1. 
Which graph best shows how the gravitational field strength, g, varies with the distance, r, from the centre of a planet? (rp is the radius of the planet.)


2. 
A satellite is in a stable circular orbit around the earth. Another satellite in a stable circular orbit at a greater altitude must have A. a smaller speed and a shorter period. B. a smaller speed and a longer period. C. a greater speed and a shorter period. D. a greater speed and a longer period.


3. 
Which graph shows gravitational potential energy plotted as a function of distance r from the centre of the earth?


4. 
How much work must be done to lift a 4.00 ×10^{4 }kg object from Earth’s surface to a height of 3.00 × 10^{5} m?


5. 
The equation Ep = mgh, in which g is 9.8 m/s^{2} , can not be used for calculating the gravitational potential energy of an orbiting Earth satellite because A. the Earth is rotating. B. of the influence of other astronomical bodies. C. the Earth’s gravity disappears above the atmosphere. D. the Earth’s gravitational field strength varies with distance. 

6. 
A 1 570 kg satellite orbits a planet in a circle of radius 5.94 × 10^{6} m. Relative to zero at infinity the gravitational potential energy of this satellite is 9.32 × 10^{11} J. What is the mass of the planet?


7. 
A satellite experiences a gravitational force of 228 N at an altitude of 4.0 × 10^{7} m above Earth. What is the mass of this satellite?


8. 
Which of the indicated areas of the graph represent the work needed to send an object from separation distance r to infinity?


9. 
Cavendish’s historic experiment is set up as shown to determine the force between two identical sets of masses. What would be the net force of attraction between one set of masses?


10. 
Sputnik I, Earth’s first artificial satellite, had an orbital period of 5760 s. What was the average orbital radius of Sputnik’s orbit?


11. 
A 620 kg satellite orbits the earth where the acceleration due to gravity is 0.233 m/s^{2}. What is the kinetic energy of this orbiting satellite?


12. 
A 1 500 kg satellite orbits the earth at 2 500 m/s . What is the satellite’s centripetal acceleration?


13. 
A satellite orbits Earth at a velocity of 3.1 × 10^{3} m/s. What is the radius of this orbit?


14. 
A 5.0 kg rock dropped near the surface of Mars reaches a speed of 15 m/s in 4.0 s. a) What is the acceleration due to gravity near the surface of Mars? (2 marks) b) Mars has an average radius of 3.38 × 10^{6} m. What is the mass of Mars? (5 marks) 

15. 
A space shuttle is placed in a circular orbit at an altitude of 3.00 × 10^{5} m above Earth’s surface. a) What is the shuttle’s orbital speed? (5 marks) b) The space shuttle is then moved to a higher orbit in order to capture a satellite. The shuttle’s speed in this new higher orbit will have to be: (Circle one response.) (1 mark) i) greater than in the lower orbit. ii) less than in the lower orbit. iii) the same as in the lower orbit. c) Using principles of physics, explain your answer to b). (3 marks)


16. 
A 4.00 × 10^{3 }kg object is lifted from the earth’s surface to an altitude of 3.2 × 10^{5} m. How much work does this require?


17. 
Geostationary satellites appear to remain stationary to an observer on Earth. Such satellites are placed in orbit far above the equator. Using principles of physics, explain why such satellites all have the same orbital radius. (4 marks) 

18. 
a) Mars has a mass of 6.37 × 10^{23} kg and a radius of 3. 43 ×10^{6 }m. What is the gravitational field strength on its surface? (4 marks) b) What thrust force must the rocket engine of a Martian lander exert if the 87.5 kg spacecraft is to accelerate upwards at 1.20 m/s^{2} as it leaves the surface of Mars? (3 marks)


19. 
A spacecraft of mass 470 kg rests on the surface of an asteroid of radius 1 400 m and mass 2.0 × 10^{12} kg. How much energy must be expended so that the spacecraft may rise to a height of 2 800 m above the surface of the asteroid? (7 marks)


20. 
An 884 kg satellite in orbit around a planet has a gravitational potential energy of 5.44 × 10^{10} J. The orbital radius of the satellite is 8.52 × 10^{6} m and its speed is 7.84 × 10^{3} m/s. a) What is the mass of the planet? (3 marks) b) What is the kinetic energy of the satellite? (2 marks) c) What is the total energy of the satellite? (2 marks) 
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