Self-Test: Gravitation Test #1
Suggested Time: 60 minutes

1. A satellite's orbit is maintained by a
 A. normal force. B. frictional force. C. centrifugal force. D. gravitational force.

2. A 1500 kg satellite is in a stable orbit at an altitude of 4.0 × 10 5 m above Earth's surface. What is the satellite's total energy in this orbit?
 A. -8.8 × 10 10 J B. -4.4 × 10 10 J C. 4.4 × 10 10 J D. 5.0 × 10 10 J

3. Which of the following graphs shows how the gravitational force varies with the distance of separation between two objects?

4. A 5.2 × 10 4 kg rocket is initially at rest on the surface of the earth. If 3.0 × 10 11 J of work is done on this rocket, what maximum altitude h will the rocket reach? (Assume the rocket's mass does not change.)

 A. 5.9× 10 5 m B. 6.5 × 10 5 m C. 5.8 × 10 6 m D. 6.9 × 10 7 m

5. A 450 kg piece of space debris initially at rest falls from an altitude of 6.2 × 10 5 m above the earth's surface. What is its kinetic energy just before impact with the surface? (Ignore air resistance.)

 A. 2.5 × 10 9 J B. 2.7 × 10 9 J C. 2.6 × 10 10 J D. 2.9 × 10 11 J

6. A planet is in orbit as shown in the diagram below.

The planet's gravitational potential energy will

A. be constant throughout its orbit.

B. always be equal to its kinetic energy.

C. increase as the planet goes from point R to point S.

D. decrease as the planet goes from point R to point S.

7. What is the magnitude of the centripetal acceleration of the moon as it orbits the earth?
 A. 2.7 × 10 -3 m/s2 B. 0.16 m/s2 C. 1.6 m/s2 D. 9.8 m/s2

8. A space station has an outer radius of 140 m. The station rotates so that the occupants at X at the outer wall experience an acceleration of 9.8 m/s2. What acceleration will the occupants at Y experience at the 100 m radius?

 A. 7.0 m/s2 B. 8.3 m/s2 C. 9.8 m/s2 D. 14 m/s2

9. A 9.0 × 10 3 kg satellite with an orbital radius of 3.20 × 10 7 m orbits the earth at an altitude of 2.56 × 10 7 m. What is the orbital period?
 A. 1.1× 10 4 s B. 4.1 × 10 4 s C. 5.7 × 10 4 s D. 1.5 × 10 15 s

10. A planet travels in an elliptical path around a star. The areas X, Y and Z were swept out in equal time intervals.

Which of the following describes the relationship between the areas?

A. Area X is greater than area Z.

B. Area X is equal to the sum of areas Y and Z.

C. Area X is less than area Z.

D. Area X is equal to area Y which is equal to area Z.

11. A satellite orbits the Sun with a period of 220 days. An asteroid orbits the Sun with twice the orbital radius of the satellite. What is the asteroid's period?
 A. 110 days B. 220 days C. 440 days D. 620 days

12. A space shuttle is in orbit about the earth at an altitude where the acceleration due to gravity is 8.70 m/s2. What is the shuttle's speed at this altitude?
 A. 2.65 × 10 3 m/s B. 7.45 × 10 3 m/s C. 7.68 × 10 3 m/s D. 7.91 × 10 3 m/s

13. Relative to zero at infinity, what is the gravitational potential energy of a 7.2 × 10 2 kg satellite that is at a distance of 3.4 × 10 7 m from earth's centre?
 A. -2.4 × 10 11 J B. -8.4 × 10 9 J C. 8.4 × 10 9 J D. 2.4 × 10 11 J

14. An object is located on the surface of a planet. The work required to remove this object from the planet's gravitational field depends on which combination of the following three variables: mass of the planet, mass of the object, and radius of the planet?
 MASS OF PLANET MASS OF OBJECT RADIUS OF PLANET A. Yes Yes Yes B. Yes Yes No C. Yes No Yes D. No Yes Yes

15. A 120 kg astronaut stands on the surface of an asteroid of radius 600 m. The astronaut leaves the surface with 15 J of kinetic energy and reaches a maximum height of 300 m above the surface. What is the mass of the asteroid?
 A. 5.6 × 10 11 kg B. 2.2 × 10 12 kg C. 3.4 × 10 12 kg D. 5.1 × 10 12 kg

16. What minimum kinetic energy would a spacecraft of mass 1.2 × 10 4 kg need at the surface of the Earth so that it could escape to infinity?
 A. 1.1 × 10 4 J B. 1.2 × 10 5 J C. 7.5 × 10 11 J D. An infinite amount

17. A 900 kg satellite which is travelling around a planet of mass 8.1 × 10 25 kg has an orbital radius of 7.3 × 10 7 m. What is the orbital velocity of this satellite? (7 marks)
18. A 1200 kg exploratory space probe located in a circular orbit around the Sun. The orbital radius is 7.0 × 10 9 m.

a) What is the orbital speed of this satellite? (5 marks)

b) If the Sun collapsed to one-tenth its present radius without a change to its mass, the space probe's orbital radius will (circle one) (1 mark)

i) increase.

ii) decrease.

iii) stay the same.

19. A 650 kg satellite in circular orbit around Earth has an orbital period of 1.5 × 10 4 s.

a) What is the satellite's orbital radius? (5 marks).

b) What is the gravitational potential energy of this satellite? (2 marks)

20. The moon Titan orbits the planet Saturn with a period of 1.4 × 10 6 s. The average radius of this orbit is 1.2 × 10 9 m.

a) What is Titan's centripetal acceleration? (2 marks)

b) Calculate Saturn's mass. (5 marks)