51.pdf
•
0 likes•4 views
A
a aThis lecture introduces the NASA standard breakup model, which was developed using data from the SOCIT series of HVI experiments and other sources. The model can be used to calculate the number, mass, area-to-mass ratio, and velocity of fragments resulting from explosions or collisions in space. It provides empirical equations to estimate these values as a function of fragment size and other parameters based on historical data from events like satellite breakups and hypervelocity impact tests. The model is implemented in simulations to analyze and predict the evolution of space debris populations over time.
Report
Share
Report
Share
Download to read offline
Recommended
32.pdf
The lecture discusses a simulation study conducted for ESA that aimed to understand how the space debris environment is affected by key satellite and constellation parameters. The study used three evolutionary debris models to project the debris environment out to 2213 under different scenarios. A baseline case examined the impact of a 1080-satellite constellation in 20 orbital planes at 1100km altitude, with a 5-year lifetime and 90% post-mission disposal. The results of the simulation study would be covered in the next lecture.
44.pdf
This document summarizes a lecture on orbit propagation techniques used in the DAMAGE model to simulate the orbital evolution of space debris. It discusses using a general perturbations approach to model the effects of perturbations like Earth's gravity anomalies and atmospheric drag. These perturbations cause orbits to regress, precess, and decay over time. The next lectures will continue examining additional perturbations from atmospheric drag, third-body gravity, and solar radiation pressure.
37.pdf
This lecture introduced Talent's analytic model of space debris growth which mirrors an earlier systems model but with additional complexity. Talent's model uses a differential equation approach to model the number of orbital objects over time based on deposition from launches, atmospheric decay, and collision rates. The model predicts equilibrium populations where sources and sinks are balanced. Results from Talent's 1992 paper were presented to illustrate how the model can provide insights into the fundamental behavior and long-term evolution of the space debris population.
43.pdf
This lecture provides an overview of the DAMAGE evolutionary model for modeling space debris. DAMAGE was developed over three years starting in 1999 to model the long-term evolution of the debris environment in high Earth orbit. It incorporates various support models, like orbital propagation, collision prediction, break-up models, and failure models. DAMAGE can perform 200-year simulations in around two hours. Similar models are used by other space agencies. The next few lectures will cover the algorithms behind each support model.
33.pdf
The document summarizes key results from a simulation study conducted by Professor Hugh Lewis for ESA on the sensitivity of the space debris environment to satellite constellation parameters. The study found that post-mission disposal success, constellation size, satellite area, and launch vehicle behavior were among the most important parameters that affected the debris environment. Having a high post-mission disposal success rate and smaller constellations can help limit the impact on the debris environment, but may not eliminate impacts entirely. The results of this study informed guidelines from the IADC on the development of large satellite constellations.
47.pdf
The Cube method predicts collisions by dividing space into cubes and calculating collision rates for objects within the same cube. It assigns each object to a cube based on its coordinates and treats cubes containing multiple objects as gas particles. Collision rates are estimated using kinetic theory and sampling object positions over time. This approach is fast but less accurate for non-randomly orbiting objects like constellations.
46.pdf
This lecture discusses orbital perturbations included in the DAMAGE model for predicting space debris orbits. It covers the effects of third-body gravity from the Sun and Moon, known as luni-solar perturbations, which cause secular changes in the orbital elements of inclination, eccentricity, and longitude of ascending node, especially for geosynchronous and high Earth orbits. It also discusses solar radiation pressure perturbations, which have a small effect on low Earth orbit satellites but can considerably affect the eccentricity of geosynchronous satellites with large surface areas. The lecture concludes by recapping the different perturbation models covered in the previous three lectures.
50.pdf
This lecture discusses three experiments - SOCIT, DebriSat, and DebrisLV - that studied the effects of hypervelocity impacts on satellites using the light gas gun at Arnold Air Force Base. SOCIT targeted a Navy Transit satellite bus with an aluminum sphere projectile traveling at 6.1 km/s. DebriSat used a custom-built satellite and aluminum cylinder projectile impacting at 6.8 km/s. DebrisLV represented a launch vehicle stage. Diagnostic equipment measured the impact effects, and the results will be used to develop models of hypervelocity impact damage to satellites.
Recommended
32.pdf
The lecture discusses a simulation study conducted for ESA that aimed to understand how the space debris environment is affected by key satellite and constellation parameters. The study used three evolutionary debris models to project the debris environment out to 2213 under different scenarios. A baseline case examined the impact of a 1080-satellite constellation in 20 orbital planes at 1100km altitude, with a 5-year lifetime and 90% post-mission disposal. The results of the simulation study would be covered in the next lecture.
44.pdf
This document summarizes a lecture on orbit propagation techniques used in the DAMAGE model to simulate the orbital evolution of space debris. It discusses using a general perturbations approach to model the effects of perturbations like Earth's gravity anomalies and atmospheric drag. These perturbations cause orbits to regress, precess, and decay over time. The next lectures will continue examining additional perturbations from atmospheric drag, third-body gravity, and solar radiation pressure.
37.pdf
This lecture introduced Talent's analytic model of space debris growth which mirrors an earlier systems model but with additional complexity. Talent's model uses a differential equation approach to model the number of orbital objects over time based on deposition from launches, atmospheric decay, and collision rates. The model predicts equilibrium populations where sources and sinks are balanced. Results from Talent's 1992 paper were presented to illustrate how the model can provide insights into the fundamental behavior and long-term evolution of the space debris population.
43.pdf
This lecture provides an overview of the DAMAGE evolutionary model for modeling space debris. DAMAGE was developed over three years starting in 1999 to model the long-term evolution of the debris environment in high Earth orbit. It incorporates various support models, like orbital propagation, collision prediction, break-up models, and failure models. DAMAGE can perform 200-year simulations in around two hours. Similar models are used by other space agencies. The next few lectures will cover the algorithms behind each support model.
33.pdf
The document summarizes key results from a simulation study conducted by Professor Hugh Lewis for ESA on the sensitivity of the space debris environment to satellite constellation parameters. The study found that post-mission disposal success, constellation size, satellite area, and launch vehicle behavior were among the most important parameters that affected the debris environment. Having a high post-mission disposal success rate and smaller constellations can help limit the impact on the debris environment, but may not eliminate impacts entirely. The results of this study informed guidelines from the IADC on the development of large satellite constellations.
47.pdf
The Cube method predicts collisions by dividing space into cubes and calculating collision rates for objects within the same cube. It assigns each object to a cube based on its coordinates and treats cubes containing multiple objects as gas particles. Collision rates are estimated using kinetic theory and sampling object positions over time. This approach is fast but less accurate for non-randomly orbiting objects like constellations.
46.pdf
This lecture discusses orbital perturbations included in the DAMAGE model for predicting space debris orbits. It covers the effects of third-body gravity from the Sun and Moon, known as luni-solar perturbations, which cause secular changes in the orbital elements of inclination, eccentricity, and longitude of ascending node, especially for geosynchronous and high Earth orbits. It also discusses solar radiation pressure perturbations, which have a small effect on low Earth orbit satellites but can considerably affect the eccentricity of geosynchronous satellites with large surface areas. The lecture concludes by recapping the different perturbation models covered in the previous three lectures.
50.pdf
This lecture discusses three experiments - SOCIT, DebriSat, and DebrisLV - that studied the effects of hypervelocity impacts on satellites using the light gas gun at Arnold Air Force Base. SOCIT targeted a Navy Transit satellite bus with an aluminum sphere projectile traveling at 6.1 km/s. DebriSat used a custom-built satellite and aluminum cylinder projectile impacting at 6.8 km/s. DebrisLV represented a launch vehicle stage. Diagnostic equipment measured the impact effects, and the results will be used to develop models of hypervelocity impact damage to satellites.
48.pdf
This lecture discusses hypervelocity impacts in space. It focuses on the impact process, computational models used to simulate impacts, and ensuring the accuracy of models. Experimental facilities like light gas guns are used to test impacts and calibrate models. Results from experiments help develop empirical break-up models to better understand and predict how objects break apart during high-speed collisions in space.
45.pdf
This lecture discusses how orbital propagators model atmospheric drag and account for solar activity and atmospheric rotation. It explains that atmospheric drag depends on density, which comes from the CIRA-72 model tables as a function of height and exospheric temperature. Exospheric temperature is modeled as a function of solar flux F10.7 and geomagnetic activity. Atmospheric rotation is also accounted for, with drag decreasing for prograde orbits and increasing for retrograde orbits. The next lecture will cover third-body gravity effects and solar radiation pressure in orbital propagation models.
39.pdf
This lecture discussed Monte Carlo simulation and its use in evolutionary models of space debris. Monte Carlo simulation involves repeatedly sampling random inputs from a probability distribution to produce distributions of possible outcomes. For space debris models, it involves generating quantities like positions and solar activity randomly and running deterministic computations. While Monte Carlo simulation provides probabilistic information, typical reporting of results only includes mean and sometimes standard deviation, which can lead to incorrect conclusions about modeling studies. The lecture highlighted challenges and opportunities for better presenting probabilistic outputs.
41.pdf
This document describes an activity for students to compare the results of two space debris simulations - one with a proposed mega-constellation and one without. It provides the probability distributions of the number of objects in orbit at the end of each simulation. Students are asked to calculate the probability that the number of objects is below a threshold in each case and the probability that the number is lower with the mega-constellation compared to without. This is meant to help students work with uncertainty in model outputs and compare scenarios.
55.pdf
(1) Donald Kessler introduced the idea of a "critical population density" of space debris in 1978 and 1991, where above this density collisions would produce debris faster than it decays.
(2) In 2001, Kessler introduced the concept of a "critical number of objects" and applied a stability model showing regions of low Earth orbit have exceeded the critical level and become unstable.
(3) Kessler's work showed the space debris population could exponentially increase without further launches if the critical threshold is surpassed, known as the "Kessler Syndrome," though this was sometimes misunderstood to mean an immediate effect rather than gradual increase.
Detonating failed deflagration_model_of_themonuclear_supernovae_explosion_dyn...
This document summarizes a detonating failed deflagration model of Type Ia supernovae. The model involves an off-center deflagration in a massive white dwarf that fails to unbind the star. Disturbances from the failed deflagration pollute the stellar surface and eventually evolve into isolated shock regions, serving as ignition points for detonations that result in supernova explosion. Preliminary results show ejecta composed of silicon and iron group elements, with an inner egg-shaped region surrounded by an incomplete burning shell. Explosion energies are around 1.3-1.5×1051 erg.
22.pdf
This document discusses the history and effects of space debris fragmentation events. It examines data from NASA and ESA on past fragmentation events and how they increased the amount of orbital debris and collision risk over time. Examples of fragmentation simulations are provided, showing the dispersion of debris clouds from broken satellites and rocket bodies. The risks that orbital debris poses to important spacecraft like the International Space Station and Space Shuttle are also reviewed, including historical near-collisions and the shielding used to protect these vehicles.
26.pdf
This lecture discusses in-situ measurements of space debris. It describes missions like LDEF, Hubble, the International Space Station, and Space Shuttle that have enabled the collection of in-situ data on space debris. Examples are provided of impacts on these structures from debris. Estimates of small debris, like micrometer-sized particles, are also presented.
52.pdf
This lecture discusses re-entry predictions and risks from space debris. It covers:
1) How uncertainties in satellite characteristics and the atmosphere lead to uncertainties in re-entry predictions. Predictions are most accurate within 10 days and least accurate beyond that.
2) Methods for calculating risks to humans, including equivalent casualty cross-section and modeling debris footprint as a 2D Gaussian.
3) Long-term risks are low, estimated at 1 casualty every 45 years based on historical re-entries.
Bayesian Uncertainty Analysis with Application to Tipping Points
Bayesian Uncertainty Analysis for complex physical systems modelled by computer simulators, with application to tipping points. The document discusses Bayesian uncertainty quantification for complex computer models of physical systems. As an example, it summarizes work using emulators to model galaxy formation and evolution based on simulations incorporating dark matter and other factors. The simulations involve significant computational resources but provide insights into fundamental questions around galaxy formation and testing cosmologists' understanding.
28.pdf
This document summarizes a lecture on space debris and the increasing risk of collisions. It discusses how the number of predicted close approaches between debris fragments is rising even as the number of fragments decreases over time. Data is presented on close approaches related to debris from the 2007 Fengyun-1C anti-satellite test and the 2009 Iridium-Cosmos collision. While around 27,000 close approaches under 5km were predicted per week in 2019, by 2021 that number had risen to around 46,000 per week. Similarly, close approaches under 1km rose from 1,100 to 2,400 per week. This increasing risk is likely due to the dispersing and expanding cloud of fragments over time.
Alice Gabriel - Pasc18 - Keynote
Unraveling Earthquake Dynamics Through Extreme-Scale Multi-Physics Simulations
ALICE GABRIEL (LUDWIG MAXIMILIAN UNIVERSITY OF MUNICH, GERMANY)
Earthquakes are highly non-linear multiscale problems, encapsulating geometry and rheology of faults within the Earth’s crust torn apart by propagating shear fracture and emanating seismic wave radiation.
This talk will focus on using physics-based scenarios, modern numerical methods and hardware specific optimizations to shed light on the dynamics, and severity, of earthquake behaviour. It will present the largest-scale dynamic earthquake rupture simulation to date, which models the 2004 Sumatra-Andaman event - an unexpected subduction zone earthquake which generated a rupture of over 1,500 km in length within the ocean floor followed by a series of devastating tsunamis.
The core components of the simulation software will be described, highlighting the benefits of strong collaborations between domain and computational scientists. Lastly, future directions in coupling the short-term elastodynamics phenomena to long-term tectonics and tsunami generation will be discussed.
https://pasc18.pasc-conference.org/program/keynote-presentations/
20.pdf
This document provides an overview of four lectures on space debris that will examine the current state of the orbital debris environment. It will look at the number and mass of objects in orbit, as well as their distribution, using data from NASA, ESA and other sources. The lectures will also explore the history of space launches and fragmentations and how the debris population has evolved over time. Current estimates indicate there are over 34,000 pieces of debris larger than 10 cm in size, around 900,000 pieces between 1 cm and 10 cm, and approximately 128 million pieces between 1 mm and 1 cm. The total mass of all orbital debris is around 9,200 tonnes.
Autocorrelation_kriging_techniques for Hydrology
This document provides an introduction to spatial autocorrelation and kriging. It discusses Tobler's first law of geography, which states that nearby locations tend to be more related than distant locations. Spatial autocorrelation refers to the correlation of a variable with itself over space as a function of distance. The document outlines common tests for spatial autocorrelation like Moran's I and variograms. It explains how kriging uses a variogram model and nearest neighbor distances to interpolate values at unsampled locations. Kriging aims to provide the best linear unbiased predictions and estimates of uncertainty. The history of variograms, kriging, and their development by mathematicians like Matheron and geologist Krige are
Limit radius in a binary system: Cosmological and Post-Newtonian effects
Frequently, in dynamical astronomy, the quantitative effect of the large-scale cosmological expansion on local systems is studied in the light of Newtonian approach. We, however, analyze the influence of cosmological expansion on binary systems (galaxies or black holes) in the light of Post-Newtonian approximation. Furthermore, we obtain the new radius at which the acceleration due to the cosmological expansion has the same magnitude as the two-body attraction, and the classical limit radius is obtained when the Schwarzschild radius approaches zero (for example, the Solar System).
Dark energy by david spergel
The document discusses the evidence for dark energy from observations of Type Ia supernovae, the cosmic microwave background radiation, and large-scale structure like galaxy clusters. It finds that about 73% of the universe consists of dark energy, which is causing the accelerating expansion of the universe. Future experiments aim to better characterize dark energy and test whether it is due to a cosmological constant, modified gravity, or other explanations like quintessence. Precise measurements of the expansion history and growth of structure can help distinguish between theories of dark energy.
Introduction Quantitative X-Ray Diffraction Methods
This document provides an introduction to quantitative x-ray diffraction methods. It discusses that quantitative analysis aims to determine precise structural characteristics and phase proportions from experimental diffraction data. This requires accurate intensity measurements and careful sample preparation to produce uniformly sized, randomly oriented powder. Several quantitative methods are based on comparing intensity ratios between unknown and known internal standard peaks. The most effective methods involve modeling the entire diffraction pattern to duplicate the experimental pattern.
24.pdf
The lecture discusses space surveillance networks and space situational awareness. It introduces the US Space Surveillance Network, which tracks objects 10 cm and larger in low Earth orbit and 1 m and larger in geosynchronous orbit. Commercial networks like LeoLabs and ExoAnalytic Solutions are also discussed. Data from these networks is used for important services like conjunction predictions to ensure space safety. The next lecture will focus on systems used to measure and characterize space objects.
38.pdf
This lecture discusses models for predicting the evolution of space debris. Simple "particles-in-a-box" models are transparent but lack accuracy and flexibility. More complex "evolutionary" models are needed to answer important questions by simulating individual objects and their interactions over time while accounting for uncertainties. Key properties like object types and orbits must be included to predict the effects of mitigation measures and new operations on the debris environment. Monte Carlo simulation is introduced as the approach used by evolutionary models.
1314 crowe[1]
This document discusses the potential for self-deploying extremely large, low-mass space structures using rigid bubbles or foams inflated at very low pressures. Individual bubbles could reach sizes up to 100 km in microgravity environments, with areal densities under 1 g/m2. Applications include space habitats, astronomical telescopes, solar sails, and photon collection surfaces. The next phase proposes mission designs integrating these structures into proposals like the New Worlds Imager and Hypertelescope, as well as demonstrating prototype structural elements and optical surfaces in the lab.
12 Perterbations.pdf
This document provides an overview of orbital perturbations and methods for modeling them. It introduces Cowell's method and Encke's method for numerically integrating the equations of motion with perturbations. It then discusses atmospheric drag as a perturbation, describing how drag causes orbits to decay over time. It provides the US Standard Atmosphere 1976 model for atmospheric density with altitude.
4 3d orbits.pdf
This document discusses coordinate systems for describing orbits in three dimensions. It introduces the geocentric equatorial frame, which uses a right-handed Cartesian coordinate system centered on Earth with axes defined by the vernal equinox and Earth's rotation. The state vector specifies an object's position and velocity in this frame using six components. Orbital elements also uniquely define orbits using six parameters and the location of the object. Coordinate transformations allow changing between the state vector and orbital element representations.
More Related Content
Similar to 51.pdf
48.pdf
This lecture discusses hypervelocity impacts in space. It focuses on the impact process, computational models used to simulate impacts, and ensuring the accuracy of models. Experimental facilities like light gas guns are used to test impacts and calibrate models. Results from experiments help develop empirical break-up models to better understand and predict how objects break apart during high-speed collisions in space.
45.pdf
This lecture discusses how orbital propagators model atmospheric drag and account for solar activity and atmospheric rotation. It explains that atmospheric drag depends on density, which comes from the CIRA-72 model tables as a function of height and exospheric temperature. Exospheric temperature is modeled as a function of solar flux F10.7 and geomagnetic activity. Atmospheric rotation is also accounted for, with drag decreasing for prograde orbits and increasing for retrograde orbits. The next lecture will cover third-body gravity effects and solar radiation pressure in orbital propagation models.
39.pdf
This lecture discussed Monte Carlo simulation and its use in evolutionary models of space debris. Monte Carlo simulation involves repeatedly sampling random inputs from a probability distribution to produce distributions of possible outcomes. For space debris models, it involves generating quantities like positions and solar activity randomly and running deterministic computations. While Monte Carlo simulation provides probabilistic information, typical reporting of results only includes mean and sometimes standard deviation, which can lead to incorrect conclusions about modeling studies. The lecture highlighted challenges and opportunities for better presenting probabilistic outputs.
41.pdf
This document describes an activity for students to compare the results of two space debris simulations - one with a proposed mega-constellation and one without. It provides the probability distributions of the number of objects in orbit at the end of each simulation. Students are asked to calculate the probability that the number of objects is below a threshold in each case and the probability that the number is lower with the mega-constellation compared to without. This is meant to help students work with uncertainty in model outputs and compare scenarios.
55.pdf
(1) Donald Kessler introduced the idea of a "critical population density" of space debris in 1978 and 1991, where above this density collisions would produce debris faster than it decays.
(2) In 2001, Kessler introduced the concept of a "critical number of objects" and applied a stability model showing regions of low Earth orbit have exceeded the critical level and become unstable.
(3) Kessler's work showed the space debris population could exponentially increase without further launches if the critical threshold is surpassed, known as the "Kessler Syndrome," though this was sometimes misunderstood to mean an immediate effect rather than gradual increase.
Detonating failed deflagration_model_of_themonuclear_supernovae_explosion_dyn...
This document summarizes a detonating failed deflagration model of Type Ia supernovae. The model involves an off-center deflagration in a massive white dwarf that fails to unbind the star. Disturbances from the failed deflagration pollute the stellar surface and eventually evolve into isolated shock regions, serving as ignition points for detonations that result in supernova explosion. Preliminary results show ejecta composed of silicon and iron group elements, with an inner egg-shaped region surrounded by an incomplete burning shell. Explosion energies are around 1.3-1.5×1051 erg.
22.pdf
This document discusses the history and effects of space debris fragmentation events. It examines data from NASA and ESA on past fragmentation events and how they increased the amount of orbital debris and collision risk over time. Examples of fragmentation simulations are provided, showing the dispersion of debris clouds from broken satellites and rocket bodies. The risks that orbital debris poses to important spacecraft like the International Space Station and Space Shuttle are also reviewed, including historical near-collisions and the shielding used to protect these vehicles.
26.pdf
This lecture discusses in-situ measurements of space debris. It describes missions like LDEF, Hubble, the International Space Station, and Space Shuttle that have enabled the collection of in-situ data on space debris. Examples are provided of impacts on these structures from debris. Estimates of small debris, like micrometer-sized particles, are also presented.
52.pdf
This lecture discusses re-entry predictions and risks from space debris. It covers:
1) How uncertainties in satellite characteristics and the atmosphere lead to uncertainties in re-entry predictions. Predictions are most accurate within 10 days and least accurate beyond that.
2) Methods for calculating risks to humans, including equivalent casualty cross-section and modeling debris footprint as a 2D Gaussian.
3) Long-term risks are low, estimated at 1 casualty every 45 years based on historical re-entries.
Bayesian Uncertainty Analysis with Application to Tipping Points
Bayesian Uncertainty Analysis for complex physical systems modelled by computer simulators, with application to tipping points. The document discusses Bayesian uncertainty quantification for complex computer models of physical systems. As an example, it summarizes work using emulators to model galaxy formation and evolution based on simulations incorporating dark matter and other factors. The simulations involve significant computational resources but provide insights into fundamental questions around galaxy formation and testing cosmologists' understanding.
28.pdf
This document summarizes a lecture on space debris and the increasing risk of collisions. It discusses how the number of predicted close approaches between debris fragments is rising even as the number of fragments decreases over time. Data is presented on close approaches related to debris from the 2007 Fengyun-1C anti-satellite test and the 2009 Iridium-Cosmos collision. While around 27,000 close approaches under 5km were predicted per week in 2019, by 2021 that number had risen to around 46,000 per week. Similarly, close approaches under 1km rose from 1,100 to 2,400 per week. This increasing risk is likely due to the dispersing and expanding cloud of fragments over time.
Alice Gabriel - Pasc18 - Keynote
Unraveling Earthquake Dynamics Through Extreme-Scale Multi-Physics Simulations
ALICE GABRIEL (LUDWIG MAXIMILIAN UNIVERSITY OF MUNICH, GERMANY)
Earthquakes are highly non-linear multiscale problems, encapsulating geometry and rheology of faults within the Earth’s crust torn apart by propagating shear fracture and emanating seismic wave radiation.
This talk will focus on using physics-based scenarios, modern numerical methods and hardware specific optimizations to shed light on the dynamics, and severity, of earthquake behaviour. It will present the largest-scale dynamic earthquake rupture simulation to date, which models the 2004 Sumatra-Andaman event - an unexpected subduction zone earthquake which generated a rupture of over 1,500 km in length within the ocean floor followed by a series of devastating tsunamis.
The core components of the simulation software will be described, highlighting the benefits of strong collaborations between domain and computational scientists. Lastly, future directions in coupling the short-term elastodynamics phenomena to long-term tectonics and tsunami generation will be discussed.
https://pasc18.pasc-conference.org/program/keynote-presentations/
20.pdf
This document provides an overview of four lectures on space debris that will examine the current state of the orbital debris environment. It will look at the number and mass of objects in orbit, as well as their distribution, using data from NASA, ESA and other sources. The lectures will also explore the history of space launches and fragmentations and how the debris population has evolved over time. Current estimates indicate there are over 34,000 pieces of debris larger than 10 cm in size, around 900,000 pieces between 1 cm and 10 cm, and approximately 128 million pieces between 1 mm and 1 cm. The total mass of all orbital debris is around 9,200 tonnes.
Autocorrelation_kriging_techniques for Hydrology
This document provides an introduction to spatial autocorrelation and kriging. It discusses Tobler's first law of geography, which states that nearby locations tend to be more related than distant locations. Spatial autocorrelation refers to the correlation of a variable with itself over space as a function of distance. The document outlines common tests for spatial autocorrelation like Moran's I and variograms. It explains how kriging uses a variogram model and nearest neighbor distances to interpolate values at unsampled locations. Kriging aims to provide the best linear unbiased predictions and estimates of uncertainty. The history of variograms, kriging, and their development by mathematicians like Matheron and geologist Krige are
Limit radius in a binary system: Cosmological and Post-Newtonian effects
Frequently, in dynamical astronomy, the quantitative effect of the large-scale cosmological expansion on local systems is studied in the light of Newtonian approach. We, however, analyze the influence of cosmological expansion on binary systems (galaxies or black holes) in the light of Post-Newtonian approximation. Furthermore, we obtain the new radius at which the acceleration due to the cosmological expansion has the same magnitude as the two-body attraction, and the classical limit radius is obtained when the Schwarzschild radius approaches zero (for example, the Solar System).
Dark energy by david spergel
The document discusses the evidence for dark energy from observations of Type Ia supernovae, the cosmic microwave background radiation, and large-scale structure like galaxy clusters. It finds that about 73% of the universe consists of dark energy, which is causing the accelerating expansion of the universe. Future experiments aim to better characterize dark energy and test whether it is due to a cosmological constant, modified gravity, or other explanations like quintessence. Precise measurements of the expansion history and growth of structure can help distinguish between theories of dark energy.
Introduction Quantitative X-Ray Diffraction Methods
This document provides an introduction to quantitative x-ray diffraction methods. It discusses that quantitative analysis aims to determine precise structural characteristics and phase proportions from experimental diffraction data. This requires accurate intensity measurements and careful sample preparation to produce uniformly sized, randomly oriented powder. Several quantitative methods are based on comparing intensity ratios between unknown and known internal standard peaks. The most effective methods involve modeling the entire diffraction pattern to duplicate the experimental pattern.
24.pdf
The lecture discusses space surveillance networks and space situational awareness. It introduces the US Space Surveillance Network, which tracks objects 10 cm and larger in low Earth orbit and 1 m and larger in geosynchronous orbit. Commercial networks like LeoLabs and ExoAnalytic Solutions are also discussed. Data from these networks is used for important services like conjunction predictions to ensure space safety. The next lecture will focus on systems used to measure and characterize space objects.
38.pdf
This lecture discusses models for predicting the evolution of space debris. Simple "particles-in-a-box" models are transparent but lack accuracy and flexibility. More complex "evolutionary" models are needed to answer important questions by simulating individual objects and their interactions over time while accounting for uncertainties. Key properties like object types and orbits must be included to predict the effects of mitigation measures and new operations on the debris environment. Monte Carlo simulation is introduced as the approach used by evolutionary models.
1314 crowe[1]
This document discusses the potential for self-deploying extremely large, low-mass space structures using rigid bubbles or foams inflated at very low pressures. Individual bubbles could reach sizes up to 100 km in microgravity environments, with areal densities under 1 g/m2. Applications include space habitats, astronomical telescopes, solar sails, and photon collection surfaces. The next phase proposes mission designs integrating these structures into proposals like the New Worlds Imager and Hypertelescope, as well as demonstrating prototype structural elements and optical surfaces in the lab.
Similar to 51.pdf (20)
Detonating failed deflagration_model_of_themonuclear_supernovae_explosion_dyn...
Detonating failed deflagration_model_of_themonuclear_supernovae_explosion_dyn...
Bayesian Uncertainty Analysis with Application to Tipping Points
Bayesian Uncertainty Analysis with Application to Tipping Points
Limit radius in a binary system: Cosmological and Post-Newtonian effects
Limit radius in a binary system: Cosmological and Post-Newtonian effects
Introduction Quantitative X-Ray Diffraction Methods
Introduction Quantitative X-Ray Diffraction Methods
More from a a
12 Perterbations.pdf
This document provides an overview of orbital perturbations and methods for modeling them. It introduces Cowell's method and Encke's method for numerically integrating the equations of motion with perturbations. It then discusses atmospheric drag as a perturbation, describing how drag causes orbits to decay over time. It provides the US Standard Atmosphere 1976 model for atmospheric density with altitude.
4 3d orbits.pdf
This document discusses coordinate systems for describing orbits in three dimensions. It introduces the geocentric equatorial frame, which uses a right-handed Cartesian coordinate system centered on Earth with axes defined by the vernal equinox and Earth's rotation. The state vector specifies an object's position and velocity in this frame using six components. Orbital elements also uniquely define orbits using six parameters and the location of the object. Coordinate transformations allow changing between the state vector and orbital element representations.
9 rigid body dynamics.pdf
This chapter discusses rigid body dynamics and provides the foundation for developing equations of satellite attitude dynamics. It first covers the kinematics of rigid bodies using Chasles' theorem, which states that rigid body motion can be described by the displacement of any point plus a rotation about a unique axis through that point. It then discusses the equations of translational and rotational motion by analyzing the interaction between rigid body motion and applied forces. Key concepts covered include moments of inertia, Euler's equations, kinetic energy, and different methods for describing rigid body orientation including Euler angles, yaw/pitch/roll angles, and quaternions. The chapter serves as a basis for understanding satellite attitude dynamics.
10 Sat attitude.pdf
This document discusses the torque-free motion of satellites. It shows that a spinning satellite will have stable motion only if it is oblate in shape, with the equatorial radius greater than the polar radius. Oblate spinners will have prograde precession and spin, while prolate spinners will have retrograde precession and spin. The components of angular velocity and angular momentum are derived in terms of the satellite's principal moments of inertia and Euler angles.
8 Interplanetary traj.pdf
This document discusses interplanetary trajectories and Hohmann transfers between planets. It begins by outlining Hohmann transfers, which provide the most energy-efficient method of transferring between nearly circular, coplanar orbits. It then discusses the timing of opportunities for planetary rendezvous using Hohmann transfers, which depend on the relative positions and velocities of the planets. The document covers methods for calculating delta-v requirements at planetary departure and arrival points to achieve the Hohmann transfer orbit. It also introduces non-Hohmann transfer trajectories when planetary orbits are not coplanar.
6 maneuvres.pdf
This document discusses orbital maneuvers, beginning with an introduction to impulsive maneuvers where brief rocket firings instantaneously change a spacecraft's velocity vector. It then focuses on the Hohmann transfer, the most energy-efficient maneuver for transferring between two coplanar circular orbits. A Hohmann transfer uses an elliptical orbit tangent to the two circles, requiring burns at periapsis and apoapsis to place the spacecraft onto the transfer orbit and then the target orbit. An equation is provided for calculating the angular momentum of the Hohmann transfer ellipse based on the radii of the source and target orbits.
7 relative motion.pdf
This document discusses relative motion between two orbiting spacecraft, a target and chaser. It defines a local vertical/local horizontal (LVLH) coordinate frame attached to the target spacecraft, with axes along the radial direction, local horizontal, and angular momentum direction. Equations are provided to calculate the relative position, velocity, and acceleration of the chaser in this frame based on the states of both spacecraft in an inertial frame. An example problem applies these equations to calculate the relative motion between two spacecraft in slightly different elliptical orbits.
3 position by time.pdf
This document discusses how to determine the position of an orbiting body as a function of time for different orbit types. It introduces Kepler's equation, which relates the true anomaly to time through integrals that must be solved iteratively. For elliptical orbits, Kepler's equation leads to the definition of mean anomaly as a function of true anomaly. The mean anomaly is directly proportional to time through the mean motion. Eccentric anomaly is also introduced to simplify expressions relating true anomaly to time.
5 prelim determination.pdf
- The Gibbs method determines orbital elements from three position vectors of an object.
- It utilizes the fact that the position vectors must lie in the same orbital plane, defined by the angular momentum vector.
- Equations relating the position vectors and angular momentum allow solving for the angular momentum magnitude.
- Knowing the angular momentum vector and magnitude allows determining the velocities at the three observation times from the position vectors using basic orbital mechanics equations.
11 rocket dyanmics.pdf
This document discusses rocket vehicle dynamics and performance. It begins with the equations of motion for a rocket during powered ascent, accounting for thrust, drag, and gravity. It then derives the thrust equation from momentum considerations, relating thrust to propellant mass flow rate and exhaust velocity. Finally, it combines the thrust equation and equations of motion to obtain the rocket equation, which relates propellant expenditure to changes in rocket velocity (delta-v).
3 EDL.pdf
The document discusses entry, descent, and landing (EDL) for spacecraft. It covers:
1) The dynamics of atmospheric entry and re-entry, including key equations of motion.
2) Issues during EDL like deceleration, heating, and communication blackouts.
3) Methods for testing and simulating EDL, including ground and simulation testing.
The document aims to explain the EDL phase and prepare the reader to understand and analyze challenges of atmospheric entry for spacecraft.
1 Power Sys.pdf
1. The power requirements of the spacecraft loads and batteries that need to be supplied by the solar array.
2. The effects of the orbital parameters on the intensity and duration of sunlight, such as eclipse periods.
3. The degradation of the solar cell efficiency over time due to radiation damage and high temperatures in space. Accounting for this ensures the array can still produce enough power at the end of the mission lifetime.
2 Thermal Control.pdf
The document provides an overview of thermal control systems for spacecraft. It discusses passive and active thermal control systems, with passive relying on components like surface coatings and active using powered mechanisms. The document covers thermal analysis methods like conduction, convection, and radiation. It describes modeling the thermal environment from heat sources like solar radiation, planetary radiation, and albedo. Design of passive thermal control uses appropriate surface coatings to control absorptance and emittance.
59.pdf
This document discusses a lecture on space sustainability given by Professor Hugh Lewis at the University of Southampton. The lecture focuses on taking a long term view of ensuring the space environment remains usable by future generations. It includes repeated tags asking the reader to connect with the university and view a film about being connected.
56.pdf
The lecture discusses common misconceptions about the Kessler Syndrome, a concept developed by NASA scientist Donald Kessler warning of the risk of increasing amounts of space debris. Some of the misconceptions addressed are that it would be a quick collision chain reaction, that there would be no way to stop it once started, and that it would mean an end to all space travel. The lecture presents examples of these misconceptions in media reports and research articles and aims to explain in upcoming lectures why these ideas are likely incorrect.
57.pdf
This lecture discusses techniques for calculating probabilities using combinatorics, and applies them to scenarios involving satellite collisions and drawing playing cards. Two scenarios are presented:
1) Calculating probabilities of different outcomes from 10 satellite conjunctions each with a 5% chance of collision.
2) Drawing 10 cards from a deck and calculating probabilities of different numbers of hearts. The chance of a heart on each draw is 1/4. Probabilities are calculated using combinations, multiplication of probabilities, and subtraction of complementary events.
54.pdf
This lecture discusses carrying capacity and resilience as alternative representations of space sustainability. It uses a predator-prey model to demonstrate carrying capacity for two interacting populations. Solving problems like space debris is described as a "super wicked problem" due to the lack of central authority, conflicting stakeholders, and difficulty establishing irreversible solutions.
53.pdf
This lecture discusses sustainability and sustainable development as they relate to space activities. It defines space sustainability as maintaining space activities indefinitely while preserving the space environment for future generations, according to the United Nations Committee on the Peaceful Uses of Outer Space. The lecture also examines the Secure World Foundation's definition and the three pillars of sustainability: economic development, social development, and environmental protection. Sustainability aims to improve life while respecting environmental limits.
49.pdf
This lecture discusses facilities used to conduct hypervelocity impact experiments, including light gas guns at Arnold Air Force Base, the Southwest Research Institute, and the University of Kent. It also mentions a laser-based hypervelocity impact facility at MIT. The lecture focuses on the 'range G' light gas gun and previews how future lectures will examine experiments conducted there to model impacts on satellites.
58.pdf
This lecture discusses models of population growth and how they can be applied to understand the growth of space debris. An exponential model shows that space debris population growth would be smooth, with no tipping point, even from a small initial population. A super-exponential model, where the growth rate increases with population size due to higher collision likelihood, better captures space debris growth. The Kessler Syndrome is not a chain reaction but a continuous process where each collision slowly increases future collision frequency. These models help debunk misconceptions about the nature of the Kessler Syndrome.
More from a a (20)
Recently uploaded
Cherries 32 collection of colorful paintings
The cherry: beauty, softness, its heart-shaped plastic has inspired artists since Antiquity. Cherries and strawberries were considered the fruits of paradise and thus represented the souls of men.
➒➌➎➏➑➐➋➑➐➐ Kalyan Matka Satta Matka Dpboss Matka Guessing Indian Matka
➒➌➎➏➑➐➋➑➐➐ Kalyan Matka Satta Matka Dpboss Matka Guessing Indian Matka➒➌➎➏➑➐➋➑➐➐Dpboss Matka Guessing Satta Matka Kalyan Chart Indian Matka
➒➌➎➏➑➐➋➑➐➐ Kalyan Matka Satta Matka Dpboss Matka Guessing Indian Matka原版制作(UNITO毕业证书)都灵大学毕业证Offer一模一样
学校原件一模一样【微信：741003700 】《(UNITO毕业证书)都灵大学毕业证》【微信：741003700 】学位证，留信认证（真实可查，永久存档）原件一模一样纸张工艺/offer、雅思、外壳等材料/诚信可靠,可直接看成品样本，帮您解决无法毕业带来的各种难题！外壳，原版制作，诚信可靠，可直接看成品样本。行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备。十五年致力于帮助留学生解决难题，包您满意。
本公司拥有海外各大学样板无数，能完美还原。
1:1完美还原海外各大学毕业材料上的工艺：水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠。文字图案浮雕、激光镭射、紫外荧光、温感、复印防伪等防伪工艺。材料咨询办理、认证咨询办理请加学历顾问Q/微741003700
【主营项目】
一.毕业证【q微741003700】成绩单、使馆认证、教育部认证、雅思托福成绩单、学生卡等！
二.真实使馆公证(即留学回国人员证明,不成功不收费)
三.真实教育部学历学位认证（教育部存档！教育部留服网站永久可查）
四.办理各国各大学文凭(一对一专业服务,可全程监控跟踪进度)
如果您处于以下几种情况：
◇在校期间，因各种原因未能顺利毕业……拿不到官方毕业证【q/微741003700】
◇面对父母的压力，希望尽快拿到；
◇不清楚认证流程以及材料该如何准备；
◇回国时间很长，忘记办理；
◇回国马上就要找工作，办给用人单位看；
◇企事业单位必须要求办理的
◇需要报考公务员、购买免税车、落转户口
◇申请留学生创业基金
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
哪里办理(sjsu毕业证书)美国圣何塞州立大学毕业证硕士文凭证书原版一模一样
原版定制【微信:bwp0011】《(sjsu毕业证书)美国圣何塞州立大学毕业证硕士文凭证书》【微信:bwp0011】成绩单 、雅思、外壳、留信学历认证永久存档查询，采用学校原版纸张、特殊工艺完全按照原版一比一制作（包括：隐形水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠，文字图案浮雕，激光镭射，紫外荧光，温感，复印防伪）行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备，十五年致力于帮助留学生解决难题，业务范围有加拿大、英国、澳洲、韩国、美国、新加坡，新西兰等学历材料，包您满意。
【业务选择办理准则】
一、工作未确定，回国需先给父母、亲戚朋友看下文凭的情况，办理一份就读学校的毕业证【微信bwp0011】文凭即可
二、回国进私企、外企、自己做生意的情况，这些单位是不查询毕业证真伪的，而且国内没有渠道去查询国外文凭的真假，也不需要提供真实教育部认证。鉴于此，办理一份毕业证【微信bwp0011】即可
三、进国企，银行，事业单位，考公务员等等，这些单位是必需要提供真实教育部认证的，办理教育部认证所需资料众多且烦琐，所有材料您都必须提供原件，我们凭借丰富的经验，快捷的绿色通道帮您快速整合材料，让您少走弯路。
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
【关于价格问题（保证一手价格）】
我们所定的价格是非常合理的，而且我们现在做得单子大多数都是代理和回头客户介绍的所以一般现在有新的单子 我给客户的都是第一手的代理价格，因为我想坦诚对待大家 不想跟大家在价格方面浪费时间
对于老客户或者被老客户介绍过来的朋友，我们都会适当给一些优惠。
Colour Theory for Painting - Fine Artist.pdf
This document is all about Colour Theory for Fine Artist / Painter.
➒➌➎➏➑➐➋➑➐➐ Kalyan Matka Satta Matka Dpboss Matka Guessing Indian Matka
➒➌➎➏➑➐➋➑➐➐ Kalyan Matka Satta Matka Dpboss Matka Guessing Indian Matka➒➌➎➏➑➐➋➑➐➐Dpboss Matka Guessing Satta Matka Kalyan Chart Indian Matka
➒➌➎➏➑➐➋➑➐➐KALYAN MATKA | MATKA RESULT | KALYAN MATKA TIPS | SATTA MATKA | MATKA.COM | MATKA PANA JODI TODAY | BATTA SATKA | MATKA PATTI JODI NUMBER | MATKA RESULTS | MATKA CHART | MATKA JODI | SATTA COM | FULL RATE GAME | MATKA GAME | MATKA WAPKA | ALL MATKA RESULT LIVE ONLINE | MATKA RESULT | KALYAN MATKA RESULT | DPBOSS MATKA 143 | MAIN MATKAMy storyboard for a sword fight scene with lightsabers
My storyboard for a sword fight scene with lightsabers
Matka Guessing Satta Matta Matka Kalyan Chart Indian Matka Dpboss
Matka Guessing Satta Matta Matka Kalyan Chart Indian Matka Dpboss➒➌➎➏➑➐➋➑➐➐Dpboss Matka Guessing Satta Matka Kalyan Chart Indian Matka
9356872877Sattamatka.satta.matka.satta matka.kalyan weekly chart.kalyan chart.kalyan jodi chart.kalyan penal chart.kalyan today.kalyan open.fix satta.fix fix fix Satta matka nambar. Dpboss Matka Guessing Satta Matta Matka Kalyan Chart Indian Matka哪里购买美国乔治城大学毕业证硕士学位证书原版一模一样
原版一模一样【微信：741003700 】【美国乔治城大学毕业证硕士学位证书】【微信：741003700 】学位证，留信认证（真实可查，永久存档）offer、雅思、外壳等材料/诚信可靠,可直接看成品样本，帮您解决无法毕业带来的各种难题！外壳，原版制作，诚信可靠，可直接看成品样本。行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备。十五年致力于帮助留学生解决难题，包您满意。
本公司拥有海外各大学样板无数，能完美还原海外各大学 Bachelor Diploma degree, Master Degree Diploma
1:1完美还原海外各大学毕业材料上的工艺：水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠。文字图案浮雕、激光镭射、紫外荧光、温感、复印防伪等防伪工艺。材料咨询办理、认证咨询办理请加学历顾问Q/微741003700
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
Heart Touching Romantic Love Shayari In English with Images
Explore our beautiful collection of Romantic Love Shayari in English to express your love. These heartfelt shayaris are perfect for sharing with your loved one. Get the best words to show your love and care.
Tanjore Painting: Rich Heritage and Intricate Craftsmanship | Cottage9
Explore the exquisite art of Tanjore Painting, known for its vibrant colors, gold foil work, and traditional themes. Discover its cultural significance today!
❼❷⓿❺❻❷❽❷❼❽ Dpboss Matka ! Fix Satta Matka ! Matka Result ! Matka Guessing ! ...
❼❷⓿❺❻❷❽❷❼❽ Dpboss Matka ! Fix Satta Matka ! Matka Result ! Matka Guessing ! ...❼❷⓿❺❻❷❽❷❼❽ Dpboss Kalyan Satta Matka Guessing Matka Result Main Bazar chart
❼❷⓿❺❻❷❽❷❼❽ Dpboss Matka ! Fix Satta Matka ! Matka Result ! Matka Guessing ! Final Matka ! Matka Result ! Dpboss Matka ! Matka Guessing ! Satta Matta Matka 143 ! Kalyan Matka ! Satta Matka Fast Result ! Kalyan Matka Guessing ! Dpboss Matka Guessing ! Satta 143 ! Kalyan Chart ! Kalyan final ! Satta guessing ! Matka tips ! Matka 143 ! India Matka ! Matka 420 ! matka Mumbai ! Satta chart ! Indian Satta ! Satta King ! Satta 143 ! Satta batta ! Satta मटका ! Satta chart ! Matka 143 ! Matka Satta ! India Matka ! Indian Satta Matka ! Final ank一比一原版美国加州大学圣地亚哥分校毕业证（ucsd毕业证书）如何办理
一模一样【微信：A575476】【美国加州大学圣地亚哥分校毕业证（ucsd毕业证书）成绩单Offer】【微信：A575476】（留信学历认证永久存档查询）采用学校原版纸张、特殊工艺完全按照原版一比一制作（包括：隐形水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠，文字图案浮雕，激光镭射，紫外荧光，温感，复印防伪）行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备，十五年致力于帮助留学生解决难题，业务范围有加拿大、英国、澳洲、韩国、美国、新加坡，新西兰等学历材料，包您满意。
【业务选择办理准则】
一、工作未确定，回国需先给父母、亲戚朋友看下文凭的情况，办理一份就读学校的毕业证【微信：A575476】文凭即可
二、回国进私企、外企、自己做生意的情况，这些单位是不查询毕业证真伪的，而且国内没有渠道去查询国外文凭的真假，也不需要提供真实教育部认证。鉴于此，办理一份毕业证【微信：A575476】即可
三、进国企，银行，事业单位，考公务员等等，这些单位是必需要提供真实教育部认证的，办理教育部认证所需资料众多且烦琐，所有材料您都必须提供原件，我们凭借丰富的经验，快捷的绿色通道帮您快速整合材料，让您少走弯路。
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
→ 【关于价格问题（保证一手价格）
我们所定的价格是非常合理的，而且我们现在做得单子大多数都是代理和回头客户介绍的所以一般现在有新的单子 我给客户的都是第一手的代理价格，因为我想坦诚对待大家 不想跟大家在价格方面浪费时间
对于老客户或者被老客户介绍过来的朋友，我们都会适当给一些优惠。
选择实体注册公司办理，更放心，更安全！我们的承诺：可来公司面谈，可签订合同，会陪同客户一起到教育部认证窗口递交认证材料，客户在教育部官方认证查询网站查询到认证通过结果后付款，不成功不收费！
Full CAD Project Cardiovascuwhore Debut PDF CAD Meena Pittman
Full CAD Project Cardiovascuwhore Debut PDF CAD
Meena Pittman
Ealing London Independent Photography meeting - June 2024
Photographs from trip to American Deep South
Dpboss Matka Guessing Satta Matta Matka Kalyan Chart Indian Matka
Dpboss Matka Guessing Satta Matta Matka Kalyan Chart Indian Matka➒➌➎➏➑➐➋➑➐➐Dpboss Matka Guessing Satta Matka Kalyan Chart Indian Matka
9356872877Sattamatka.satta.matka.satta matka.kalyan weekly chart.kalyan chart.kalyan jodi chart.kalyan penal chart.kalyan today.kalyan open.fix satta.fix fix fix Satta matka nambar. Dpboss Matka Guessing Satta Matta Matka Kalyan Chart Indian MatkaRecently uploaded (20)
storyboard: Victor and Verlin discussing about top hat
storyboard: Victor and Verlin discussing about top hat
➒➌➎➏➑➐➋➑➐➐ Kalyan Matka Satta Matka Dpboss Matka Guessing Indian Matka
➒➌➎➏➑➐➋➑➐➐ Kalyan Matka Satta Matka Dpboss Matka Guessing Indian Matka
➒➌➎➏➑➐➋➑➐➐ Kalyan Matka Satta Matka Dpboss Matka Guessing Indian Matka
➒➌➎➏➑➐➋➑➐➐ Kalyan Matka Satta Matka Dpboss Matka Guessing Indian Matka
My storyboard for a sword fight scene with lightsabers
My storyboard for a sword fight scene with lightsabers
Matka Guessing Satta Matta Matka Kalyan Chart Indian Matka Dpboss
Matka Guessing Satta Matta Matka Kalyan Chart Indian Matka Dpboss
Heart Touching Romantic Love Shayari In English with Images
Heart Touching Romantic Love Shayari In English with Images
Tanjore Painting: Rich Heritage and Intricate Craftsmanship | Cottage9
Tanjore Painting: Rich Heritage and Intricate Craftsmanship | Cottage9
❼❷⓿❺❻❷❽❷❼❽ Dpboss Matka ! Fix Satta Matka ! Matka Result ! Matka Guessing ! ...
❼❷⓿❺❻❷❽❷❼❽ Dpboss Matka ! Fix Satta Matka ! Matka Result ! Matka Guessing ! ...
Full CAD Project Cardiovascuwhore Debut PDF CAD Meena Pittman
Full CAD Project Cardiovascuwhore Debut PDF CAD Meena Pittman
Ealing London Independent Photography meeting - June 2024
Ealing London Independent Photography meeting - June 2024
Dpboss Matka Guessing Satta Matta Matka Kalyan Chart Indian Matka
Dpboss Matka Guessing Satta Matta Matka Kalyan Chart Indian Matka
51.pdf
- 1. Space Environment Lecture 51 – Space Debris (Vol. 5) Breakup model Professor Hugh Lewis SESA3038 Space Environment
- 2. Overview of lecture 51 • In this lecture we introduce the NASA standard breakup model, which was developed using (in part) results from the SOCIT series of HVI experiments • We see how to use this empirical model to calculate: – The number of fragments resulting from an explosion or collision – The mass of the fragments – The area-to-mass ratio of the fragments – The velocity of the fragments Space Environment – Space Debris (Vol. 5)
- 3. Breakup models Space Environment – Space Debris (Vol. 5) Empirical models used for future environment projections Not hydrocodes! Simple (analytical) models based on HVI tests and observed on-orbit fragmentations Outputs: • Number of fragments • Area and mass distributions • Velocity distributions
- 4. NASA breakup model Space Environment – Space Debris (Vol. 5) “NASA’s new break-up model of EVOLVE 4.0”: Published in 2001 • https://www.sciencedirect.com/science/arti cle/pii/S0273117701004239 • Based on data from: • Solwind and USA 19 deliberate hypervelocity collisions in low Earth orbit in 1985 and 1986 • SOCIT series of HVI experiments • Ariane upper-stage explosion tests • On-orbit explosions
- 5. Explosions Space Environment – Space Debris (Vol. 5) The number of explosive fragments of size L or larger (in metres) is: Where S is a simple scaling factor that can be used to account for different explosion sources (e.g. batteries) 𝑁𝑁 𝐿𝐿 = 𝑆𝑆𝑆𝐿𝐿−1.6
- 6. Size distributions Space Environment – Space Debris (Vol. 5) Upper stage explosions from Johnson et al. 2001:
- 7. Collisions Space Environment – Space Debris (Vol. 5) The number of collision fragments of size L or larger (in metres) is: For a non-catastrophic collision: For a catastrophic collision: 𝑁𝑁 𝐿𝐿 = 0.1𝑀𝑀0.75 𝐿𝐿−1.71 𝑀𝑀 = 𝑚𝑚𝑝𝑝𝑣𝑣𝑟𝑟 2 𝑀𝑀 = 𝑚𝑚𝑝𝑝 + 𝑚𝑚𝑡𝑡 * 𝑣𝑣𝑟𝑟 in km/s
- 8. Collisions Space Environment – Space Debris (Vol. 5) Catastrophic collisions: Kinetic energy of projectile divided by mass of target (in grammes) > 40 J/g 𝐸𝐸𝐸𝐸𝐸𝐸 = 1 2 𝑚𝑚𝑝𝑝𝑣𝑣𝑟𝑟 2 𝑚𝑚𝑡𝑡 × 1000
- 9. Mass distributions Space Environment – Space Debris (Vol. 5) For on-orbit and terrestrial hypervelocity collisions from Johnson et al. 2001:
- 10. A/m distribution Space Environment – Space Debris (Vol. 5) Combination of two Normal distributions, each functions of fragment size and object type (spacecraft or upper stage), from Johnson et al. 2001:
- 11. ∆V distribution Space Environment – Space Debris (Vol. 5) Normal distribution, a function of fragment A/m and event type (explosion or collision), from Johnson et al. 2001:
- 12. Simulation Space Environment – Space Debris (Vol. 5) Before break-up 4 minutes 40 minutes 100 minutes 1 day 1 week
- 13. Simulation Space Environment – Space Debris (Vol. 5) 1 year 1 month 6 months
- 14. Overview of lecture 51 • In this lecture we introduced the NASA standard breakup model, which was developed using (in part) results from the SOCIT series of HVI experiments • We saw how to use this empirical model to calculate: – The number of fragments resulting from an explosion or collision – The mass of the fragments – The area-to-mass ratio of the fragments – The velocity of the fragments Space Environment – Space Debris (Vol. 5)
- 15. Activty Space Environment – Space Debris (Vol. 5) “NASA’s new break-up model of EVOLVE 4.0”: This is available for you to read online or by downloading from the blackboard site • https://www.sciencedirect.com/science/arti cle/pii/S0273117701004239 In addition, the correct implementation of the breakup model is explained in NASA’s Orbital Debris Quarterly Newsletter (also available on blackboard): • https://orbitaldebris.jsc.nasa.gov/quarterly- news/pdfs/odqnv15i4.pdf