Remember to show all of your work for every problem, and to write your final answers in complete English sentences.
Problem 1:
a) Look up the mass of the Moon and the radius of the Moon in the book, and compute the density of the Moon, in gm/cm^{3}.
b) Based on that average density, would you say the moon is made mostly of ice (density = 0.9 gm/cm^{3}), rock (density = 3.0 gm/cm^{3}), or iron (density = 9.0 gm/cm^{3})?
Problem 1 is a straightforward application of the Density formula. Example 1 on the density handout is especially relevant. Do for the Moon what Example 1 does for the Earth!Confirm your answer by looking up the density of the Moon in the text.
Problem 2:In late August of 2003, Mars was at its closest point to Earth in about 60,000 years! This was due to the coincidence that Mars and Earth lined up with the Sun when the Earth was close to its farthest point from the Sun (called aphelion) and Mars was close to its closest approach to the Sun (called perihelion).
a) When Mars is at perihelion and Earth is at aphelion, how far apart are the two planets, in kilometers? How many miles is that, if there are approximately 1.6 kilometers in a mile?
b) What is the angular diameter of Mars when the Earth and Mars are separated by this distance, in seconds of arc? This is about how large Mars appeared to be in August 2003.
c) Mars is about 200 million kilometers from Earth on average. What is the average angular diameter of Mars? How many times smaller is this than the August 2003 figure?
You can find the perihelion and aphelion distances for Mars and Earth, as well as the actual diameter of Mars, in the chapters devoted to those planets. This problem uses the Angular Size formula. Remember to be careful about units, and don’t confuse radius and diameter!
3. a) Jupiter is about 5 times farther from the Sun than the Earth is, and has about 300 times the mass of the Earth. Compare the gravitational force between Jupiter and the Sun to the gravitational force between the Earth and the Sun.b) Perform the same computation for Saturn which is 10 times farther away from the Sun than Earth, and 100 times more massive than the Earth.
Warning! If you have to look up the values for G, the mass of the Earth, etc., you’re making it unduly hard on yourself… Refer to the gravity handout for a model!You should not need to look up anything for this problem! All that you need is in the problem and the gravity handout! To avoid having to know numbers such as big G, the mass of the Earth, and so on, use the “comparison by dividing” technique illustrated in the gravity handout. If you don’t understand that technique, PLEASE come see me!
Essentially, for part a, you must construct two separate gravity equations, one for the Earth and Sun, and another for Jupiter and the Sun. Compare the two forces by dividing one equation by the other. Some things should drop out! Remember to substitute and eliminate as much as you can before you make a single calculation!
