Quantitative

1. An astronaut is in equilibrium when he is positioned 140 km from planet X and 581 km from planet Y, along the straight line joining the planets' centers. What is the ratio of the masses X/Y?

a. 17.2 b. 0.0581 c. 0.241 d. 4.15

2. At what distance from the Earth should an astronaut be placed so that he will feel no net force when the Earth and the moon and he are aligned?

a. 0.38 x 108 m b. 0.47 x 108 m c. 3.44 x 108 m d. 4.29 x 108 m

3. From what height off the surface of the Earth should an object be dropped to initially experience an acceleration of 0.9200 g?

a. 260 km b. 271 km c. 510 km d. 554 km

4. What is the initial speed of a rocket launched from the surface of the Earth and reaching a height of 27 km?

a. 72.7 m/s b. 72.7 km/s c. 727 m/s d. 727 km/s

5. Use energy conservation to find the mass of planet Π where it is observed that a meteor is approaching in a collision course. At 7514 km from the center of the planet, the meteor has a speed of 136.0 m/s and later at 2823 km a speed of 392.0 m/s.

a. 4.582 x 1020 kg b. 4.582 x 1021 kg c. 9.164 x 1027 kg d. 6.112 x 1028 kg

6. What is the ratio of the escape speed of a rocket launched from sea level and one launched from Mt. Everest (altitude 8.85 km)?

a. 0.9986 b. 0.9993 c. 1.0007 d. 1.0014

7. A huge cannon is assembled on an airless planet. The planet has a radius of 5.00 x 106 m and a mass of 3.95 x 1023 kg. The cannon fires a projectile straight up at 2000 m/s. An observation satellite orbits the planet at a height of 1000 km. What is the projectile's speed as it passes the satellite??

a. 1280 m/s b. 1380 m/s c. 1500 m/s d. 1610 m/s

8. Consider a spherical asteroid with a mass of 3.5 x 1016 kg and a radius of 8.8 km. What is the escape speed from the asteroid?

a. 16 m/s b. 23 m/s c. 520 m/s d. 730 m/s

9. If we assume that an electron is orbiting a proton just like the moon orbits the Earth, find the electron's orbital speed due to the gravitational attraction between itself and the proton. Take the orbital radius as 1.00 x 10-10 m.

a. 1.06 x 10-27 m/s b. 1.11 x 10-27 m/s c. 3.33 x 10-14 m/s d. 1.11 x 10-13 m/s

10. Spaceman Speff orbits planet X with his spaceship. To remain in orbit at 421 km from the planet's center, he should maintain a speed of 80 m/s. What is the mass of planet X?

a. 4.0 x 1019 kg b. 5.1 x 1017 kg c. 4.0 x 1016 kg d. 5.1 x 1014 kg

11. A gaseous planet (like Jupiter) suddenly loses part of its mass. An orbiter about the planet needs to reduce its orbital radius to 0.10 of the original orbit and needs to slow down to 0.70 of its original speed, in order to remain in orbit. What is the ratio of the planet's new mass to the old mass?

a. 0.049 b. 0.07 c. 14 d. 20

12. You are the science officer on a visit to a distant solar system. Prior to landing on a planet you measure its diameter to be 1.8 x 107 m and its rotation period to be 22.3 hours. You have previously determined that the planet orbits 1.81 x 1011 m from its star with a period of 402 earth days. Once on the surface you find that the acceleration due to gravity is 59.7 m/s2. What are the mass of (a) the planet and (b) the star?

a. (a) 7.2 x 1025 kg, (b) 2.9 x 1030 kg

b. (a) 1.3 x 1026 kg, (b) 2.9 x 1030 kg

c. (a) 7.2 x 1025 kg, (b) 1.7 x 1030 kg

d. (a) 1.3 x 1026 kg, (b) 1.7 x 1030 kg

13. Suppose we want a satellite to revolve around the Earth 5 times a day. What should the radius of its orbit be? (Neglect the presence of the moon.)

a. 0.69 x 107 m b. 1.44 x 107 m c. 2.11 x 107 m d. 7.22 x 107 m

True/False

14. If the earth had twice as much mass as it now does but were also twice its present diameter, the acceleration due to gravity at its surface would be the same as it now is.

15. The earth's gravity is caused by our planet's spin on its axis.

16. If the mass of the earth and all objects on it were suddenly doubled, the acceleration due to gravity at the surface would become 4 times what it now is.

17. Orbiting satellites accelerate toward the earth at 9.8 m/s2.

18. A satellite is orbiting the earth. If a payload of material is added until it doubles the satellite's mass, the earth's pull of gravity on this satellite will double but the satellite's orbit will not be affected.

19. For satellites in orbit, their kinetic energy is equal to their gravitational potential energy.

20. An earth satellite needs to have its orbit changed so the new orbit will be twice as far from the center of the earth as the original orbit. The new orbital period will be twice as long as the original period.

21. If a planet were found half way between the earth and the sun, its orbital period would have to be 1/2 year.

Conceptual

22. If an astronaut were exactly halfway between the Earth and the Moon, the net gravitational force exerted on the astronaut by these two objects would be.

a. zero

b. directed towards Earth.

c. directed towards the Moon.

23. Two planets having equal masses are in circular orbit around a star. Planet A has a smaller orbital radius than planet B. Which statement is true?

a. Planet A and planet B have the same amount of mechanical energy (potential plus kinetic).

b. Planet A has less kinetic energy, less potential energy, and less mechanical energy (potential plus kinetic) than planet B.

c. Planet A has more kinetic energy, less potential energy, and more mechanical energy (potential plus kinetic) than planet B.

d. Planet A has more kinetic energy, more potential energy, and more mechanical energy (potential plus kinetic) than planet B.

e. Planet A has more kinetic energy, less potential energy, and less mechanical energy (potential plus kinetic) than planet B.

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