Explorations: An Introduction to Astronomy (Arny), 7th Edition

Chapter 3: Gravity and Motion

Problems

1
If you apply a force F to a mass m, it results in an acceleration a. What acceleration would result if you applied a force of (a) 2F to m, (b) 2F to 2m, (c) 10F to m, and (d) 10F to 3m?
2
You are working at the hockey rink, and your resurfacing machine breaks down in the middle of the ice. Assuming you can get it moving, how much force will you need to apply to accelerate it to 2 m/sec in 25 seconds if it has a mass of 2500 kg?
3
Calculate your weight on the Moon.
4
Given that Neptune is about 30 times farther from the Sun than the Earth, calculate its orbital speed if the mass of the Sun is 2 × 1030 kg. How many years does it take Neptune to complete one orbit?
5
Assuming that the mass of the Milky Way Galaxy is 1011 times that of the Sun and that the Sun is 2.6×1020 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 body. Strictly speaking, this isn't correct, but the more elaborate math needed to calculate the problem properly ends up giving almost the same answer.)
6
Gliese 581e is an exoplanet with a mass of 1.9 Earths that orbits a red dwarf star at a distance of 5 × 1010 m (0.33 AU). If its orbital period is 124 days, find the mass of the star in kg. Divide your answer by the Sun's mass to see how much more or less massive the star is than our Sun.
7
Using the method of section 3.7, compare the surface gravity of the Earth with the surface gravities of Jupiter and Pluto.
8
Calculate the escape velocity from the Earth, given that the mass of the Earth is 6×1024 kilograms and its radius 6×106 meters. In this problem, round off G to 7×10-11 meters3/(kg.sec2).
9
Convert the escape velocity of Earth (problem 8) into miles per hour.
10
Calculate the escape velocity from the Sun, given that its mass is 2×1030 kg and its radius is 7×108 meters.
11
Which body has a larger escape velocity, Mars or Saturn? Solve this problem using ratios in a way similar to the comparison of the Earth's and the Moon's gravity in section 3.7. Show your work. In the appendix you can find values for Mars's and Saturn's radii and masses in terms of Earth's.
12
Calculate the ratio of the escape velocities from the Moon and Earth.
13
A good baseball pitcher can throw a ball at 100 miles/hour (about 45 meters/sec). If the pitcher were on Sinope, one of Jupiter's smaller moons, could the pitcher throw the ball fast enough to escape Sinope's gravity? Sinope is roughly spherical with a radius of 18,000 m and a mass of 6 ×1016 kg.
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