Q: Two bowling balls, each of mass $$7.3\ \mathrm{kg}$$, are placed $$0.22\ \mathrm{m}$$ apart. What is the magnitude of the gravitational force between them? Use $$G = 6.67 \times 10$$^{-11}$$\ \mathrm{N}\cdot\mathrm{m}^2/\mathrm{kg}^2.$$

$$7.0 \times 10$$^{-11}$$\ \mathrm{N}$$

Q: A geostationary satellite orbits Earth with a period of $$T = 8.64 \times 10^4$\ \mathrm{s}. $$What is the radius of its orbit? Use $$G = 6.67 \times 10$$^{-11}$$\ \mathrm{N}\cdot\mathrm{m}^2/\mathrm{kg}^2$$ and $$M_{\text{Earth}} = 5.98 \times 10$$^{24}$$\ \mathrm{kg}.$$

$$4.22 \times 10^7$\ \mathrm{m}$$

Question 1

According to Newton's law of universal gravitation, what happens to the gravitational force between two objects if the distance between them is tripled?

Accepted Answer

The force decreases by a factor of 9.

Question 2

Two bowling balls, each of mass $$7.3\ \mathrm{kg}$$, are placed $$0.22\ \mathrm{m}$$ apart. What is the magnitude of the gravitational force between them? Use $$G = 6.67 	imes 10$$^{-11}$$\ \mathrm{N}\cdot\mathrm{m}^2/\mathrm{kg}^2.$$

Accepted Answer

$$7.0 	imes 10$$^{-11}$$\ \mathrm{N}$$

Question 3

A $$70\ \mathrm{kg}$$ astronaut wearing an $$80\ \mathrm{kg}$$ spacesuit weighs $$330\ \mathrm{lb} on $$Earth. What would be his weight on the Moon, where $$g_{	ext{moon}} = 1.62\ \mathrm{m}/\mathrm{s}^2$$?

Accepted Answer

$$54\ \mathrm{lb}$$

Question 4

If the gravitational force between two asteroids is $$1,000,000\ \mathrm{N}$$, what will the force be if the distance between them is doubled?

Accepted Answer

$$250,000\ \mathrm{N}$$

Question 5

Planet X has a free-fall acceleration of $$8\ \mathrm{m}/\mathrm{s}^2 at $$the surface. Planet Y has twice the mass and twice the radius of Planet X. What is the free-fall acceleration on Planet Y?

Accepted Answer

$$4\ \mathrm{m}/\mathrm{s}^2$$

Question 6

A $$60\ \mathrm{kg}$$ person stands on three different planets: A ($$M$$, $$R$$), B ($$2M$$, $$2R$$), and C ($$3M$$, $$3R). On $$which planet is her weight the greatest?

Accepted Answer

Planet A

Question 7

Which of the following best describes the relationship between the gravitational force and the masses and distance between two objects?

Accepted Answer

The force is directly proportional to the product of the masses and inversely proportional to the square of the distance.

Question 8

Two satellites have circular orbits with the same radius around Earth. One satellite has more mass than the other. Which has a higher orbital speed?

Accepted Answer

They have the same speed.

Question 9

Two identical satellites have different circular orbits around Earth. Which satellite has a higher speed?

Accepted Answer

The one in the smaller orbit.

Question 10

A Space Shuttle crew boosts a satellite into a higher orbit around Earth. Which of the following quantities increases?

Accepted Answer

Period

Question 11

A geostationary satellite orbits Earth with a period of $$T = 8.64 	imes 10^4$\ \mathrm{s}. $$What is the radius of its orbit? Use $$G = 6.67 	imes 10$$^{-11}$$\ \mathrm{N}\cdot\mathrm{m}^2/\mathrm{kg}^2$$ and $$M_{	ext{Earth}} = 5.98 	imes 10$$^{24}$$\ \mathrm{kg}.$$

Accepted Answer

$$4.22 	imes 10^7$\ \mathrm{m}$$

Question 12

Which equation gives the speed required for a satellite to maintain a circular orbit of radius $$r$$ about a planet of mass $$M$$?

Accepted Answer

$$v = \sqrt{\dfrac{GM}{r}}$$

Question 13

A planet has mass $$M$$ and radius $$R. $$What is the free-fall acceleration $$g at $$its surface?

Accepted Answer

$$g = \dfrac{GM}{R^2$}$$

Question 14

If the period $$T$$ and radius $$r of a $$satellite's orbit are related by $$T^2$$ = \dfrac{4\$$pi^2$$}{GM} $$r^3$$, what happens to the period if the radius is doubled?

Accepted Answer

The period increases by a factor of $$2\sqrt{2}$$

Question 15

A projectile is launched into a very low orbit around Deimos (radius $$6.3 	imes 10^3$\ \mathrm{m}$$, $$g = 0.0030\ \mathrm{m}/\mathrm{s}^2). $$What is its orbital speed?

Accepted Answer

$$4.3\ \mathrm{m}/\mathrm{s}$$

Question 16

Which of the following statements about gravitational force is true?

Accepted Answer

It acts between any two objects with mass, regardless of distance.

Question 17

Phobos orbits Mars at a radius of $$9.4 	imes 10^6$\ \mathrm{m}$$, and Mars has mass $$6.4 	imes 10$$^{23}$$\ \mathrm{kg}. $$What is the orbital period of Phobos? Use $$G = 6.67 	imes 10$$^{-11}$$\ \mathrm{N}\cdot\mathrm{m}^2/\mathrm{kg}^2.$$

Accepted Answer

$$7.8\ \mathrm{hours}$$

Question 18

Which of the following best explains why astronauts feel weightless while orbiting Earth?

Accepted Answer

The net force is provided by gravity alone, and both astronaut and spacecraft are in free fall.

Newton's Law of Gravity and Orbital Motion: Study Notes

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