Explorations: Introduction to Astronomy (Arny), 6th Edition

Chapter 3: Gravity and Motion

Problems

1
How many times greater is the Earth's gravitational force on the Moon than the Moon's gravitational force on the Earth? Think about Newton's third law of motion before answering this.
2
Calculate the escape velocity from the Earth, given that the mass of the Earth is 6 x 1024 kilograms and its radius 6 x 106 meters. In this problem, round off G to 7 x 10-11 meters3/(-s-2kg-1).
3
Calculate the escape velocity from the Sun, given that its mass is 7 x 1030 kg and its radius is 7 x 108 meters.
4
Which body has a larger escape velocity, Mars or Saturn? M Mars = 0.1 M Earth M Saturn = 95 M Earth R Mars = 0.5 R Earth R Saturn = 9.4 R Earth
5
Calculate the ratio of the escape velocities from the Moon and Earth.
6
Calculate your weight on the Moon.
7
Given that Jupiter is about 5 times farther from the Sun than the Earth, calculate its orbital velocity. How many years does it take Jupiter to complete an orbit around the Sun?
8
Given that the mass of the Milky Way galaxy is 1011 times that of the Sun and that the Sun is 2.6 x 1020 meters from its center, what is the Sun's orbital speed around the center of the galaxy? How long does it take the Sun to orbit the Milky Way? (In this problem, we assume that the galaxy can be treated as a single spherical blob of matter. Strictly speaking, this isn't correct, but the far more elaborate math needed to calculate the problem properly ends up giving almost the same answer.)
9
A good baseball pitcher can throw a ball at 100 miles/hr (about 45 meters/s). If the pitcher were on the fictional asteroid Cochise, could the pitcher throw the ball fast enough so it would escape from Cochise? (Note: Assume Cochise is a sphere and that its mass is M = 9.6 x 1016 kg and its radius is 20 km = 2.0 x 104 meters.)
10
Use the modified form of Kepler's third law to find the mass of the imaginary star 57 Fungaloid, given that a planet is in a circular orbit around it at a distance of 3 x 1011 meters with an orbital period of 3 years. Divide your answer by the Sun's mass to see how much more (less) massive the star is than our Sun.
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