Essential Cosmic Perspective
9th Edition
ISBN: 9780135795033
Author: Bennett
Publisher: PEARSON
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Chapter 4, Problem 12EAP
Explain why orbits cannot change spontaneously, and how a gravitational encounter can cause a change. How can an object achieve escape velocity?
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a. What is a repeat ground-track orbit?
b. Explain why repeat ground-track and Sun-synchronous orbits are typically used for Earth observation missions.
=
c. The constraint for a Sun-synchronous and repeat ground-track orbit is given by T 86, 400, where T is the orbital period in seconds, m the
number of days and k the number of revolutions. Explain why this is, in fact, a constraint on the semi-major axis of the orbit.
m
25. A rocket is launched from the surface of a planet with mass M and radius R. What is the minimum velocity the
rocket must be given to completely escape from the planet’s gravitational field?
A. (2GM/R)1/2
B. (2GM/R)3
C. (GM/R)1/2
D. 2GM/R
2. The simplest way to increase the size of a circular orbit is method called a Hohmann
Transfer (transfers the satellite from a small circular orbit to a larger one). It involves
firing thrusters to create a change in velocity to get the satellite into a transfer orbit
(elliptical), then later firing the thrusters again for another change in velocity to increase
the size of the orbit (back to circular). Diagram:
b
Avb
Transfer
Initial
Final
Ava
a
Let us
say we have the satellite from the previous problem in a circular orbit. We want to
increase the altitude of the circular orbit from 418 km to 1000 km. (a) Find the change in
velocity necessary to go into the transfer orbit, Ava. (b) Find the change in velocity
necessary to go into the final circular orbit, Av. (c) How long will the transfer take?
Constants needed:
=
G = 6.674 × 10-11 Nm²
²/kg²
Re = 6.378 x 106m
Mo
5.974 x 1024 kg
Chapter 4 Solutions
Essential Cosmic Perspective
Ch. 4 - Prob. 1VSCCh. 4 - Check your understanding of some of the many types...Ch. 4 - Check your understanding of some of the many types...Ch. 4 - Check your understanding of some of the many types...Ch. 4 - Check your understanding of some of the many types...Ch. 4 - Define speed, velocity, and acceleration. What are...Ch. 4 - Define momentum and force. What do we mean when we...Ch. 4 - What is free-fall, and why does it make you...Ch. 4 - Prob. 4EAPCh. 4 - Prob. 5EAP
Ch. 4 - Define kinetic energy, radiative energy, and...Ch. 4 - Define and distinguish temperature and thermal...Ch. 4 - Prob. 8EAPCh. 4 - Summarize the universal law of gravitation both in...Ch. 4 - What is the difference between a bound and an...Ch. 4 - Under what conditions can we use Newton’s version...Ch. 4 - Explain why orbits cannot change spontaneously,...Ch. 4 - Explain how the Moon creates tides on Earth. Why...Ch. 4 - How do the tides vary with the phase of the Moon?...Ch. 4 - Decide whether the statement makes sense (or is...Ch. 4 - Decide whether the statement makes sense (or is...Ch. 4 - Decide whether the statement makes sense (or is...Ch. 4 - Decide whether the statement makes sense (or is...Ch. 4 - Decide whether the statement makes sense (or is...Ch. 4 - Decide whether the statement makes sense (or is...Ch. 4 - Decide whether the statement makes sense (or is...Ch. 4 - Decide whether the statement makes sense (or is...Ch. 4 - Decide whether the statement makes sense (or is...Ch. 4 - Decide whether the statement makes sense (or is...Ch. 4 - A car is accelerating when it is (a) traveling on...Ch. 4 - Compared to their values on Earth, on another...Ch. 4 - Which person is weightless? (a) a child in the air...Ch. 4 - Consider the statement “There’s no gravity in...Ch. 4 - To make a rocket turn left, you need to (a) fire...Ch. 4 - Compared to its angular momentum when it is...Ch. 4 - Prob. 31EAPCh. 4 - If Earth were twice as far from the Sun, the force...Ch. 4 - According to the law of universal gravitation,...Ch. 4 - If the Moon were closer to Earth, high tides would...Ch. 4 - Prob. 35EAPCh. 4 - Testing Gravity. Scientists are constantly trying...Ch. 4 - How Does the Table Know? Thinking deeply about...Ch. 4 - Perpetual Motion Machines. Every so often, someone...Ch. 4 - Group Activity: Your Ultimate Energy Source. Work...Ch. 4 - Weightlessness. Astronauts are weightless when in...Ch. 4 - Einstein’s Famous Formula. a. What is the meaning...Ch. 4 - The Gravitational Law. a. How does quadrupling the...Ch. 4 - Prob. 44EAPCh. 4 - Head to Foot Tides. You and Earth attract each...Ch. 4 - Space Elevator. Some people have proposed using a...Ch. 4 - Prob. 47EAPCh. 4 - Prob. 48EAPCh. 4 - Prob. 49EAPCh. 4 - Prob. 50EAP
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