Chapter 37, Our Moon Video Solutions, Pathways to Astronomy

Problem 1

Our ideas about how the Moon formed and how those ideas were gradually discarded are excellent examples of how science works: If a hypothesis is disproved it must be either modified or thrown out. Explain in terms of the origin of the Moon. What were the problems for the early hypotheses?

Kayla Day

Numerade Educator

01:03

Problem 2

Galileo was able to estimate the height of mountains on the Moon by measuring the length of their shadows. Make a drawing of a tall mountain sitting on a flat plane viewed from the side. With a protractor, draw a line with a $10^{\circ}$ angle to the plane that touches the mountain peak. This shows how long the shadow is when the Sun is $10^{\circ}$ above the horizon.
a. If a shadow is 5 kilometers long when the Sun is $10^{\circ}$ above the horizon, estimate how tall the mountain is.
b. Estimate at what angle the Sun must be above the horizon for the shadow to be twice as long as the height of the mountain.

Raj Bala

Numerade Educator

02:42

Problem 3

The Moon's density is $3.3 \mathrm{kg} / \mathrm{L}$. Suppose that the Moon is made of just two substances: silicates with a density of $3.0 \mathrm{kg} / \mathrm{L}$ and iron with a density of $7.9 \mathrm{kg} / \mathrm{L}$
a. What fraction of its mass must be iron?
b. What fraction of its volume must be iron?

Km Neeraj

Numerade Educator

13:29

Problem 4

The Moon is currently moving away from the Earth at about
$4 \mathrm{cm}$ per year.
a. At this rate, how many years would it have taken the Moon to move half the current distance between the two bodies?
b. Would the effects leading to this recession have been larger or smaller in the past? Why?

Mark Mathison

Numerade Educator

03:26

Problem 5

As the Moon moves away from the Earth, the radius of its orbit grows larger, although its orbital speed grows smaller. The angular momentum of the Moon is equal to the product of its mass and its orbital velocity and radius $(M \times V \times R)$ Is the Moon's orbital angular momentum growing larger or smaller? Use Newton's version of Kepler's third law (Unit 17 ) to determine the Moon's speed as a function of its orbital radius, and show whether the angular momentum is increasing or decreasing.

Mayukh Banik

Numerade Educator

04:15

Problem 6

Assume that the density of an average asteroid is $3.0 \mathrm{kg} / \mathrm{L}$, and that the craters on the Moon are roughly 20 times the size of the impacting body.
a. What was the diameter of the asteroid that created the $240-\mathrm{km}$ -diameter Clavius crater? Using the density of an average asteroid, calculate the mass of this asteroid.
b. Calculate the kinetic energy of this impact if the speed of the asteroid was $20 \mathrm{km} /$ sec relative to the Moon.

Amit Srivastava

Numerade Educator

02:03

Problem 7

The largest impact basin on the Moon is Aitken, near the lunar south pole. It is approximately 2500 kilometers in diameter. Repeat the calculations you made in problem $6 .$ Compare the kinetic energy of this asteroid to the kinetic energy of the Moon in its orbit around the Earth of $1.0 \mathrm{km} / \mathrm{sec}$. (The Moon's mass is $7.35 \times 10^{22} \mathrm{kg} .$ )

Satpal Satpal

Numerade Educator