A221 HW #5

Handed out: September 30, 2009
Due (in class): October 14, 2009

The rules: Collaborative work is encouraged. This homework can be done in consultation with your fellow classmates, the AI, or the professor. However, everyone must submit their own solutions to get credit, and all help should be acknowledged (a single sentence mentioning the others in your study group is sufficient). Show your work.

1. Just the facts [5 pts]

(a) [2 pts] Craters on the moon are primarily due to _____________.
(b) [3 pts] Order the following in terms of increasing height above the Earth's surface: Ozone Layer, Mesosphere, Troposhere, Stratopause, Thermosphere, and Mesopause.

2. Going Ballistic [26 pts]

(a) [6 pts] What is the escape speed from the surface of (i) the Moon; (ii) Jupiter, and (iii) the Sun?

(b) [5 pts] A stone is released from rest at the Moon's orbit and falls towards Earth. What is the stone's speed when it is 192,000 km from the center of Earth?

(c) [5 pts] Calculate the energy required to move a satellite of mass m from a circular orbit of radius 2 R_e to one of radius 3 R_e.

(d) [5 pts] Calculate the escape velocity from the Earth for a 5000 kg space craft and determine the kinetic energy it must have at the Earth's surface.

(e) [5 pts] Cape Canaveral is at longitude 80^o23' W and latitude 28^o30' N. A rocket is launched from there due south, and it lands on the equator 10 min later. What is the longitude of impact?

3. Lunacy [19 pts]

(a) [6 pts] (i) At what distance between the Earth and the Moon will an Apollo spaceship experience no net gravitational acceleration? (ii) How long will it take the ship to circumnavigate the Moon in a circular orbit 50 km above the lunar surface?

(b) [5 pts] If the moon had a core of radius R_m/10 and the remainder of its interior had a uniform density of 3000 kg/m³, what must be the uniform density of this core?

(c) [4 pts] Compare the Earth's tidal forces on the Moon at the perigee and apogee of the Moon's orbit. Comment on your results.

(d) [4 pts] The main constituent of the Moon's atmosphere is neon. What would be the lifetime of neon gas on the Moon's surface [mass of Neon = 20.2 amu]? Assume typical daytime temperatures for the Moon. Hint: if v_esc/v_rms = 1, the lifetime is a few years; for 4, several thousand years; for 5, a few hundred million years; for > 10, several billion years.