SPH4U:   TEST OUTLINE: PLANETARY MECHANICS
• Simple outline of history of planetary discoveries (Early Greeks, Copernicus, Kepler, Galileo) in a "true'false, fill-in-blank or matching format

• Kepler's Three Laws (theory and simple calculation)

• Law of Universal Gravitation (calculations)

• Gravitational potential energy in general (including escape velocity, total energy, binding energy, extra energy needed to place an object as position "r" into sustained orbit...)

• SAMPLE QUESTIONS:
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 1027 kg and a radius of 7.2 x 107 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.

Discuss the differences between the flights of mass A (in a sustained orbit), mass B (bound to Earth but not on surface) and mass C (travelling in deep space)with respect to various planetary mechanics issues including those listed below. Also indicate what happens to the masses an the end of their flight.
• initial kinetic energy needed
• changes in kinetic/potential energy as the satellite rises
• total energy
• binding energy
• escape velocity
Answer:   see text page 288 and (for a better explanation) your classroom notes

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?

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 1011m.   What is its orbital period?   Answer = 4.9 E7 seconds

HINTS:

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