Physics Principle and Problems

Paul W. Zitzewitz, Todd George Elliott, David G. Haase

Chapter 7

Gravitation - all with Video Answers

Educators

Section 1

Planetary Motion and Gravitation

Problem 1

If Ganymede, one of Jupiter's moons, has a period of 32 days, how many units are there in its orbital radius? Use the information given in Example Problem 1.

Sean Dougherty

Sean Dougherty

Numerade Educator

Problem 2

An asteroid revolves around the Sun with a mean orbital radius twice that of Earth's. Predict the period of the asteroid in Earth years.

Sean Dougherty

Numerade Educator

Problem 3

From Table $7-1,$ on page $173,$ you can find that, on average, Mars is 1.52 times as far from the Sun as Earth is. Predict the time required for Mars to orbit the Sun in Earth days.

Sean Dougherty

Numerade Educator

Problem 4

The Moon has a period of 273 days and a mean distance of $3.90 \times 10^{5} \mathrm{km}$ from the center of Earth.
a. Use Kepler's laws to find the period of a satellite in orbit $6.70 \times 10^{3} \mathrm{km}$ from the center of Earth.
b. How far above Earth's surface is this satellite?

Sean Dougherty

Numerade Educator

Problem 5

Using the data in the previous problem for the period and radius of revolution of the Moon, predict what the mean distance from Earth's center would be for an artificial satellite that has a period of exactly 1.00 day.

Sean Dougherty

Numerade Educator

Problem 6

Neptune's Orbital Period Neptune orbits the Sun with an orbital radius of $4.495 \times 10^{12} \mathrm{m},$ which
allows gases, such as methane, to condense and form an atmosphere, as shown in Figure $7-8$ If the mass of the Sun is $1.99 \times 10^{30} \mathrm{kg},$ calculate the period of Neptune's orbit.

Sean Dougherty

Numerade Educator

Problem 7

Gravity If Earth began to shrink, but its mass remained the same, what would happen to the value of $g$ on Earth's surface?

Sean Dougherty

Numerade Educator

Problem 8

Gravitational Force What is the gravitational force between two 15 -kg packages that are $35 \mathrm{cm}$ apart? What fraction is this of the weight of one package?

Sean Dougherty

Numerade Educator

Problem 9

Universal Gravitational Constant Cavendish did his experiment using lead spheres. Suppose he had replaced the lead spheres with copper spheres of equal mass. Would his value of $G$ be the same or different? Explain.

Sean Dougherty

Numerade Educator

Problem 10

Laws or Theories? Kepler's three statements and Newton's equation for gravitational attraction are called "laws." Were they ever theories? Will they ever become theories?

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Numerade Educator

Problem 11

Critical Thinking Picking up a rock requires less effort on the Moon than on Earth.
a. How will the weaker gravitational force on the Moon's surface affect the path of the rock if it is thrown horizontally?
b. If the thrower accidentally drops the rock on her toe, will it hurt more or less than it would on Earth? Explain.

Sean Dougherty

Numerade Educator