Physics, Books a la Carte Edition (5th Edition)
5th Edition
ISBN: 9780134020853
Author: James S. Walker
Publisher: PEARSON
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Chapter 12, Problem 56PCE
To determine
The radius of sun for escape speed equal to the speed of light .
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Consider the process of escaping from the solar system starting from the surface of Earth. Assume there are no other bodies involved. Earth has an orbital speed about the Sun of 29.8 km/s. Hint:
2GM
does not apply. Use mv,?
GM_m GM m
2
GM-m
GMs" which includes the potential energy of both Earth and the Sun.
2.5
V.
esc
2,E
(a) What minimum speed relative to Earth (in km/s) would be needed?
km/s
In what direction should you leave Earth?
O opposite the direction of Earth's orbital velocity
O towards the Sun
O away from the Sun
O in the direction of Earth's orbital velocity
(b) What will be the shape of the trajectory?
O a circle
O an ellipse
O a hyperbola
O a parabola
A space probe of mass 3.9 x 103 kg is orbiting a star of mass 3.6 x 1030 kg in a circular orbit at a distance of 1.7 x 1011 m from its center. Calculate the minimum energy, in units of 109 J, required to transfer the probe to a circular orbit 5.5 x 1011 m from the star. Use G = 6.7 x 10-11 N m2/ kg2.
(Please answer to the fourth decimal place - i.e 14.3225)
The escape velocity from a massive object is the speed needed to reach an infinite distance from it and have just slowed to a stop, that is, to have just enough kinetic energy to climb out of the gravitational potential well and have none left. You can find the escape velocity by equating the total kinetic and gravitational potential energy to zero
E=12mv2esc−GmM/r=0E=12mvesc2−GmM/r=0
vesc=2GM/r−−−−−−√vesc=2GM/r
where GG is Newton's constant of gravitation, MM is the mass of the object from which the escape is happening, and rr is its radius. This is physics you have seen in the first part of the course, and you should be able to use it to find an escape velocity from any planet or satellite. For the Earth, for example the escape velocity is about 11.2 km/s, and for the Moon it is 2.38 km/s. A very important point about escape velocity: it does not depend on what is escaping. A spaceship or a molecule must have this velocity or more away from the center of the planet to be free…
Chapter 12 Solutions
Physics, Books a la Carte Edition (5th Edition)
Ch. 12.1 - Rank the four systems shown in Figure 12-6 in...Ch. 12.2 - Suppose the Sun suddenly collapsed to half its...Ch. 12.3 - Satellite A orbits the Earth at the radius r,...Ch. 12.4 - Prob. 4EYUCh. 12.5 - Prob. 5EYUCh. 12.6 - If the radius of the Moons orbit around the Earth...Ch. 12 - It is often said that astronauts in orbit...Ch. 12 - When a person passes you on the street, you do not...Ch. 12 - Imagine bringing the tips of your index fingers...Ch. 12 - Does the radius vector of Mars sweep out the same...
Ch. 12 - When a communications satellite is placed in a...Ch. 12 - The Mass of Pluto On June 22, 1978, James Christy...Ch. 12 - Rockets are launched into space from Cape...Ch. 12 - One day in the future you may take a pleasure...Ch. 12 - Apollo astronauts orbiting the Moon at low...Ch. 12 - Prob. 10CQCh. 12 - The force exerted by the Sun on the Moon is more...Ch. 12 - Prob. 12CQCh. 12 - System A has masses m and m separated by a...Ch. 12 - A 6.3-kg bowling ball and a 7.1-kg bowling ball...Ch. 12 - A communications satellite with a mass of 520 kg...Ch. 12 - The Attraction of Ceres Ceres, the largest...Ch. 12 - In one hand you hold a 0.13-kg apple, in the other...Ch. 12 - Predict/Calculate A spaceship of mass m travels...Ch. 12 - At new moon, the Earth, Moon, and Sun are in a...Ch. 12 - When the Earth, Moon, and Sun form a right...Ch. 12 - Repeat the previous problem, this time finding the...Ch. 12 - Predict/Calculate Three 7.25-kg masses are at the...Ch. 12 - Predict/Calculate Four masses are positioned at...Ch. 12 - Suppose that three astronomical objects (1, 2, and...Ch. 12 - Find the acceleration due to gravity on the...Ch. 12 - At what altitude above the Earths surface is the...Ch. 12 - Two 6.4-kg bowling balls, each with a radius of...Ch. 12 - What is the acceleration due to Earths gravity at...Ch. 12 - Extrasolar Planet Gravity Kepler-62e is an...Ch. 12 - Predict/Calculate At a certain distance from the...Ch. 12 - The acceleration due to gravity on the Moons...Ch. 12 - Gravitational Tug of War At some point along the...Ch. 12 - Predict/Calculate An Extraterrestrial Volcano...Ch. 12 - Consider an asteroid with a radius of 19 km and a...Ch. 12 - Prob. 23PCECh. 12 - Predict/Explain The Earth-Moon Distance Is...Ch. 12 - Apollo Missions On Apollo missions to the Moon,...Ch. 12 - Prob. 26PCECh. 12 - An Extrasolar Planet In July of 1999 a planet was...Ch. 12 - Phobos, one of the moons of Mars, orbits at a...Ch. 12 - Predict/Calculate An Asteroid with Its Own Moon...Ch. 12 - GPS Satellites GPS (Global Positioning System)...Ch. 12 - Predict/Calculate Two satellites orbit the Earth,...Ch. 12 - Predict/Calculate Satellite A has a mass of 1000...Ch. 12 - Predict/Calculate The Martian moon Deimos has an...Ch. 12 - Predict/Calculate (a) Calculate the orbital period...Ch. 12 - Binary Stars Alpha Centauri A and Alpha Centauri B...Ch. 12 - Prob. 36PCECh. 12 - How much gravitational potential energy is...Ch. 12 - Predict/Explain (a) Is the amount of energy...Ch. 12 - Prob. 39PCECh. 12 - Calculate the gravitational potential energy of a...Ch. 12 - Prob. 41PCECh. 12 - Two 0.59-kg basketballs, each with a radius of 12...Ch. 12 - Find the minimum kinetic energy needed for a...Ch. 12 - Predict/Explain Suppose the Earth were to suddenly...Ch. 12 - Prob. 45PCECh. 12 - Prob. 46PCECh. 12 - Meteorites from Mars Several meteorites found in...Ch. 12 - What is the launch speed of a projectile that...Ch. 12 - A projectile launched vertically from the surface...Ch. 12 - Prob. 50PCECh. 12 - Predict/Calculate Halleys Comet Halleys comet,...Ch. 12 - The End of the Lunar Module On Apollo Moon...Ch. 12 - Prob. 53PCECh. 12 - Prob. 54PCECh. 12 - A projectile is launched vertically from the...Ch. 12 - Prob. 56PCECh. 12 - Predict/Calculate Two baseballs, each with a mass...Ch. 12 - On Earth, a person can jump vertically and rise to...Ch. 12 - The magnitude of the tidal force exerted on a...Ch. 12 - The magnitude of the tidal force between the...Ch. 12 - A dumbbell has a mass m on either end of a rod of...Ch. 12 - Prob. 62PCECh. 12 - CE You weigh yourself on a scale inside an...Ch. 12 - Figure 12-37 Problems 64 and 65 64. CE Rank...Ch. 12 - CE Referring to Figure 12-37, rank objects A, B,...Ch. 12 - CE The Crash of Skylab Skylab, the largest...Ch. 12 - Consider a system consisting of three masses on...Ch. 12 - An astronaut exploring a distant solar system...Ch. 12 - Predict/Calculate When the Moon is in its...Ch. 12 - Prob. 70GPCh. 12 - Suppose that each of the three masses in Figure...Ch. 12 - A Near Miss! In the early morning hours of June...Ch. 12 - Predict/Calculate Suppose a planet is discovered...Ch. 12 - Prob. 74GPCh. 12 - Walking into Orbit A spherical asteroid of average...Ch. 12 - Prob. 76GPCh. 12 - Find the orbital period of the binary star system...Ch. 12 - Exploring Mars In the not-too-distant future...Ch. 12 - Comet Wild 2 In 2004, a NASA spacecraft named...Ch. 12 - Predict/Calculate (a) If you want to launch a...Ch. 12 - Predict/Calculate A satellite is placed in Earth...Ch. 12 - Show that the force of gravity between the Moon...Ch. 12 - The astronomical unit AU is defined as the mean...Ch. 12 - Prob. 84GPCh. 12 - Predict/Calculate Space Station Orbit The...Ch. 12 - Approaching the ISS A Russian Soyuz module, with...Ch. 12 - Prob. 87GPCh. 12 - Prob. 88GPCh. 12 - Three identical stars, at the vertices of an...Ch. 12 - Prob. 90GPCh. 12 - If life exists elsewhere in our solar system, it...Ch. 12 - If life exists elsewhere in our solar system, it...Ch. 12 - If life exists elsewhere in our solar system, it...Ch. 12 - If life exists elsewhere in our solar system, it...Ch. 12 - If life exists elsewhere in our solar system, it...Ch. 12 - Predict/Calculate Referring to Example 12-8...Ch. 12 - Predict/Calculate Referring to Example 12-17 (a)...Ch. 12 - Predict/Calculate Referring to Example 12-17...
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