# Lesson Worksheet: Gravitational Potential Energy in a Radial Field Physics

In this worksheet, we will practice calculating the gravitational potential energy between two massive objects and changes in this potential energy as the object changes position.

**Q1: **

Two astronauts are trying to land a spacecraft on the Moon. The spacecraft is initially at rest at a position 4 km above the surface of the Moon, and the mass of the spacecraft and the two astronauts is 2,900 kg. The spacecraft is allowed to fall under the effect of gravity until it is 500 m above the surface of the Moon, when its thrusters are engaged. What is the speed of the spacecraft just before the thrusters are engaged? Use a value of 1,740 km for the radius of the Moon and a value of kg for the mass of the Moon. Give your answer to the nearest meter per second.

**Q2: **

An asteroid with a mass of 3,500 kg moves from a position 40,000 km away from the center of mass of Earth to a position 22,000 km away. What is the change in the gravitational potential energy between the asteroid and Earth? Use a value of kg for the mass of Earth. Give your answer in scientific notation to two decimal places.

- A J
- B J
- C J
- D J
- E J

**Q3: **

The distance between the centers of mass of two massive objects is . If this distance is increased to , by what factor does the gravitational potential energy between the two objects change?

- A3
- B
- C9
- D
- E1

**Q4: **

Which of the following formulas correctly shows the relation between the gravitational potential energy between two objects with masses and , where their centers of mass are separated by a distance ?

- A
- B
- C
- D
- E

**Q5: **

An asteroid is heading straight for Earth. When it is at a distance of 40,000 km from the surface of Earth, it has a velocity of 55 m/s straight toward Earth. The asteroid has a mass of 16,000 kg. Ignoring the effect of any resistance as the asteroid moves through Earth’s atmosphere, what would the speed of the asteroid be just before it hits Earth’s surface? Use a value of kg for the mass of Earth and a value of 6,370 km for the radius of Earth. Give your answer to one decimal place.

**Q6: **

A satellite orbiting Earth has a mass of 1,500 kg. Earth has a mass of kg. If the gravitational potential energy of the Earth-and-satellite system is GJ, what is the satellite’s orbital radius? Give your answer in scientific notation to two decimal places.

- A km
- B km
- C km
- D8.00 km
- E km

**Q7: **

Which of the following formulas correctly shows the relation between the magnitude of the gravitational potential energy between two massive objects, , and the distance between their centers of mass, ?

- A
- B
- C
- D
- E

**Q8: **

Fill in the blanks: An asteroid is in space near a planet. As the distance between the centers of mass of the planet and the asteroid decreases, the gravitational potential energy between the two objects . As the distance between the centers of mass of the planet and the asteroid increases, the gravitational potential energy between the two objects .

- Aincreases, decreases
- Bdecreases, decreases
- Cdecreases, increases
- Dstays the same, stays the same
- Eincreases, increases

**Q9: **

A spacecraft sent to investigate a comet moves from a position 10 km away from the comet’s
center of mass to the surface of the comet, 2.1 km away from its center of mass.
The spacecraft has a mass of 1,890 kg and the comet
has a mass of kg.
If all of the gravitational potential energy lost by the spacecraft is converted into kinetic energy of the spacecraft,
what is the kinetic energy of the spacecraft just before it reaches the surface of the comet?
Use a value of m^{3}/kg⋅s^{2}
for the universal gravitational constant.
Give your answer to the nearest joule.

**Q10: **

Which of the lines shown on the graph shows how the magnitude of the gravitational potential energy between two massive objects varies with the radial distance between their centers of mass?

- AThe green line
- BThe purple line
- CThe red line
- DThe black line
- EThe blue line