Chapter 32, The Structure of the Solar System Video Solutions, Pathways to Astronomy

Problem 1

In Appendix Tables 5 and $6,$ look up the sizes and distances from the Sun of Jupiter, Neptune, Earth, Mercury, Pluto, and Ceres. Imagine the Sun is scaled down to the size of a large beach ball, 1 meter in diameter.
a. What diameter would these six objects have if scaled down by the same factor?
b. What would their masses be if their density remained the same?

Joseph Petrullo

Numerade Educator

02:50

Problem 2

What would be the distance from the Sun for each of the bodies listed in problem 1 , scaled down by the same factor that would make the Sun 1 meter in diameter?

Teresa Fuston

Numerade Educator

01:59

Problem 3

To arrive at the average density of Mercury $(\rho=5.43 \mathrm{kg} / \mathrm{L}),$ we could imagine different combinations of materials than given in the text. What would be the problems with the following models?
a. A rocky interior $(\rho \approx 3 \mathrm{kg} / \mathrm{L})$ surrounded by an iron crust $(\rho \approx 8 \mathrm{kg} / \mathrm{L}) ?$
b. An iron interior surrounded by a thick layer of ice $(\rho \approx 1 \mathrm{kg} / \mathrm{L}) ?$

Narayan Hari

Numerade Educator

07:27

Problem 4

Calculate the densities of Venus and Jupiter from the following data: The mass and radius of Venus are $4.87 \times 10^{24}$ kilograms and 6051 kilometers, respectively. The mass and radius of Jupiter are about $1.9 \times 10^{27}$ kilograms and 71,492 kilometers, respectively. How do these numbers compare with the density of rock (about $3 \mathrm{kg} / \mathrm{L}$ ) and water $(1 \mathrm{kg} / \mathrm{L}) ?$

Ronald Prasad

Numerade Educator

02:55

Problem 5

Use the data in Appendix Table $5,^{*}$ Physical Properties of the Planets," to list the planets in order according to several different parameters:
a. smallest to largest radius.
b. smallest to largest mass.
c. most to least dense. Note that the order of some planets is changed in each case. Can you draw any approximate conclusions from these results? For example, are smaller planets always more dense? What other factors might explain why some planets are out of order with the overall trends you find?

Joseph Petrullo

Numerade Educator

07:15

Problem 6

You can calculate the acceleration due to gravity at the surface of a planet using the formula from Unit $16.3: g=^{G M} / R^{2}$ where $M$ and $R$ are the mass and radius of the planet, and $G$ is the gravitational constant (see Appendix Table 1). How much do you weigh on Earth? Determine how much you would weigh on Jupiter, Mars, and Ceres. (Hint: Because your mass would not change, you can simply compare the values of $g$ for the other planets with that of Earth, $9.8 \mathrm{m} / \mathrm{sec}^{2} .$)

Dading Chen

Numerade Educator