Chapter 6

1. Determine the orbital period of a planet with a mean distance of 2.0 X 10¹¹ m from the sun.

2. A planetoid has an orbital period twice that of Earth's period. How many times farther from the

sun would this planetoid be?

3. Given that the orbital radius and period of revolution of the moon are 3.8 X 10⁸ m, and

2.36 X 10⁶ s respectively, determine Kepler's constant for any satellite of the Earth?

4. The centers of mass of two large boats are 94 m apart. Calculate the force of attraction

between the boats if they both have a mass of 1.8 X 10⁸ kg.

5. The distance of a woman from the center of the earth is 6.38 X 10⁶ m. If her mass is 50.0 kg,

and the mass of the Earth is 5.98 X 10²⁴ kg, calculate the force of gravity on the woman.

6. Two space rocks have a gravitational attraction between them of 36 N. The mass of one of

the rocks in a second pair of space rocks, is double the mass of one of the rocks in the first

pair. The other rock in the second pair of space rocks, is equal to the mass of the other rock

in the first pair of space rocks. If the distance between the second pair of rocks is triple the

distance between the first pair, what is the force of attraction between the second pair of space

rocks?

7. The radius and mass of Mars are 0.54 and 0.11 times the radius and mass of Earth respectively.

The force of gravity on an object on Earth is 600 N. What would the force of gravity be on

this object if it were on Mars?

8. Determine the acceleration due to gravity on Jupiter if the planet's mass and radius are

1.9 X 10²⁷ kg, and 7.2 X 10⁷ m respectively.

9. Given that the gravitational attraction between two masses M₁ and M₂ is 26 N. Calculate the

new attractive force if the mass of M₂ is tripled, and the distance between the two masses is

halved?

10. The mass of C is doubled and the distance between C and D is halved. Calculate the new

gravitational force between them if the original force was 100 N.

11. For the diagram below, determine the net gravitational force on M₁ resulting from the other

three masses.

12. If the radius and mass of Mars are respectively, half and one eighth the radius and mass of

Earth, determine the acceleration due to gravity on Mars.

13. Calculate the acceleration due to gravity on a planet with a mass of 5.67 X 10²⁶ kg and a

radius of 6.3 X 10⁷ m. On this planet, determine the gravitational force on a 60 kg person.

14. A newly discovered planet is observed to have a moon with a period of 1.5 X 10⁵ s. This

moon has an average radius of orbit of 4.2 X 10⁸ m. What is the mass of the planet this moon

orbits?

15. A satellite is going to be placed in orbit around the moon at a height of 100 km above the

moon's surface. The moon has a mass of 7.34 X 10²² kg, and a radius of 1.74 X 10⁶ m.

What period will this satellite have?

16. Determine the altitude of a satellite in a synchronous orbit above Mars. Data that you need to

know about Mars is:

Mass = 6.37 X 10²³ kg

Radius = 3.43 X 10⁶ m

Period of rotation = 8.85 X 10⁴ s

17. At some height above the Earth's surface, an astronaut will have a weight that is one half what

it is on the Earth's surface. What is this height expressed in Earth radii?

18. What is the period of revolution of a weather satellite which is 6.38 X 10⁶ m above the Earth's

surface?

19. Phobos and Deimos are Mars’ two moons. The period of Deimos is 30 h 18 minutes, and

its average distance from the Mars’ center is 2.3 X 10⁴ km. Mars has a mass of

6.37 X 10²³ kg , and Phobos has a period of 7 h 39 minutes. Determine the average distance

of Phobos from Mars's center.

20. The sun circles the center of our galaxy every 200 million years (approximately). The center

of the galaxy is about 2.7 X 10²⁰ m from our sun. Some astronomers believe there is a black

hole at the center of our galaxy which causes this motion. Others believe that the attraction of

a large number of stars at the hub of our galaxy is responsible for the motion.

a) Determine the mass of the black hole, or total mass of the stars at the hub of our

galaxy.

b) If the cause is a large number of stars, how many stars are there, assuming their

average mass is equal to the mass of the sun (2.0 X 10³⁰ kg)?

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November 21, 2013