This document provides information about constants and laws related to gravitational fields that commonly appear on exams for the PAU (University Access Test) in Castilla y León, Spain. It includes the values of gravitational acceleration on Earth (g0), Earth's radius (RT), Earth's mass (MT), and the gravitational constant (G). It then provides example problems applying Kepler's laws and Newton's law of universal gravitation to calculate orbital properties of planets, moons, and satellites. Sample problems calculate orbital periods, velocities, distances, and gravitational accelerations for bodies in the solar system like Jupiter, Mars, Mercury, the Moon, and artificial satellites.
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.
Motions for systems and structures in space, described by a set denoted Avd. ...Premier Publishers
In order to describe general motions and matter in space, functions for angular velocity and density are assumed and denoted Avd, as an abbreviation. The framework provides a unified approach to motions at different scales. It is analysed how Avd enters and rules, in terms of results from equations, in field experiments and observations at Earth. Chaos may organize according to Avd, such that more order, Cosmos, appear in complex nonlinear dynamical systems. This reveals that Avd may be governing and that deterministic systems can be created without assuming boundaries and conditions for initial values and forces from outside. A mathematical model for the initiation of Logos (when a paper accelerates into a narrow circular orbit), was described, and denoted local implosion; Li. The theorem for dl, provides discrete solutions to a power law, and this is related to locations of satellites and moons.
Science with small telescopes - exoplanetsguest8aa6ebb
The search for extrasolar planets has become one of the most attractive problems in modern astrophysics. The biggest observatories in the world are involved in this task as well as little amateur instruments. There is also a huge variety of astronomical methods used for their investigation. Here I present the projects for searching for exoplanets by transit method and our observations of the planet WASP-2b. We observed a transit on 3/4 August 2008 with a 354 mm Schmidt-Cassegrain Celestron telescope and CCD SBIG STL 11000M camera. By precise photometry made using MaximDL software we obtained the light curve of the star system. Decrease of brightness by 0.02m is detected. Analyzing our data we estimate the radius of the planet and inclination of its orbit. Our results are in good correlation with the published information in literature.
Gaussian Orbital Determination of 1943 AnterosMatthew Li
Paper detailing the theory, methods, calculations, and results regarding the investigation of the orbit of asteroid 1943 Anteros through approximately six weeks of celestial observation and data collection.
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.
Motions for systems and structures in space, described by a set denoted Avd. ...Premier Publishers
In order to describe general motions and matter in space, functions for angular velocity and density are assumed and denoted Avd, as an abbreviation. The framework provides a unified approach to motions at different scales. It is analysed how Avd enters and rules, in terms of results from equations, in field experiments and observations at Earth. Chaos may organize according to Avd, such that more order, Cosmos, appear in complex nonlinear dynamical systems. This reveals that Avd may be governing and that deterministic systems can be created without assuming boundaries and conditions for initial values and forces from outside. A mathematical model for the initiation of Logos (when a paper accelerates into a narrow circular orbit), was described, and denoted local implosion; Li. The theorem for dl, provides discrete solutions to a power law, and this is related to locations of satellites and moons.
Science with small telescopes - exoplanetsguest8aa6ebb
The search for extrasolar planets has become one of the most attractive problems in modern astrophysics. The biggest observatories in the world are involved in this task as well as little amateur instruments. There is also a huge variety of astronomical methods used for their investigation. Here I present the projects for searching for exoplanets by transit method and our observations of the planet WASP-2b. We observed a transit on 3/4 August 2008 with a 354 mm Schmidt-Cassegrain Celestron telescope and CCD SBIG STL 11000M camera. By precise photometry made using MaximDL software we obtained the light curve of the star system. Decrease of brightness by 0.02m is detected. Analyzing our data we estimate the radius of the planet and inclination of its orbit. Our results are in good correlation with the published information in literature.
Gaussian Orbital Determination of 1943 AnterosMatthew Li
Paper detailing the theory, methods, calculations, and results regarding the investigation of the orbit of asteroid 1943 Anteros through approximately six weeks of celestial observation and data collection.
•Lunar laser telemetry consists in determining the round-trip travel time of the light between a transmitter on the Earth and a reflector on the Moon, which is an equivalent measurement of the distance between these two points
- Astrônomos descobriram que uma pequena estrela, do tamanho de Júpiter, possui uma tempestade muito parecida com a Grande Mancha Vermelha e que está ali, persistente por dois anos.
- Enquanto nos planetas, esse tipo de característica é normal, em estrelas essa é a melhor evidência encontrada até hoje.
- A estrela é chamada de W1906+40 e pertence a uma classe de objetos frios chamados de Anãs-L.
- Elas são consideradas estrelas pois fundem átomos e geram luz, como o Sol faz, enquanto que as anãs marrons são conhecidas como estrelas que falharam, pois elas não possuem o processo de fusão atômica em seu interior.
- Nesse novo estudo os astrônomos foram capazes de verificar as mudanças na atmosfera da estrela por dois anos. A técnica usada foi semelhante à de detecção de exoplanetas, analisando a curva de luz da estrela, que apresentava quedas, mas que não era por questão de planetas.
- Os astrônomos usaram o Spitzer e estudaram a luz infravermelha da estrela, que revelou uma gigantesca mancha escura que não era uma mancha magnética estelar, mas sim uma tempestade com um diâmetro equivalente ao de 3 Terras. O spitzer foi capaz de estudar camadas diferentes da atmosfera da estrela e esses dados junto com os dados do Kepler, revelaram com clareza a tempestade estelar.
- Futuras observações serão realizadas usando os dois equipamentos para tentar identificar esse tipo de tempestade em anãs marrons, por exemplo, e tentar descobrir se esse tipo de fenômeno é muito comum, ou é raro no universo.
Invited Seminar presented at the VIA Forum Astroparticle Physics Forum COSMOVIA
21 March 2020
http://viavca.in2p3.fr/2010c_o_s_m_o_v_i_a__forum_sd24fsdf4zerfzef4ze5f4dsq34sdteerui45788789745rt7yr68t4y54865h45g4hfg56h45df4h86d48h48t7uertujirjtiorjhuiofgrdsqgxcvfghfg5h40yhuyir/viewtopic.php?f=73&t=3705&sid=c56cbf76f87536fc4c3ff216d9edaba2
Author: O.M. Lecian
Speaker: O.M. Lecian
Abstract: The LHAASO experiment is aimed at detecting highly-energetic particles of cosmological origin within a large
range of energies.
The sensitivity of the experimental apparatus can within the frameworks of statistical fluctuations of the
background.
Acceleration and lower-energy particles can be analyzed.
The anisotropy mass composition of cosmic rays can analytically described.
The LHAASO Experiment is also suited for detecting particles of cosmological origin originated from the breach
(and/or other kinds of modifications) of particle theories paradigms comprehending other symmetry groups.
Some physical implications of anisotropies can be looked for.
The study of anisotropy distribution for particles of cosmological origin as well as the anisotropies of their velocities
both in the case of a flat Minkowskian background as well as in the case of curved space-time can be investigated,
as far as the theoretical description of the cross-section is concerned, as well as for the theoretical expressions of
such quantities to be analyzed.
The case of a geometrical phase of particles can be schematized by means of a geometrical factor.
Particular solutions are found under suitable approximations.
A comparison with the study of ellipsoidal galaxies is achieved.
The case of particles with anisotropies in velocities falling off faster than dark matter (DM) is compared.
The study of possible anisotropies in the spatial distribution of cosmological particles can therefore be described
also deriving form the interaction of cosmic particles with the gravitational field, arising at quantum distances, at
the semiclassical level and at the classical scales, within the framework of the proper description of particles
anisotropies properties.
IOSR Journal of Applied Physics (IOSR-JAP) is an open access international journal that provides rapid publication (within a month) of articles in all areas of physics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in applied physics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
The stellar orbit distribution in present-day galaxies inferred from the CALI...Sérgio Sacani
Galaxy formation entails the hierarchical assembly of mass,
along with the condensation of baryons and the ensuing, selfregulating
star formation1,2
. The stars form a collisionless system
whose orbit distribution retains dynamical memory that
can constrain a galaxy’s formation history3
. The orbits dominated
by ordered rotation, with near-maximum circularity
λz≈ 1, are called kinematically cold, and the orbits dominated
by random motion, with low circularity λz≈ 0, are kinematically
hot. The fraction of stars on ‘cold’ orbits, compared with
the fraction on ‘hot’ orbits, speaks directly to the quiescence
or violence of the galaxies’ formation histories4,5
. Here we
present such orbit distributions, derived from stellar kinematic
maps through orbit-based modelling for a well-defined,
large sample of 300 nearby galaxies. The sample, drawn from
the CALIFA survey6, includes the main morphological galaxy
types and spans a total stellar mass range from 108.7 to 1011.9
solar masses. Our analysis derives the orbit-circularity distribution
as a function of galaxy mass and its volume-averaged
total distribution. We find that across most of the considered
mass range and across morphological types, there are more
stars on ‘warm’ orbits defined as 0.25 ≤λz≤ 0.8 than on either
‘cold’ or ‘hot’ orbits. This orbit-based ‘Hubble diagram’ provides
a benchmark for galaxy formation simulations in a cosmological
context.
The mass of_the_mars_sized_exoplanet_kepler_138_b_from_transit_timingSérgio Sacani
Artigo da revista Nature, descreve o trabalho de astrônomos para medir o tamanho e a massa de um exoplaneta parecido com Marte, além de caracterizar por completo o sistema planetário da estrela Kepler-138.
A rocky planet_transiting_a_nearby_low_mass_starSérgio Sacani
Um exoplaneta rochoso do tamanho da Terra, orbita uma estrela pequena e próxima, poderia ser o mundo mais importante já encontrado além do Sistema Solar, disseram os astrônomos.
O planeta localiza-se na constelação de Vela, no hemisfério sul do céu e é próximo o suficiente para que os telescópios possam observar qualquer atmosfera que ele possua, um procedimento que poderia ajudar a registrar algum tipo de vida, se ela existisse em outros planetas, no futuro.
Denominado de GJ 1132b, o exoplaneta é cerca de 16% maior que a Terra, e está localizado a cerca de 39 anos-luz de distância, o que faz com que ele seja três vezes mais próximo da Terra do que qualquer outro exoplaneta rochoso já descoberto. Nessa distância, espera-se que os telescópios sejam capazes de fazer uma análise química de sua atmosfera, a velocidade dos seus ventos e as cores do pôr-do-Sol, que acontecem no exoplaneta.
Os astrônomos registraram o planeta à medida que ele passava na frente da sua estrela, uma estrela do tipo anã vermelha, com somente um quinto do tamanho do Sol. Apesar de muito mais fria e muito mais apagada que o Sol, o GJ 1132b, tem uma órbita tão próxima da estrela que as suas temperaturas superficiais atingem cerca de 260 graus Celsius.
Essa temperatura, obviamente, é muito alta para reter a água em estado líquido na superfície do exoplaneta, fazendo com que ele seja inóspito para a vida, mas não tão quente para queimar toda uma atmosfera que pode ter se formado no planeta.
•Lunar laser telemetry consists in determining the round-trip travel time of the light between a transmitter on the Earth and a reflector on the Moon, which is an equivalent measurement of the distance between these two points
- Astrônomos descobriram que uma pequena estrela, do tamanho de Júpiter, possui uma tempestade muito parecida com a Grande Mancha Vermelha e que está ali, persistente por dois anos.
- Enquanto nos planetas, esse tipo de característica é normal, em estrelas essa é a melhor evidência encontrada até hoje.
- A estrela é chamada de W1906+40 e pertence a uma classe de objetos frios chamados de Anãs-L.
- Elas são consideradas estrelas pois fundem átomos e geram luz, como o Sol faz, enquanto que as anãs marrons são conhecidas como estrelas que falharam, pois elas não possuem o processo de fusão atômica em seu interior.
- Nesse novo estudo os astrônomos foram capazes de verificar as mudanças na atmosfera da estrela por dois anos. A técnica usada foi semelhante à de detecção de exoplanetas, analisando a curva de luz da estrela, que apresentava quedas, mas que não era por questão de planetas.
- Os astrônomos usaram o Spitzer e estudaram a luz infravermelha da estrela, que revelou uma gigantesca mancha escura que não era uma mancha magnética estelar, mas sim uma tempestade com um diâmetro equivalente ao de 3 Terras. O spitzer foi capaz de estudar camadas diferentes da atmosfera da estrela e esses dados junto com os dados do Kepler, revelaram com clareza a tempestade estelar.
- Futuras observações serão realizadas usando os dois equipamentos para tentar identificar esse tipo de tempestade em anãs marrons, por exemplo, e tentar descobrir se esse tipo de fenômeno é muito comum, ou é raro no universo.
Invited Seminar presented at the VIA Forum Astroparticle Physics Forum COSMOVIA
21 March 2020
http://viavca.in2p3.fr/2010c_o_s_m_o_v_i_a__forum_sd24fsdf4zerfzef4ze5f4dsq34sdteerui45788789745rt7yr68t4y54865h45g4hfg56h45df4h86d48h48t7uertujirjtiorjhuiofgrdsqgxcvfghfg5h40yhuyir/viewtopic.php?f=73&t=3705&sid=c56cbf76f87536fc4c3ff216d9edaba2
Author: O.M. Lecian
Speaker: O.M. Lecian
Abstract: The LHAASO experiment is aimed at detecting highly-energetic particles of cosmological origin within a large
range of energies.
The sensitivity of the experimental apparatus can within the frameworks of statistical fluctuations of the
background.
Acceleration and lower-energy particles can be analyzed.
The anisotropy mass composition of cosmic rays can analytically described.
The LHAASO Experiment is also suited for detecting particles of cosmological origin originated from the breach
(and/or other kinds of modifications) of particle theories paradigms comprehending other symmetry groups.
Some physical implications of anisotropies can be looked for.
The study of anisotropy distribution for particles of cosmological origin as well as the anisotropies of their velocities
both in the case of a flat Minkowskian background as well as in the case of curved space-time can be investigated,
as far as the theoretical description of the cross-section is concerned, as well as for the theoretical expressions of
such quantities to be analyzed.
The case of a geometrical phase of particles can be schematized by means of a geometrical factor.
Particular solutions are found under suitable approximations.
A comparison with the study of ellipsoidal galaxies is achieved.
The case of particles with anisotropies in velocities falling off faster than dark matter (DM) is compared.
The study of possible anisotropies in the spatial distribution of cosmological particles can therefore be described
also deriving form the interaction of cosmic particles with the gravitational field, arising at quantum distances, at
the semiclassical level and at the classical scales, within the framework of the proper description of particles
anisotropies properties.
IOSR Journal of Applied Physics (IOSR-JAP) is an open access international journal that provides rapid publication (within a month) of articles in all areas of physics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in applied physics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
The stellar orbit distribution in present-day galaxies inferred from the CALI...Sérgio Sacani
Galaxy formation entails the hierarchical assembly of mass,
along with the condensation of baryons and the ensuing, selfregulating
star formation1,2
. The stars form a collisionless system
whose orbit distribution retains dynamical memory that
can constrain a galaxy’s formation history3
. The orbits dominated
by ordered rotation, with near-maximum circularity
λz≈ 1, are called kinematically cold, and the orbits dominated
by random motion, with low circularity λz≈ 0, are kinematically
hot. The fraction of stars on ‘cold’ orbits, compared with
the fraction on ‘hot’ orbits, speaks directly to the quiescence
or violence of the galaxies’ formation histories4,5
. Here we
present such orbit distributions, derived from stellar kinematic
maps through orbit-based modelling for a well-defined,
large sample of 300 nearby galaxies. The sample, drawn from
the CALIFA survey6, includes the main morphological galaxy
types and spans a total stellar mass range from 108.7 to 1011.9
solar masses. Our analysis derives the orbit-circularity distribution
as a function of galaxy mass and its volume-averaged
total distribution. We find that across most of the considered
mass range and across morphological types, there are more
stars on ‘warm’ orbits defined as 0.25 ≤λz≤ 0.8 than on either
‘cold’ or ‘hot’ orbits. This orbit-based ‘Hubble diagram’ provides
a benchmark for galaxy formation simulations in a cosmological
context.
The mass of_the_mars_sized_exoplanet_kepler_138_b_from_transit_timingSérgio Sacani
Artigo da revista Nature, descreve o trabalho de astrônomos para medir o tamanho e a massa de um exoplaneta parecido com Marte, além de caracterizar por completo o sistema planetário da estrela Kepler-138.
A rocky planet_transiting_a_nearby_low_mass_starSérgio Sacani
Um exoplaneta rochoso do tamanho da Terra, orbita uma estrela pequena e próxima, poderia ser o mundo mais importante já encontrado além do Sistema Solar, disseram os astrônomos.
O planeta localiza-se na constelação de Vela, no hemisfério sul do céu e é próximo o suficiente para que os telescópios possam observar qualquer atmosfera que ele possua, um procedimento que poderia ajudar a registrar algum tipo de vida, se ela existisse em outros planetas, no futuro.
Denominado de GJ 1132b, o exoplaneta é cerca de 16% maior que a Terra, e está localizado a cerca de 39 anos-luz de distância, o que faz com que ele seja três vezes mais próximo da Terra do que qualquer outro exoplaneta rochoso já descoberto. Nessa distância, espera-se que os telescópios sejam capazes de fazer uma análise química de sua atmosfera, a velocidade dos seus ventos e as cores do pôr-do-Sol, que acontecem no exoplaneta.
Os astrônomos registraram o planeta à medida que ele passava na frente da sua estrela, uma estrela do tipo anã vermelha, com somente um quinto do tamanho do Sol. Apesar de muito mais fria e muito mais apagada que o Sol, o GJ 1132b, tem uma órbita tão próxima da estrela que as suas temperaturas superficiais atingem cerca de 260 graus Celsius.
Essa temperatura, obviamente, é muito alta para reter a água em estado líquido na superfície do exoplaneta, fazendo com que ele seja inóspito para a vida, mas não tão quente para queimar toda uma atmosfera que pode ter se formado no planeta.
Stellar-like objects with effective temperatures of 2700K and below are referred to as
20 "ultracool dwarfs"1. This heterogeneous group includes both extremely low-mass stars
21 and brown dwarfs (substellar objects not massive enough to sustain hydrogen fusion),
22 and represents about 15% of the stellar-like objects in the vicinity of the Sun2. Based on
23 the small masses and sizes of their protoplanetary disks3,4, core-accretion theory for
24 ultracool dwarfs predicts a large, but heretofore undetected, population of close-in
25 terrestrial planets5, ranging from metal-rich Mercury-sized planets6 to more hospitable
26 volatile-rich Earth-sized planets7. Here we report the discovery of three short-period
27 Earth-sized planets transiting an ultracool dwarf star 12 parsecs away. The inner two
28 planets receive four and two times the irradiation of Earth, respectively, placing them
29 close to the inner edge of the habitable zone of the star8. Eleven orbits remain possible
30 for the third planet based on our data, the most likely resulting in an irradiation
31 significantly smaller than Earth's. The infrared brightness of the host star combined
32 with its Jupiter-like size offer the possibility of constraining the composition and
33 thoroughly characterizing the atmospheric properties of the components of this nearby
34 planetary system, notably to detect potential biosignatures.
An Earth-sized exoplanet with a Mercury-like compositionSérgio Sacani
Earth, Venus, Mars and some extrasolar terrestrial planets1
have a mass and radius that is consistent with a mass fraction
of about 30% metallic core and 70% silicate mantle2
. At the
inner frontier of the Solar System, Mercury has a completely
different composition, with a mass fraction of about 70%
metallic core and 30% silicate mantle3
. Several formation or
evolution scenarios are proposed to explain this metal-rich
composition, such as a giant impact4, mantle evaporation5
or the depletion of silicate at the inner edge of the protoplanetary
disk6. These scenarios are still strongly debated.
Here, we report the discovery of a multiple transiting planetary
system (K2-229) in which the inner planet has a radius
of 1.165 ± 0.066 Earth radii and a mass of 2.59 ± 0.43 Earth
masses. This Earth-sized planet thus has a core-mass fraction
that is compatible with that of Mercury, although it was
expected to be similar to that of Earth based on host-star
chemistry7
. This larger Mercury analogue either formed with
a very peculiar composition or has evolved, for example, by
losing part of its mantle. Further characterization of Mercurylike
exoplanets such as K2-229 b will help to put the detailed
in situ observations of Mercury (with MESSENGER and
BepiColombo8) into the global context of the formation and
evolution of solar and extrasolar terrestrial planets.
Periodic mass extinctions_and_the_planet_x_model_reconsideredSérgio Sacani
The 27 Myr periodicity in the fossil extinction record has been con-
firmed in modern data bases dating back 500 Myr, which is twice the time
interval of the original analysis from thirty years ago. The surprising regularity
of this period has been used to reject the Nemesis model. A second
model based on the sun’s vertical galactic oscillations has been challenged
on the basis of an inconsistency in period and phasing. The third astronomical
model originally proposed to explain the periodicity is the Planet
X model in which the period is associated with the perihelion precession
of the inclined orbit of a trans-Neptunian planet. Recently, and unrelated
to mass extinctions, a trans-Neptunian super-Earth planet has been proposed
to explain the observation that the inner Oort cloud objects Sedna
and 2012VP113 have perihelia that lie near the ecliptic plane. In this
Letter we reconsider the Planet X model in light of the confluence of the
modern palaeontological and outer solar system dynamical evidence.
Key Words: astrobiology - planets and satellites - Kuiper belt:
general - comets: general
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
The simplified electron and muon model, Oscillating Spacetime: The Foundation...RitikBhardwaj56
Discover the Simplified Electron and Muon Model: A New Wave-Based Approach to Understanding Particles delves into a groundbreaking theory that presents electrons and muons as rotating soliton waves within oscillating spacetime. Geared towards students, researchers, and science buffs, this book breaks down complex ideas into simple explanations. It covers topics such as electron waves, temporal dynamics, and the implications of this model on particle physics. With clear illustrations and easy-to-follow explanations, readers will gain a new outlook on the universe's fundamental nature.
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar Kanvaria
Executive Directors Chat Leveraging AI for Diversity, Equity, and InclusionTechSoup
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
Thinking of getting a dog? Be aware that breeds like Pit Bulls, Rottweilers, and German Shepherds can be loyal and dangerous. Proper training and socialization are crucial to preventing aggressive behaviors. Ensure safety by understanding their needs and always supervising interactions. Stay safe, and enjoy your furry friends!
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
Safalta Digital marketing institute in Noida, provide complete applications that encompass a huge range of virtual advertising and marketing additives, which includes search engine optimization, virtual communication advertising, pay-per-click on marketing, content material advertising, internet analytics, and greater. These university courses are designed for students who possess a comprehensive understanding of virtual marketing strategies and attributes.Safalta Digital Marketing Institute in Noida is a first choice for young individuals or students who are looking to start their careers in the field of digital advertising. The institute gives specialized courses designed and certification.
for beginners, providing thorough training in areas such as SEO, digital communication marketing, and PPC training in Noida. After finishing the program, students receive the certifications recognised by top different universitie, setting a strong foundation for a successful career in digital marketing.
1. I.E.S. “JULIÁN MARÍAS”- VALLADOLID DEPARTAMENTO DE FÍSICA Y QUÍMICA
PAU CASTILLA Y LEON 2007-19 JUNIOY SEPTIEMBRE CAMPOGRAVITATORIO
Página1
En los exámenesde PAUsiempre hay disponibles4 constantesrelacionadas con el campo gravitatorio:
g0=9,8 m/s2
RT=6,37·106
m MT=5,98·1024
kg G=6,67·10–11
N·m2
·kg–2
Leyesde Kepler:
1. (79-SE10) Sabiendoque ladistanciamediaSol –Júpiteres5,2 vecesmayorque la distanciamediaSol –
Tierra,y suponiendoórbitascirculares:
a) Calcule el periodode Júpiterconsiderandoque el periodode laTierraes1 año.(1 punto)
b) ¿Qué ángulorecorre JúpiterensuórbitamientraslaTierrada unavueltaal Sol?(1 punto)
S: 11,86 años terrestres; 30,4°
2. (154-J14) a) Enuncie lastresleyesde Kepler. (1,2puntos)
b) Describaalgúnprocedimientoque permitaladeterminaciónexperimental de g.(0,8puntos)
S: El péndulo; 𝑻 = 𝟐𝝅√
𝒍
𝒈
3. (144-S13) a) Enuncie lasleyesde Kepler. (1punto)
b) Alrededordel Sol,entre lasórbitasde Marte y Júpiter, giranunaserie de objetosde pequeñotamaño
llamadosasteroides.El mayorde ellosesCeres,consideradohoycomounplanetaenano. Considerando
que lasórbitasson circulares,use losdatosde la tablapara calcular el periodode rotaciónorbital de Ceres
enaños terrestresylamasa del Sol. (1 punto)
Radiode la órbita(m) Periodode rotación(s)
Júpiter 7,78·1011
3,74·108
Ceres 4,21·1011
S: TCeres=0,4 TJupiter=4,72 años terrestres; MSol=1,97·1030
kg.
4. (99-S11) La distanciamediade laTierraal Sol es 1,495·108
kmy la Tierratarda 365,24 días endar una
vueltaa sualrededor.Mercuriotiene unperiodode 88días ensu giroalrededordel Sol.Suponiendo
órbitascirculares,determine:
a) la distanciamediaentre Mercurioyel Sol;(1 punto)
b) lavelocidadorbital mediade Mercurio.(1punto)
S: a) RM=0,387RT=5,789·107
km; v=4,78·104
m/s
Ley de la gravitación universal.
5. (9-S07) La masa de la Luna es0,0123 veceslade laTierra y suradio mide 1,74·106
m.Calcule:
a) La velocidadconque llegaráal suelounobjetoque cae libremente desde unaalturade 5 m sobre la
superficie lunar(1,5puntos).
b) El períodode oscilaciónenlaLunade unpéndulocuyoperíodoenla Tierraesde 5 s (1,5 puntos).
S: v=4,03 m/s TL=2,5TT=17,3 s
6. (64-JE10) La Luna tiene unamasa ML=7,35·1022
kg y unradio RL=1,74·106
m. Determine:
a) La distanciaque recorre en10 s un cuerpoque cae libremente enlaproximidadde su superficie.(1
punto) b) El trabajo necesarioparalevantaruncuerpode 50 kg hastauna alturade 10 m. (1 punto)
S: a) 81 m; b) 810 J
7. (84-SE10) a) ¿Cuál debe serladuracióndel día terrestre paraque el pesoaparente de losobjetossituados
enel ecuadorsea igual a cero?(1,5 puntos)
b) ¿Cuál sería,en ese caso,el periodode unpéndulosimplede 1m de longitudsituadoenel ecuador?( 0,5
puntos)
S: a) 84 minutos; b) No se moveria
Momentode una fuerza. Momento angular. Justificaciónde las leyesde Kepler:
8. (1-J07) Dos satélitesde igual masaorbitanentornoa un planetade masamuchomayor siguiendoórbitas
circularescoplanariasde radiosRy 3R y recorriendoamboslasórbitasensentidoscontrarios. Deduzcay
calcule:
a) la relaciónentre susperiodos(1,5puntos).
b) la relaciónentre susmomentosangulares(módulo,direcciónysentido)(1,5puntos).
S: T3R=√𝟐𝟕 TR; b) L3R=√𝟑/𝟑LR sentidos opuestos
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9. (59-JE10) La distanciamediaentre laLunay la Tierraes RT-L= 3,84·108
m, y la distanciamediaentre laTierra
y el Sol es RT-S=1496·108
m La Luna tiene unamasa ML=7,35·1022
kg y el Sol MS=1,99·1030
kg . Considere las
órbitascircularesylos astrospuntuales.
a) Comparandolavelocidadlinealde losastrosensusórbitasrespectivas,determine cuántasveces más
rápidose desplazalaTierraalrededordel Sol que laLuna alrededorde laTierra. (1 punto)
b) En el alineamientode lostresastrosdurante uneclipse de Sol (cuando laposiciónde laLunase
interpone entre laTierrayel Sol),calcule lafuerzanetaque experimentalaLunadebidoala acción
gravitatoriadel Sol yde laTierra.Indique el sentido(signo)de dichafuerza. (1punto)
S: vT=29vL Resultante=2,39·1020
N hacia el sol
10. (49-JG10) a) Enuncie lasleyesde Kepler.(1punto)
b) Suponiendoórbitascirculares,deduzcalaterceraleyde Keplerapartirde la leyde GravitaciónUniversal.
(1 punto)
11. (164-S14) a) La Luna describe unaórbitacircularentorno a la Tierra,con unperiodode 27,3 días y un radio
de 3,84·105
km.Aplicandolasleyesde Kepler,determine el periodode unsatélite artificialque gira
alrededorde laTierraa una altura sobre susuperficie igual al radioterrestre.(1punto)
b) Explique si laLunay el satélite artificial mencionadotienenlamismavelocidadareolar.(1punto)
S: a) T=0,165 dias= 4 h; b) vareaolar=
𝒅𝑺
𝒅𝒕
=
|𝑳
⃗
⃗ |
𝟐𝒎
=
√𝑮𝑴𝒓
𝟐
, distintas al ser r distintos
12. (184-S15) a) ¿Dónde tendrámayorvelocidadorbital unsatéliteterrestre conórbitaelíptica:enel apogeo
(puntomásdistante de laTierra) o en el perigeo?Expliqueporqué. (1punto)
b) Definalavelocidadde escape de unobjetoenunplanetayexplique cómovaríasi se duplicalamasa del
objeto. (1punto)
Satélites.Aspectodinámico.
13. (249-J19) a) De un satélite artificialque orbitaalrededorde laTierrase conoce el periodoyel radiode la
órbita.¿Se puede utilizarestainformaciónylaleyfundamental de ladinámicaparacalcularsu masa? ¿Y la
masa de la Tierra?Razone lasrespuestas. (1punto)
b) Un satélite artificial se pone enórbitaauna distanciade lasuperficie terrestre tal que laaceleraciónde
la gravedadesla terceraparte del valorde dicha aceleraciónenlasuperficie terrestre.¿Cuál esel periodo
de revolucióndel satéliteentornoa laTierra? (1 punto)
S: m no, MT sí, 𝑴𝑻 =
𝟒𝝅𝟐
𝑮𝑻𝟐
𝒓𝟑, 𝒉 = (√𝟑−𝟏)𝑹𝑻, T=11529 s
14. (124-S12) Galileoobservóporprimeravezlaslunasde Júpiteren1610. Encontróque Io, el satélite más
cercano a Júpiterque pudoobservarensuépoca,poseíaun periodoorbital de 1,8 días y el radio de su
órbitaera, aproximadamente,3vecesel diámetrode Júpiter.Asimismo,encontróque el periodoorbital de
Calisto(lacuarta lunamás alejadade Júpiter) erade 16,7 días. Con esosdatos,suponiendoórbitas
circularesyusandoque el radio de Júpiter es7,15·107
m, calcule:
a) La masa de Júpiter. (1punto)
b) El radio de la órbitade Calisto. (1punto)
S: a) MJ=1,93·1023
kg; b) Rcalixto-Jupiter=1,89·109
m
15. (46-S09) Júpiteresel mayorplanetadel sistemasolar.Sumasaes318 vecesla masa terrestre,suradio
11,22 vecesel de laTierra y sudistanciaal sol 5,2 vecesmayor que ladistanciamediade la Tierra al Sol.
Determine:
a) el valorde la aceleraciónde lagravedadenla superficiede Júpiterenrelaciónconsuvalor enla
superficie terrestre yel periodode rotaciónde Júpiteralrededordel Sol,sabiendoque el periodoterrestre
esde 365 días y las órbitasde ambosplanetasse considerancirculares (2puntos).
b) el periodoyla velocidadmediaorbital de Calisto,su segundamayorluna,sabiendoque describe una
órbitacircular de 1,88·106
kmde radio(1 punto).c) Tc=1,44·106
s=
S: g0J=2.53g0T=24,8 m/s2
; TJ=11,86TT=11,86 años terrestres; TC=1,44·106
s=16,6 dias, vc=8,21·108
m/s
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16. (34-J09) Júpiter, el mayorde losplanetasdel sistemasolarycuyamasa es 318,36 veceslade la Tierra, tiene
orbitandodoce satélites.El mayorde ellos,Ganimedes(descubiertoporGalileo),giraen unaórbitacircular
de radio igual a 15 vecesel radiode Júpiterycon un períodode revolución de 6,2·105
s.Calcule:
a) la densidadmediade Júpiter(1,5puntos).
b) el valor de la aceleraciónde lagravedadenlasuperficie de Júpiter(1,5puntos).
S: dJ=1240,6 kg/m3
; g0J=24,8 m/s2
17. (169-J15) a) Un satélite artificialdescribeunaórbitacircularenel planoecuatorial de laTierracon una
velocidadde 3073 m·s─1
.¿A qué alturasobre la superficie de laTierraestáorbitando?Determine su
periodode rotaciónenhoras. (1 punto)
b) ¿Qué esuna órbitageoestacionaria?¿Cuántovalelaaceleraciónde lagravedadendichaórbita? (1
punto)
S: ≈24 h; R=42,2·106
m; h=35,9·106
m; g=0,22 m/s2
Campo gravitatorio:
18. (244-S18) a) Explique qué esuncampoconservativoyrazone si el campo gravitatorioloeso no. (0,75
puntos)
b) Explique losconceptosde fuerzagravitatoriaycampogravitatorioe indique qué relaciónexisteentre
ellos. (0,75puntos)
19. (234-J18) a) Considerandoque lasórbitasde losplanetasdel sistemasolarsonaproximadamente
circulares,utilice losdatosde laórbitaterrestre (radio,150·106
km; periodo,365 días) para calcularla
velocidadde traslaciónde Mercurio,sabiendoque el radiode suórbitamide 57,9·106
km. (0,75 puntos)
b) Calcule el diámetrode Mercurio,sabiendoque laaceleraciónde lagravedadensusuperficie es3,7m·s–2
y su densidadmediaes5,43 g·cm–3
. (0,75 puntos)
S: 87,53 días, 48 km/s y 4877 (4880 según Wikipedia)
20. (54-JG10) En tresde losvérticesde uncuadradode 1 m de ladohay tresmasas igualesde 2 kg.Calcule:
a) La intensidaddel campogravitatorioenel otrovértice.(1,5puntos)
b) La fuerzaque actúa sobre una masa de 5 kg colocadaenél.(0,5 puntos)
S: a) 𝒈
⃗⃗ =–18,06·10–11
(𝒊 + 𝒋) N/kg; 𝑭
⃗
⃗ =–90,3·10–11
(𝒊 + 𝒋) N/kg
21. (134-J13) La masade laLuna es 0,012 vecesla masade laTierra, el radiolunares0,27 vecesel radiode la
Tierray la distanciamediaentre suscentroses60,3 radiosterrestres.
a) Calcule lagravedadenla superficielunar.(0,8puntos)
b) ¿En qué puntointermedioentre laTierrayla Luna se equilibranlasfuerzasque ambasejercen sobre un
cuerpode masa m? Realice unesquemailustrativode lasfuerzas.(1,2puntos)
S: gOL=0,165goT=1,62 m/s2
; x=2,51·108
m
22. (114-J12) a) ¿Cómose modificael pesode unobjetocuandose elevadesdeel nivel del marhastauna
alturaigual a dosvecesel radioterrestre? (1punto)
b) Júpitertiene unadensidadmediade 1,34·103
kg·m–3
y un radioigual a 7,18·107
m.¿Cuál es laaceleración
de la gravedadensu superficie? (1punto)
S: gh=g0T/9 ; g0J=26,89 m/s2
23. (179-S15) Dos masasigualesde 10 kg estánsituadasenlospuntosde coordenadas(3,0) y (-3, 0),medidas
enmetros.Calcule:
a) La intensidadde campogravitatoriogeneradoporlasdosmasasen el punto(0, 2). (1 punto)
b) El potencial gravitatorioenel origende coordenadas. (1punto)
S: g= –5,7·10–11
j N/kg; V= 4,45·10–10
J/kg
24. (204-S16) a) El planeta1 tiene unradiotresvecesmayorque el planeta2. Si ladensidadde ambosplanetas
esla misma,¿encuál de losdoses mayorel pesode un mismocuerpo?Razone surespuesta. (1punto)
b) Dibuje laslíneasdel campogravitatoriocreadopor dosmasas igualesseparadasunaciertadistancia.
¿Existe algúnpuntodonde el campogravitatorioseanulo?Razone larespuesta. (1punto)
S: g1/g2=3
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Energía potencial.Energíamecánica:
25. (259-S19) Un satélite de 100 kg describe unaórbitacircularalrededorde unplanetaconun periodode 45
mina una velocidadde 3,1·104
m s-1
.Calcule:
a) La masadel planeta. (1punto) b) La energíamecánicadel satélite.(1punto)
S: MPlaneta=1,92·1026
kg, Emecánica=-4,805·1010
J
26. (7-J07) Un planetasigue unaórbitaelípticaalrededorde unaestrella.Cuandopasaporel periastroP,punto
de su trayectoriamás próximoala estrella,yporel apoastroA,punto másalejado,expliqueyjustifiquelas
siguientes afirmaciones:
a) Su momentoangularesigual enambospuntos(0,5 puntos) ysuceleridadesdiferente(0,5puntos).
b) Su energíamecánicaes igual enambospuntos(1 punto).
S: a) si, ya que M=0, L=cte rAvA=rpvp; Em=constante, por ser Fgravitatoria central y por tanto conservativa
27. (17-J08) Se deseaponerenórbitacircularun satélite meteorológicode 1000 kg de masa a una altura de
300 kmsobre la superficie terrestre.Deduzcaycalcule:
a) La velocidad,el periodoyaceleración que debetenerenlaórbita(2puntos).
b) El trabajo necesarioparaponerenórbitael satélite (1punto).
S: 8,97 m/s2
; 7,7·103
m/s; y 90 minutos; 3,27·1010
J
28. (25-S08) Un ciertosatélite enórbitacircularalrededorde laTierra esatraído por éstacon una fuerzade
1000 N y la energíapotencial gravitatoriaTierra-satélite es−3·1010
J, siendonulaenel infinito. Calcule:
a) La altura del satélite sobre lasuperficie terrestre (1,5puntos).
b) La masa del satélite (1,5puntos).
S: h=2,363·107
m ; 2,26·103 kg
29. (31-S08) a) Escriba la expresiónde laenergíapotencial gravitatoriaterrestre de unobjetosituadocerca de
la superficiede laTierra.¿Enqué lugar esnula?(1 punto).
b) Considere ahorael caso de un satélite enórbitaalrededorde laTierra.Escribala expresión de suenergía
potencial gravitatoriaterrestree indique el lugardonde se anula(1punto).
30. (39-J09)Considere dossatélitesde masasigualesenórbitaalrededorde laTierra.Uno de ellosgiraen una
órbitade radioR y el otro enuna de radio 2R. Conteste razonadamentelassiguientes preguntas:
a) ¿Cuál de losdos se desplazaconmayor celeridad?(0,5puntos).
b) ¿Cuál de losdos tiene mayorenergíapotencial?(0,5puntos).
c) ¿Cuál de ellostiene mayorenergíamecánica?(1punto).
S: v1=(2)1/2
v2; Ep1=2Ep2; Em1=2Em2
31. (229-J18) La estaciónespacial internacional (ISS),cuyamasaes4,5·105
kg, describe unaórbita
aproximadamente circularalrededorde laTierra,de periodo92 minutos.
a) Determine sualturasobre lasuperficie de laTierraysu velocidadorbital. (0,75puntos)
b) Calcule laenergíanecesariaparaduplicarel radiode su órbita. (0,75 puntos)
S: 382 km de altura, 7686 m/s y 6,65·1013
J
32. (69-SG10) Un satélite artificialde 250 kg se encuentraenuna órbitacircularalrededorde laTierra a una
alturade 500 km de su superficie.Si queremostransferirloaunanuevaórbitaenla que su periodode
revoluciónseatresvecesmayor:
a) Calcule laalturade estanuevaórbitay su velocidadlineal.(1punto)
b) Obtengalaenergíanecesariapararealizarla transferenciaentre ambasórbitas.(1punto)
S: a) 7,93·106
m; v=5,3 km/s=5,28·103
m/s; W=3,77·109
J
33. (74-SG10) Se tienendosmasas MA=100 kg y MB=400 kg colocadasenlospuntosde coordenadasA(2,0) y
B(−1,0) medidasenmetros.
a) Calcule enqué puntode la recta que une ambasmasas se anulael campo gravitatoriodebidoaellas.(1
punto)
b) Determine el trabajonecesarioparatrasladarunobjetode masa m=10 kg desde dichopuntoal origen
de coordenadas.Interprete el signo.(1punto)
S: en el (1,0); W=10–6
J
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34. (94-J11) Desde lasuperficiede laTierrase pone enórbitaun satélite,lanzándoloendirecciónvertical con
una velocidadinicial de 6000 ms-1
.Despreciandoel rozamientoconel aire,determine:
a) la alturamáximaque alcanzael satélite;(1punto)
b) el valorde la gravedadterrestre adicha alturamáxima.(1punto)
S: a) h=2,27·106
m=2270 km; g=g0T·0,51=4,98 m/s2
.
35. (139-S13) Dos partículasde masas4 kg y 0,5 kg se encuentranenel vacío y separadas20 cm.Calcule:
a) La energíapotencial inicial del sistemayel trabajorealizadoporlafuerzagravitatoriaal aumentarla
separaciónentre laspartículashasta 40 cm. (1 punto)
b) El trabajode la fuerzagravitatoriaparaseparar laspartículas desde laposiciónde partidahastael
infinitoyel trabajode lafuerzagravitatorianecesariopararestablecerladistribucióninicial. (1punto)
S: a) Epi= –6,67·10–10
J; W=–3,335·10–10
J; b) –6,67·10–10
J y 6,67·10–10
J
36. (119-S12) La lanzaderaespacial Columbiagirabaenunaórbita circulara 250 km de altura sobre la
superficie terrestre.Pararepararel telescopioespacial Hubble,se desplazóhastaunanuevaórbitacircular
situadaa 610 km de alturasobre la Tierra.Sabiendoque lamasadel Columbiaera75000 kg, calcule:
a) El periodoylavelocidadorbital inicialesde lalanzaderaColumbia. (1punto)
b) La energíanecesariaparasituarlaenla órbitadonde estáel Hubble. (1punto)
S: T=89 min 19 s; 7,76·103
m/s; b) W=1,17·1011
J
37. (109-J12) Dos masaspuntuales, m1 = 5 kgy m2 = 10 kg,se encuentransituadasenel planoXYenlospuntos
de coordenadas(x1,y1) = (0, 1) y (x2,y2) = (0, 7), respectivamente.Sabiendoque todaslascoordenadas
estánexpresadasenmetros,calcule:
a) La intensidaddel campogravitatoriodebidoalasdosmasas enel punto(4, 4). (1 punto)
b) El trabajo necesarioparatrasladaruna masa de 1 kg situadaenel punto(0, 4) hasta el punto(4, 4), en
presenciade lasotrasdos masas,indicandolainterpretaciónfísicaque tiene el signodeltrabajocalculado.
(1 punto)
S: 𝒈
⃗⃗ =-3,1416·10–11
𝒊 + 8,004·10–12
𝒋 N/kg; W=–1,334·10–10
J
38. (159-S14) a) Calcule el valorde la gravedada unaaltura sobre la superficiede laTierraigual a lacuarta
parte de suradio.¿Cuánto pesaráunobjetode masa 100 kga dichaaltura?(1 punto)
b) Si no existiese atmósferayse dejase caerel objeto anteriordesdedichaaltura,¿conqué velocidad
llegaríaa la Tierra?(1 punto)
S: a) g=0,64g0T; P=627,2 N; b) v=5·103
m/s
39. (174-J15) Sobre el cometa67P/Churiumov-Guerasimenko(de masaM= 1013 kg y 25 km3
de volumen) se
posóel móduloespacial Philae(de masam = 100 kg),transportadopor lasonda espacial Rosetta.Debidoa
que el módulo Philaeno dispone de propulsiónpropia,lasonda Rosetta se aproximóhasta22,5 km de la
superficie delcometayallíabandonóal módulo Philaeen caída libre con unavelocidadinicialnularespecto
al cometa,que supondremosesférico.Calcule:
a) La velocidadconlaque Philaeimpactósobre el cometa. (1 punto)
b) El pesodel módulo Philaesobre lasuperficiedel cometa. (1punto)
S: 8,25 m/s; 2,03 N
40. (214-J17) Un meteoritode 350 kg que cae libremente hacialaTierra,tiene unavelocidadde 15 m s–1
a una
alturade 500 km sobre la superficieterrestre.Determine: a) El pesodel meteoritoadichaaltura. (0,75p)
b) La velocidadconlaque impactará sobre lasuperficie terrestre (despreciandolafricciónconla
atmósfera). (0,75puntos)
S: 8,45 m/s2
; P=2957 N; v=2135 m/s
Satélitesartificiales:Planteamientoenergético. Velocidadde escape. Energíade enlace:
41. (254-J19) Un satélite artificialde 1500 kg describe unaórbitacircularde 6500 km de radioalrededorde la
Tierra.
a) Calcule lavelocidad,el periodoylaenergíamecánicadel satélite. (1,2puntos)
b) Determine lavelocidadde escape parael satélitedesdeesaórbita. (0,8puntos)
S: a) v=7833,5 m/s, T=5213,6 s, Em=-4,602·1010
J; b) v=11078 m/s
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42. (264-S19) El radiode Júpiteres11,2 vecesmayorque el radio de la Tierray la masa de Júpiteres318 veces
la masa de la Tierra.Determine:
a) El valorde lagravedadenla superficie de Júpiter. (1punto)
b) La velocidadde escape desde lasuperficie de Júpiter. (1punto)
S: 24,84 m/s2
, 2,54 veces la de la Tierra; vescape=59,6 km/s (salir es complicado)
43. (219-S17) a) El periodode rotaciónde Marte es24,6229 horas.Si el radiode la órbitaareoestacionaria
(equivalente aunaórbitageoestacionariaenlaTierra) es20425 km, ¿cuál es lamasa del planeta? (0,75
puntos)
b) Se sabe que la velocidadde escape de Marte es5,027 km s-1.¿Cuál esel radio del planeta? (0,75puntos)
S: 6,42·1023
kg; 3388 km
44. (239-S18) a) La velocidadde escape desde lasuperficiede Uranoes19,9 kms–1
y la gravedadensu
superficie es7,8m s–2
. Calcule el radiode Urano. (0,75 puntos)
b) El radiomediode laórbitade Urano alrededordel Sol es19,19 vecesmayorque el de la Tierraalrededor
del Sol.Encuentre laduracióndel añouraniano. (0,75 puntos)
S: 2,54·107
m (aproximadamente 25400 km); 84,06 años terrestres
47. (224-S17) Un satélite artificialde 250 kg describe una órbitacirculara unaaltura h sobre lasuperficie
terrestre.El valorde la gravedada dichaaltura esla quintaparte de su valoren lasuperficie de laTierra.
a) Calcule el períodode revolucióndelsatélite enlaórbita. (0,75puntos)
b) Calcule laenergíamecánicadel satélite. (0,75puntos)
S: 4,7 h y –º,4·107
J
45. (209-J17) a) Calcule laenergíapotencial gravitatoriade unsatélitede masam = 100 kg que estáorbitandoa
una alturade 1000 kmsobre la superficie terrestre. (0,75puntos)
b) Explique si parael cálculoanteriorpodríautilizarse laexpresiónE= m g h. (0,75 puntos)
46. (15-S07) El radio de un planetaeslatercera parte del radioterrestre ysu masa lamitad.Calcule la
gravedadensu superficie(1punto) ylavelocidadde escape del planeta,enfunciónde sus
correspondientes valoresterrestres (1punto).
47. (24-J08) Velocidadde escape:definicióny aplicación al casode un cuerpoenla superficieterrestre(2
puntos).
48. (44-S09) a) ¿Qué se entiendeporvelocidadde escape?(1punto).
b) Si la masade laTierra se cuadruplicara,manteniendoel radio,¿cómose modificaríala velocidadde
escape?(1 punto).
49. (89-J11) La masa de Marte, su radioy el radiode suórbita alrededordel Sol,referidosalasmagnitudesde
la Tierra,son,respectivamente:0,107, 0,532 y 1,524. Calcule:
a) la duraciónde un año marciano(periodode rotaciónalrededordel Sol);(1punto)
b) el valorde la gravedady lavelocidadde escape enlasuperficiede Marte enrelaciónconlas de la Tierra.
(1 punto)
50. (104-S11) a) Dibuje unesquemade laslíneasde campoy las superficiesequipotencialesasociadasal campo
gravitatoriocreadoporla Tierra.(1 punto)
b) ¿Qué relaciónexisteentre el potencial gravitatorioylaenergíapotencial gravitatoria?¿Qué relación
existe entre el campoyel potencial gravitatorio?(1punto)
51. (129-J13) a) Definacon precisiónlossiguientesconceptosrelacionadosconel campogravitatorio:
velocidadde escape;líneasdel campogravitatorio;potencialgravitatorio;superficiesequipotenciales;
energíade enlace. (1,5 puntos)
b) ¿Puedencortarse laslíneasde campogravitatorio?Razone larespuesta. (0,5puntos)
52. (149-J14) En el caso del campo gravitatoriocreadoporun planeta:
a) Demuestre que lavelocidadde escape de uncuerpoesindependiente de sumasa. (1punto)
b) Demuestre que parauncuerpoen órbitacircularla Ecinética = ½ |Epotencial|. (1 punto)
7. I.E.S. “JULIÁN MARÍAS”- VALLADOLID DEPARTAMENTO DE FÍSICA Y QUÍMICA
PAU CASTILLA Y LEON 2007-19 JUNIOY SEPTIEMBRE CAMPOGRAVITATORIO
Página7
53. (189-J16) a) ¿A qué se llamavelocidadde escape?¿Cómose calcula?(1punto)
b) Mediante observacionesastronómicasse hadescubierto recientemente unplanetaextrasolar(Gliese
581b) orbitandoentornoa una estrellade laclase de lasenanasrojas.La órbitaescircular,tiene unradio
de 6,076 millonesde kilómetrosyunperiodode rotaciónorbital de 5,368 días. Determine lamasade la
estrella.(1punto).
S: 2,86·1052
kg (enorme, es una Estrella)
54. (194-J16) La Lunase mueve alrededorde laTierradescribiendounaórbitacircularde radio3,84·108
m y
periodo27,32 días. a) Calcule lavelocidadylaaceleraciónde laLuna respectoa laTierra y realice un
esquemade latrayectoriaenel que se muestrenambosvectores.(1punto)
b) Si desde lasuperficieterrestrese lanzaunobjetoverticalmenteconunavelocidadinicial igual alamitad
de su velocidadde escape, ¿qué alturamáximaalcanzarásintenerencuentael efectode laatmósfera?(1
punto)
55. (199-S16) El radiodel planetaMarte mide 3400 km y laaceleraciónde lagravedadensu superficie es g0 =
3,7 m s-2
.a) Determine lamasadel planetayla velocidadde escape desdelasuperficie. (1punto)
b) ¿A qué altura desde lasuperficiedeberásituarse unsatélite paraque recorrauna órbitacircular enun
día marciano de 24,6 horas? (1 punto)
S: 6,41·1013
kg, 5,02·103
m/s; 1,7·107
m