Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 11, Problem 24P
To determine
To show: The orbital speed
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A "treetop satellite" moves in a circular orbit just above the surface of a planet, assumed to offer no air resistance. Show that its orbital speed v and the escape speed from the planet are related by
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(a) What is the escape speed on a spherical asteroid whose radius is 274 km and whose gravitational acceleration at the surface is 0.444 m/s2? (b) How far from the surface will a particle go if it leaves the asteroid's surface with a radial speed of 311 m/s? (c) With what speed will an object hit the asteroid if it is dropped from 289.4 km above the surface?
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Chapter 11 Solutions
Principles of Physics: A Calculus-Based Text
Ch. 11.1 - A planet has two moons of equal mass. Moon 1 is in...Ch. 11.3 - An asteroid is in a highly eccentric elliptical...Ch. 11.4 - Prob. 11.3QQCh. 11.5 - Prob. 11.4QQCh. 11 - Prob. 1OQCh. 11 - The gravitational force exerted on an astronaut on...Ch. 11 - Prob. 3OQCh. 11 - Prob. 4OQCh. 11 - A system consists of five particles. How many...Ch. 11 - Suppose the gravitational acceleration at the...
Ch. 11 - Prob. 7OQCh. 11 - Prob. 8OQCh. 11 - Prob. 9OQCh. 11 - Rank the following quantities of energy from...Ch. 11 - Prob. 11OQCh. 11 - Prob. 12OQCh. 11 - Prob. 13OQCh. 11 - Prob. 14OQCh. 11 - Prob. 1CQCh. 11 - Prob. 2CQCh. 11 - Prob. 3CQCh. 11 - Prob. 4CQCh. 11 - Prob. 5CQCh. 11 - Prob. 6CQCh. 11 - Prob. 7CQCh. 11 - Prob. 8CQCh. 11 - In his 1798 experiment, Cavendish was said to have...Ch. 11 - Prob. 1PCh. 11 - Prob. 2PCh. 11 - A 200-kg object and a 500-kg object are separated...Ch. 11 - Prob. 4PCh. 11 - Prob. 5PCh. 11 - Prob. 6PCh. 11 - Prob. 7PCh. 11 - Prob. 8PCh. 11 - Prob. 9PCh. 11 - Prob. 10PCh. 11 - A spacecraft in the shape of a long cylinder has a...Ch. 11 - (a) Compute the vector gravitational field at a...Ch. 11 - Prob. 13PCh. 11 - Two planets X and Y travel counterclockwise in...Ch. 11 - Prob. 15PCh. 11 - Prob. 16PCh. 11 - Prob. 17PCh. 11 - Prob. 18PCh. 11 - Plasketts binary system consists of two stars that...Ch. 11 - As thermonuclear fusion proceeds in its core, the...Ch. 11 - Comet Halley (Fig. P11.21) approaches the Sun to...Ch. 11 - Prob. 22PCh. 11 - Prob. 23PCh. 11 - Prob. 24PCh. 11 - Prob. 25PCh. 11 - A space probe is fired as a projectile from the...Ch. 11 - Prob. 27PCh. 11 - Prob. 28PCh. 11 - Prob. 29PCh. 11 - Prob. 30PCh. 11 - Prob. 31PCh. 11 - Prob. 32PCh. 11 - Prob. 33PCh. 11 - Prob. 34PCh. 11 - Prob. 35PCh. 11 - Prob. 36PCh. 11 - Prob. 37PCh. 11 - Prob. 38PCh. 11 - Prob. 39PCh. 11 - Prob. 40PCh. 11 - Prob. 41PCh. 11 - Prob. 42PCh. 11 - Prob. 43PCh. 11 - Prob. 44PCh. 11 - Prob. 45PCh. 11 - Prob. 46PCh. 11 - Let gM represent the difference in the...Ch. 11 - Prob. 48PCh. 11 - Prob. 49PCh. 11 - Two stars of masses M and m, separated by a...Ch. 11 - Prob. 51PCh. 11 - Prob. 52PCh. 11 - Prob. 53PCh. 11 - Prob. 54PCh. 11 - Prob. 55PCh. 11 - Prob. 56PCh. 11 - Prob. 57PCh. 11 - Prob. 58PCh. 11 - Prob. 59PCh. 11 - Prob. 60PCh. 11 - Prob. 61PCh. 11 - Prob. 62PCh. 11 - Prob. 63PCh. 11 - Prob. 64PCh. 11 - Prob. 65P
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- Find the escape speed of a projectile from the surface of Jupiter.arrow_forwardIf a spacecraft is headed for the outer solar system, it may require several gravitational slingshots with planets in the inner solar system. If a spacecraft undergoes a head-on slingshot with Venus as in Example 11.6, find the spacecrafts change in speed vS. Hint: Venuss orbital period is 1.94 107 s, and its average distance from the Sun is 1.08 1011 m.arrow_forwardUsing the technique shown in Satellite Orbits and Energy, show that two masses m1 and m2 in circular orbits about their common center of mass, will have total energy E=K+E=K1+K2Gm1m2r=Gm1m22r . We have shown the kinetic energy of both masses explicitly. (Hint: The masses orbit at radii r1 and r2 , respectively, where r=r1+r2 . Be sure not to confuse the radius needed for centripetal acceleration with that for the gravitational force.)arrow_forward
- What is the orbital radius of an Earth satellite having a period of 1.00 h? (b) What is unreasonable about this result?arrow_forwardIt was stated that a satellite with negative total energy is in a bound orbit, whereas one with zero or positive total energy is in an unbounded orbit. Why zero or positive total energy is in an unbounded orbit. Why is this true? What choice for gravitational potential energy was made such that this is true?arrow_forwardShow that the areal velocity for a circular orbit of radius r about a mass M is At=12GMr . Does your expression give the correct value for Earth’s areal vilocity about the Sun?arrow_forward
- Find the escape speed of a projectile from the surface of Mars.arrow_forwardGiven the perihelion distance, p , and aphelion distance, q , for an elliptical orbit, show that the velocity at perihelion, vp , is given by vp=2GMSun(q+p)qp . (Hint: Use conservation of angular momentum to relate vp and vq , and then substitute into the conservation fo energy equation.)arrow_forwardSuppose the gravitational acceleration at the surface of a certain moon A of Jupiter is 2 m/s2. Moon B has twice the mass and twice the radius of moon A. What is the gravitational acceleration at its surface? Neglect the gravitational acceleration due to Jupiter, (a) 8 m/s2 (b) 4 m/s2 (c) 2 m/s2 (d) 1 m/s2 (e) 0.5 m/s2arrow_forward
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