including the cell, tissue, organ, individual plant, plot, and field levels. With the rapid development of novel sensors, imaging technology,
and analysis methods, numerous infrastructure platforms have been developed for phenotyping.
The binding of cosmological structures by massless topological defectsSérgio Sacani
Assuming spherical symmetry and weak field, it is shown that if one solves the Poisson equation or the Einstein field
equations sourced by a topological defect, i.e. a singularity of a very specific form, the result is a localized gravitational
field capable of driving flat rotation (i.e. Keplerian circular orbits at a constant speed for all radii) of test masses on a thin
spherical shell without any underlying mass. Moreover, a large-scale structure which exploits this solution by assembling
concentrically a number of such topological defects can establish a flat stellar or galactic rotation curve, and can also deflect
light in the same manner as an equipotential (isothermal) sphere. Thus, the need for dark matter or modified gravity theory is
mitigated, at least in part.
When I was asked to give a companion lecture in support of ‘The Philosophy of Science’ (https://shorturl.at/4pUXz) I decided not to walk through the detail of the many methodologies in order of use. Instead, I chose to employ a long standing, and ongoing, scientific development as an exemplar. And so, I chose the ever evolving story of Thermodynamics as a scientific investigation at its best.
Conducted over a period of >200 years, Thermodynamics R&D, and application, benefitted from the highest levels of professionalism, collaboration, and technical thoroughness. New layers of application, methodology, and practice were made possible by the progressive advance of technology. In turn, this has seen measurement and modelling accuracy continually improved at a micro and macro level.
Perhaps most importantly, Thermodynamics rapidly became a primary tool in the advance of applied science/engineering/technology, spanning micro-tech, to aerospace and cosmology. I can think of no better a story to illustrate the breadth of scientific methodologies and applications at their best.
Describing and Interpreting an Immersive Learning Case with the Immersion Cub...Leonel Morgado
Current descriptions of immersive learning cases are often difficult or impossible to compare. This is due to a myriad of different options on what details to include, which aspects are relevant, and on the descriptive approaches employed. Also, these aspects often combine very specific details with more general guidelines or indicate intents and rationales without clarifying their implementation. In this paper we provide a method to describe immersive learning cases that is structured to enable comparisons, yet flexible enough to allow researchers and practitioners to decide which aspects to include. This method leverages a taxonomy that classifies educational aspects at three levels (uses, practices, and strategies) and then utilizes two frameworks, the Immersive Learning Brain and the Immersion Cube, to enable a structured description and interpretation of immersive learning cases. The method is then demonstrated on a published immersive learning case on training for wind turbine maintenance using virtual reality. Applying the method results in a structured artifact, the Immersive Learning Case Sheet, that tags the case with its proximal uses, practices, and strategies, and refines the free text case description to ensure that matching details are included. This contribution is thus a case description method in support of future comparative research of immersive learning cases. We then discuss how the resulting description and interpretation can be leveraged to change immersion learning cases, by enriching them (considering low-effort changes or additions) or innovating (exploring more challenging avenues of transformation). The method holds significant promise to support better-grounded research in immersive learning.
Authoring a personal GPT for your research and practice: How we created the Q...Leonel Morgado
Thematic analysis in qualitative research is a time-consuming and systematic task, typically done using teams. Team members must ground their activities on common understandings of the major concepts underlying the thematic analysis, and define criteria for its development. However, conceptual misunderstandings, equivocations, and lack of adherence to criteria are challenges to the quality and speed of this process. Given the distributed and uncertain nature of this process, we wondered if the tasks in thematic analysis could be supported by readily available artificial intelligence chatbots. Our early efforts point to potential benefits: not just saving time in the coding process but better adherence to criteria and grounding, by increasing triangulation between humans and artificial intelligence. This tutorial will provide a description and demonstration of the process we followed, as two academic researchers, to develop a custom ChatGPT to assist with qualitative coding in the thematic data analysis process of immersive learning accounts in a survey of the academic literature: QUAL-E Immersive Learning Thematic Analysis Helper. In the hands-on time, participants will try out QUAL-E and develop their ideas for their own qualitative coding ChatGPT. Participants that have the paid ChatGPT Plus subscription can create a draft of their assistants. The organizers will provide course materials and slide deck that participants will be able to utilize to continue development of their custom GPT. The paid subscription to ChatGPT Plus is not required to participate in this workshop, just for trying out personal GPTs during it.
The ability to recreate computational results with minimal effort and actionable metrics provides a solid foundation for scientific research and software development. When people can replicate an analysis at the touch of a button using open-source software, open data, and methods to assess and compare proposals, it significantly eases verification of results, engagement with a diverse range of contributors, and progress. However, we have yet to fully achieve this; there are still many sociotechnical frictions.
Inspired by David Donoho's vision, this talk aims to revisit the three crucial pillars of frictionless reproducibility (data sharing, code sharing, and competitive challenges) with the perspective of deep software variability.
Our observation is that multiple layers — hardware, operating systems, third-party libraries, software versions, input data, compile-time options, and parameters — are subject to variability that exacerbates frictions but is also essential for achieving robust, generalizable results and fostering innovation. I will first review the literature, providing evidence of how the complex variability interactions across these layers affect qualitative and quantitative software properties, thereby complicating the reproduction and replication of scientific studies in various fields.
I will then present some software engineering and AI techniques that can support the strategic exploration of variability spaces. These include the use of abstractions and models (e.g., feature models), sampling strategies (e.g., uniform, random), cost-effective measurements (e.g., incremental build of software configurations), and dimensionality reduction methods (e.g., transfer learning, feature selection, software debloating).
I will finally argue that deep variability is both the problem and solution of frictionless reproducibility, calling the software science community to develop new methods and tools to manage variability and foster reproducibility in software systems.
Exposé invité Journées Nationales du GDR GPL 2024
Current Ms word generated power point presentation covers major details about the micronuclei test. It's significance and assays to conduct it. It is used to detect the micronuclei formation inside the cells of nearly every multicellular organism. It's formation takes place during chromosomal sepration at metaphase.
EWOCS-I: The catalog of X-ray sources in Westerlund 1 from the Extended Weste...Sérgio Sacani
Context. With a mass exceeding several 104 M⊙ and a rich and dense population of massive stars, supermassive young star clusters
represent the most massive star-forming environment that is dominated by the feedback from massive stars and gravitational interactions
among stars.
Aims. In this paper we present the Extended Westerlund 1 and 2 Open Clusters Survey (EWOCS) project, which aims to investigate
the influence of the starburst environment on the formation of stars and planets, and on the evolution of both low and high mass stars.
The primary targets of this project are Westerlund 1 and 2, the closest supermassive star clusters to the Sun.
Methods. The project is based primarily on recent observations conducted with the Chandra and JWST observatories. Specifically,
the Chandra survey of Westerlund 1 consists of 36 new ACIS-I observations, nearly co-pointed, for a total exposure time of 1 Msec.
Additionally, we included 8 archival Chandra/ACIS-S observations. This paper presents the resulting catalog of X-ray sources within
and around Westerlund 1. Sources were detected by combining various existing methods, and photon extraction and source validation
were carried out using the ACIS-Extract software.
Results. The EWOCS X-ray catalog comprises 5963 validated sources out of the 9420 initially provided to ACIS-Extract, reaching a
photon flux threshold of approximately 2 × 10−8 photons cm−2
s
−1
. The X-ray sources exhibit a highly concentrated spatial distribution,
with 1075 sources located within the central 1 arcmin. We have successfully detected X-ray emissions from 126 out of the 166 known
massive stars of the cluster, and we have collected over 71 000 photons from the magnetar CXO J164710.20-455217.
The technology uses reclaimed CO₂ as the dyeing medium in a closed loop process. When pressurized, CO₂ becomes supercritical (SC-CO₂). In this state CO₂ has a very high solvent power, allowing the dye to dissolve easily.
Cytokines and their role in immune regulation.pptx
Rocket
1. MATHEMATICAL MODEL OF THE
MOTION OF A SATELLITE LAUNCH
VEHICLE FROM LAUNCH TILL ORBIT
(AN ANALYSIS)
[9]
Varun Suriyanarayana Guided by Dr. Ranganath Navalgund
2. CONTENTS
INTRODUCTION.......................................................................................................................................3
WHAT IS A SATELLITE? ............................................................................................................................3
WHAT IS A ROCKET?................................................................................................................................4
FORCES AFFECTING THE LAUNCH VEHICLE OF THE SATELLITE(ROCKET)................................................5
DESCRIPTION OF EACH FORCE................................................................................................................5
MODELLING THE PROCESS BY WHICH A SATELLITE IS PLACED INTO ORBIT BY ITS LAUNCH
VEHICLE(ROCKET) BY WRITING EQUATIONS...........................................................................................6
DERIVATION OF EQUATIONS FOR ROCKET MOTION..............................................................................6
EQUATION FOR THRUST .........................................................................................................................6
TSIOKOVOLSKY ROCKET EQUATION........................................................................................................7
EQUATION FOR LINEAR MOTION............................................................................................................8
CONCLUSION.........................................................................................................................................10
BIBLIOGRAPHY ......................................................................................................................................12
3. INTRODUCTION
Satellites are a product of path breaking advances in technology which has resulted in huge benefits
to mankind. The first satellite ever launched was the Sputnik 1, which the USSR launched in 1957. [5]
Since then, over 6600 satellites have been launched and approximately 3600 are in orbit. [6]
Of these
3600 satellites, approximately 1000 are operational. [5]
The satellite is taken into orbit by its corresponding launch vehicle, a rocket. In order to understand
and model its motion until it is placed into orbit, one must treat the whole system as a rocket which
operates on the principle of the law of conservation of momentum. [1] [2]
Satellites serve a variety of military and civilian purposes. On the military front, satellites serve the
purposes of defence, spying and when necessary launching and detecting missiles. The civilian
purposes include weather forecasting, mapping, communication and navigation. Satellites are also
used for the purpose of research. They orbit the earth trying to gather data pertinent to our own
planet. One such example is environmental data such as temperatures which can often be measured
by satellites. Satellites also detect changes in environmental composition of a large space over a long
period of time effectively, due to their location. In addition, some satellites carry parts of space
stations which are assembled in phases over a period of time. These space stations are used to
understand the effect of the earth’s gravitational field on various phenomena. [7]
The usefulness and importance of satellites leads to a fundamental question-How do they get into
orbit and how can we use physics to explain and model this process.
To understand this process one must first understand what a satellite is and what its launch vehicle,
a rocket is. Only then can one mathematically model the motion of the system
WHAT IS A SATELLITE?
A satellite is defined as “a moon, planet or machine that orbits a planet or star.”[1]
There are two
kinds of satellites-Natural satellites and Artificial satellites. The Natural satellites include celestial
bodies such as the planets revolving around the sun and moons revolving around planets. It can also
extend to include asteroids in orbit around a planet. The earth’s most well-known natural satellite is
the moon. Artificial satellites are all man-made devices that have been sent into orbit. This includes
all satellites that are currently in orbit and all the debris that has resulted from their operations
including collisions with other satellites. Therefore even dysfunctional satellites are still artificial
satellites.
Space probes which are not in orbit but are sent into space for the purpose of investigating other
planets are not considered as Artificial Satellites. Often, launching gear falls back into the
atmosphere and disintegrates or reaches the earth. In neither case do these count as satellites.
Space probes that orbit other celestial bodies like the sun or other planets are satellites of the sun or
those planets, not the earth. Similarly, objects that were in orbit around the earth but are no longer
in orbit, possibly because of larger gravitational forces due to other planets, are not satellites
although they were satellites when they were orbiting around the Earth. [1]
4. [3]
WHAT IS A ROCKET?
A cylindrical projectile that can be propelled to a great height or distance by the combustion of its
contents.[2]
The acceleration required for launching a satellite is provided by a rocket engine. The
rocket provides a force greater than the weight of the rocket. This allows it to overcome the force
due to gravity and go upwards. The rocket operates on a principle known as the law of conservation
of momentum. The rocket has a fuel which is called the propellant, a combustion chamber and the
exhaust. The propellant can be liquid hydrogen, solid propellants, earth storable liquid propellants
and other cryogenic fuels. There is also research being conducted in the area of semi-cryogenic fuels.
Upon combustion, a large amount of energy is released. This heats up the gas giving it a greater
kinetic energy and hence a greater velocity. This velocity is directed towards the earth. However,
because the rocket has lost mass and the lost mass has a velocity towards the earth it must gain a
velocity upwards and hence accelerate upwards.
5. [4]
FORCES AFFECTING THE LAUNCH VEHICLE OF THE
SATELLITE(ROCKET)
The forces acting on the launch vehicle of the satellite are gravity, air resistance and the force from
the release of exhaust gasses (thrust). [8] [8] [10] [11] [12] [13]
All of these forces combine to produce a
function of acceleration which in turn can be used to find functions for speed and distance from
which one can identify values of mass, energy, efficiency etc. However in order to do this one must
understand each of these forces and how each force works.
DESCRIPTION OF EACH FORCE
Gravity- Since the distances over which a satellite must travel are significant and the strength of the
earth’s gravitational field decreases with distance, the simple F=mg is not quite appropriate. We
must use the equation from Newton’s law of gravitation, F= GMm/r2
where F is the force, G is the
universal gravitation constant, M is the mass of the earth, m is the mass of the rocket including the
propellant and the satellite r is the distance from the centre of the earth.
Air resistance-The force of air resistance acts against the direction of motion. It is defined by the
equation F=bvn
. b is the coefficient of drag and depends on the shape of the rocket whilst n
determines how the force varies with velocity. The coefficient of drag is dependent on air density
which is not a constant. Therefore one must use a function of air density with height from the centre
of the earth. The domain should begin at height = the height of the surface of the earth, for which
sea level should be used.
6. Thrust-This is the force that propels the launch vehicle of the satellite into space. This force must
overcome the forces of gravity and air resistance and is provided by the release of exhaust gasses.
This force arises due to the law of conservation of momentum. As the launch vehicle of the satellite
loses mass and this mass accelerates towards the earth, an equal and opposite gain in the
momentum of the launch vehicle of the satellite is observed and since the mass is decreasing, by the
equation p=mv the velocity must increase. p is momentum of the launch vehicle of the satellite, m is
the mass of the launch vehicle of the satellite and v is the velocity of the rocket.
MODELLING THE PROCESS BY WHICH A SATELLITE IS
PLACED INTO ORBIT BY ITS LAUNCH VEHICLE(ROCKET)
BY WRITING EQUATIONS
In order to model the motion of the launch vehicle carrying the satellite one has to consider the
various forces acting on it. From these forces one can understand the motion of the rocket at various
stages. From the equations of motion one can derive formulae for energy and mass. One factor that
has not been considered is relativistic effects because the maximum speed, although significantly
larger than speeds that we are used to on earth, is not comparable to the speed of light (satellites
and their launch vehicles can attain speeds of the order of 103
ms-1
to 104
ms-1
while the speed of
light is 3 X 108
ms-1
which is more than 10,000 times greater.
The equations for motion will be broken down into various parts, first the rocket equations will be
derived and then they will be applied to define the motion of the rocket at t=0 and for when the
rocket is on its way to the required orbit level. Note that the final stage, when the satellite is in orbit
does not require any of these equations in that there is no effect of air resistance or thrust. Only
gravity acts on it and thus its motion and energy can be expressed by applying Newton’s law of
gravitation.
DERIVATION OF EQUATIONS FOR ROCKET MOTION
The equations for thrust, mass as a function of time, velocity as a function of time, distance as a
function of time, the burnout time and the burnout velocity provide analysts who are designing the
rocket with tools to determine which rocket, what propellant and how much payload must be
included in the launch vehicle and the satellite itself. They also provide scientists who are observing
the launch vehicle’s path an idea of how close to or far from the ideal position, velocity and mass the
rocket actually is and what correction measures must be taken for the particular space mission as
well as similar future missions.
EQUATION FOR THRUST
The thrust required by a rocket to accelerate is greater than the weight of the rocket. However, in
order to escape the atmosphere as quickly as possible and minimise the effects of gravity and air
resistance as quickly as possible it is essential to accelerate the rocket as fast as possible. However, if
it accelerates too fast, the air resistance becomes too strong and causes the rocket to disintegrate.
Therefore an optimal thrust: weight ratio is 5:1.
In infinitesimal time:
7. Initial momentum of rocket = Mivi
Momentum of rocket after time dt: (Mi+dm)(vi+dv)
Momentum of exhaust gas after time dt: -dm(vg)
Miv= Miv+ Mdv + vidm + dmdv - dm(vg)
Divding by dt: Mdv/dt + vdm/dt + dmdv/dt - vg(dm/dt)=0
Ma +(v+dv -vg)(dm/dt)= 0
Ma = -(v+ dv-vg)(dm/dt)
Thrust = -(v+ dv- vg)(dm/dt)
Since -(v+dv - vg) = velocity of the exhaust gasses relative to the rocket, if velocity of the exhaust
gasses relative to the rocket = vexhaust and dm/dt = R which is a constant, thrust can be re-written as:
Thrust= vexhaustR[9] [10] [12]
TSIOKOVOLSKY ROCKET EQUATION
The equation for thrust can in turn can be used to find the Tsiokovolsky rocket equation which
connects the mass of the rocket to the change in its velocity in order to understand what the
efficiency of energy conversion is and how much energy is being produced.
M(dv/dt) = +(v+ dv -vg)(dm/dt)
dv = (vexhaust)(dm/M)
Integrating both sides one gets:
∫v
vf
dv = (vexhaust)∫m0
mf
1/M dm
vf – v = (vexhaust)(ln(m0/mf))
vf = (vexhaust)(ln(m0/mf)) + v
Δv = (vexhaust)(ln(m0/mf))
This equation can be written in terms of a quantity referred to as specific impulse, commonly
denoted as Isp. It is has two definitions, one which means that it measures impulse per unit mass, the
more common one measures the impulse per unit weight where weight is g (standard gravity at the
surface of the earth) times mass. In the first case, Isp =Thrust/ R whilst in the second case, it is
defined to be Isp=Thrust/Rg.
In the second case, the Tsiokovolsky rocket equation can be written as:
Δv = Ispg(ln(m0/mf))[12]
8. EQUATION FOR LINEAR MOTION
The rocket’s burnout velocity and burnout time are the important aspects of modelling the launch
vehicle’s motion. The burnout velocity and time express when the rocket is out of fuel and what its
velocity is at that moment in time. [12]
It is essential to optimise this value because if it is too much,
the satellite can spiral away into outer space after the rocket has detached and if it is too little, the
satellite will spiral into the earth after the rocket has been detached and the corresponding impact
could be disastrous. This section will provide equations for these and thereby provide a model for
the launch vehicle’s motion from the surface of the earth till the required orbit. Also given below is
an equation for the distance a rocket has travelled as a function of time. This equation however is a
second order differential equation and cannot be solved analytically. The equation has been
presented in various forms which show that an analytical solution in this case is not possible.
This equation however neglects both air resistance and gravity. If one is to factor both in one
reaches the equation:
mdv/dt = md2
r/dt2
= Rvexhaust – b(dr/dt)2
– GMm/r2
= Rvexhaust - b(dr/dt)2
– GM(m0 –
tdm/dt)/r2
d2
r/dt2
= Rvexhaust/(m0 – tR) – b(dr/dt)2
/(m0 – tR) – GM/r2
dr/dt = -vexhaustln(m0 – tR) - b∫(1/(m0 – tR))(dr)(dr/dt) – GM∫1/r2
dt + c
r + b∫∫(1/(m0 – tR)) dr dr + GM∫∫1/r2
dt dt = -vexhausttln(m0-tR) + (vexhaust/R)(t+m0ln(m0-tR)+d) +
ct
In order to calculate burnout velocity and time
But now having an external force of gravity, mg
Solving for dv gives
Or as an equation of motion
Integrating over v, t and m (Where tbo is the burn-time of the rocket)
9. Gives an equation for the velocity at burnout
The term -gt is referred to as gravity loss. This represents the losses endured by launching in a
gravity well. To maximize burnout velocity you want to minimize gravity
becomes useful to rewrite this equation in terms of a new parameter, thrust-to-weight ratio. We
define thrust-to-weight ratio, Ψ, as the thrust (which we assume is constant) divided by the weight
at liftoff, m0g. loss, which means burning the fuel as fast as possible. This makes sense because when
you spend a long time burning fuel you are wasting energy lifting unburnt fuel to a higher altitude
rather than your payload.
Practically, rocket motors are usually categorized by thrust and not burn time. So it
If we realize that thrust is
then
We can find a relation to the time it takes to burn through the fuel. If we take the burn rate to be
constant (again, not a bad assumption) then the time is to burn out is
10. However we see that mf - m0 is negative! This okay because m-dot is also negative. What we actually
want is the fuel mass divided by a (positive) burn rate.
We also want this in terms of mass ratio and thrust-to-weight ratio.
Now if we multiply by "one" we get
We recognize the term as the inverse of Ψ Thus we have the burnout time in reasonably
terms
Plugging this in for t in our burnout velocity equation gets
Now we can also introduce the symbol μ for the mass ratio and replace ve with gIsp
[12]
CONCLUSION
One must therefore conclude that while it is possible to mathematically model the motion of a
satellite and its launch vehicle from launch till orbit, it is beset by some inherent limitations. It is
possible to develop the model so as to estimate burnout time and velocity which are crucial factors
when making the launch vehicle for the satellite, deciding what kind of fuel and how much of it will
be needed . Although the model serves the purpose of explaining, through the use of equations,
how a rocket system takes a satellite up into orbit, the model is not comprehensive enough to
account for certain critical and related factors.
The first and most important factor is the presence of air resistance. Its importance is best explained
in projectile motion where air can reduce the distance a projectile travels by a factor of
approximately 10. Therefore for a model to be comprehensive, it must factor in air resistance. In
order to do this one must solve a second order differential equation. However, only first order
11. differential equations can be solved analytically. To use the second order differential equation, one
must use numeric methods which are too complicated and time consuming to do manually and
therefore supercomputers are used. This second order differential equation has been represented
above. Another essential point to note is that air resistance depends on the density of air which in
turn is related to air pressure. As altitude increases, the density of air reduces resulting in the
decrease of air resistance to the extent that satellites in higher orbits do not have any air around
them. Therefore an accurate model must factor this as well.
The second factor is that as the satellite and its launch vehicle ascend vertically, the value of g, the
gravitational field strength decreases. This decrease is related to 1/r2
where r is the distance from
the centre of the earth. Since the distances that a satellite and its launch vehicle must travel are of
the order of 7 times the earth’s radius, the value of g decreases by a factor of almost 50 during the
course of its journey. This means that the value of g decreases from 9.81 ms-2
to less than 0.2 ms-2
. If
it is assumed to be 9.81 ms-2
throughout, the calculations based on the model above would suggest
that a satellite launch vehicle needs more and higher energy fuel than it actually needs and if this
extra fuel is used, the satellite and its launch vehicle could continue into outer space. Alternatively,
its higher than calculated velocity could cause a collision with another satellite and damage both
significantly while liberating space debris that could damage current and future satellites. There are
two other aspects of gravity that have been neglected. The first is the variation in g due to the
earth’s surface not being uniform and its density varying throughout however, given the distances
involved, the impact of this is negligible. The second is the gravitational force of other celestial
bodies. Although this may be of greater importance than the variation in density and lack of
uniformity of the earth’s surface, given that the satellites are far closer to the earth than any other
celestial body, this is also something that is often insignificant.
The third factor is the need for the rocket to change angle of flight with respect to the vertical
because the satellite must be placed into orbit with a velocity perpendicular to the vertical. This
necessity and its implication that some of the rocket’s thrust must be horizontal has also been
neglected in this model. Naturally, in order for a model to be useful and accurate this horizontal
thrust must be recognised and calculated.
The fourth factor is presence of lift force. This force acts perpendicular to the flow of air and is due
to a difference in air pressure at various points on the launch vehicle of the satellite. This is most
significant when the rocket is moving at an angle as opposed to straight upwards. As mentioned
earlier, practical rockets must slowly tilt because they need to place the satellite in orbit with the
requisite horizontal velocity.
The fifth factor that is overlooked is that rockets often do not follow the prescribed path and have
deviations. Therefore a complete model would analyse the probability and magnitude of such
deviations as well as provide a probabilistic estimate as to how much correction fuel the rocket
should have. The same also applies to the satellite itself once it is placed into orbit. If the satellite
deviates from its required path, it must have the fuel required to correct its path. A truly useful
model must provide values related to this and therefore account for this possibility.
12. BIBLIOGRAPHY
[1]
http://www.nasa.gov/audience/forstudents/5-8/features/what-is-a-satellite-58.html 15 July 2014
[2]
http://encyclopedia2.thefreedictionary.com/rocket 9 August 2014
[3]
http://www.spacetoday.org/images/Sats/MilSats/DSCS_SatInSpaceLockheedMartin.jpg 9 August
2014
[4]
http://img.dictionary.com/rocket-145671-400-307.jpg 9 August 2014
[5]
http://www.universetoday.com/42198/how-many-satellites-in-space/ 9 August 2014
[6]
http://seattletimes.com/html/nationworld/2022236028_apxfallingsatellite.html 9 August 2014
[7]
http://satellites.spacesim.org/english/function/index.html 9 August 2014
[8]
http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/lecture-
notes/supplement8.pdf 18 July 2014
[9]
http://www.real-world-physics-problems.com/rocket-physics.html 26 July 2014
[10]
http://hyperphysics.phy-astr.gsu.edu/hbase/rocket.html 20 July 2014
[11]
http://www2.estesrockets.com/pdf/Physics_Curriculum.pdf 31 July 2014
[12]
http://www.braeunig.us/space/basics.htm 29 July 2014
[13]
http://web.mit.edu/16.00/www/aec/rocket.html 29 July 2014