1. Match the concept in planetary mechanics with the person (or group) who originated the idea:

A. heliocentric model of universe

B. Law of Universal Gravitation

C. geocentric model of universe

D. Concept that planets move about the
sun in elliptical orbits, with the sun at
one focus of the ellipse

_____ Galileo

_____Early Greeks

_____Brahe

_____Copernicus

_____Kepler

_____Newton

Answers: (A) Copernicus (B) Newton
(C) Early Greeks (D) Kepler

2. The planet Jupiter has a mass of 1.9 x 10^{27} kg and a radius of 7.2 x 10^{7} m. Calculate the
acceleration due to gravity on an object on the surface of Jupiter.

3. A 500 kg satellite is in circular orbit 200 km above the Earth's surface. Calculate:

(A) The gravitational potential energy of the satellite

(B) The kinetic energy of the satellite

(C) Its binding energy

Answers: (A) -3.03 E10 Joules (B) 1.52 E10 Joules (C) -1.52 E10 Joules

4. Imagine a diagram (since I don't have the actual graphic scanned) similar to **Figure 4,
page 288 text**, showing the paths of three objects launched from the Earth.

- initial kinetic energy needed
- changes in kinetic/potential energy as the satellite rises
- total energy
- binding energy
- escape velocity

5. The force of gravity between A and B is 100 N. When the mass of B is doubled and the distance between it and A is halved, what is the new force?

Answer: 800 N

6.A 500 kg communications satellite is to be placed in a synchronous orbit around the Earth. A synchronous orbit means that the satellite remains over the exactly the same place on Earth; it has a period of 24 hours.

(A) What is the radius of its circular orbit? Answer = 4.22 E7 m

(B) What is the gravitational potential energy of the satellite when it is still on the surface of the Earth? Answer = -3.12 E 10 J

(C) What is the total energy of the satellite when in synchronous orbit. (note: in this orbit, the satellite is still bound to the Earth.) Answer = -2.36 E 9 Joules

(D) How much work is needed to placed the satellite to place it in orbit? Answer = 2.36 E9 J

(E) Once in orbit, how much additional energy must the satellite must receive, in order to escape from th Earth's potential well? Answer = 2.36 E9 J

7. A planet's mean distance from the sun is 2.0 x 10

HINTS:

- See text, page 139, page 279 and notes taken in class
- Uses equation: Universal Law of Gravitation, p. 140
- See page 290 - 291 text
- See test page 288 and your classroom notes
- Uses Equation: Universal Law of Gravitation
- Same hint as for #3
- Uses Kepler's equation, page 279