# Worksheet: Surface Gravity

In this worksheet, we will practice calculating the surface gravity of a planet or moon given its mass and its radius.

**Q1: **

The International Space Station orbits Earth at a distance of 409 km above the surface. Earth has a mass of kg and a radius of 6,370 km. What is the local acceleration due to gravity at the height at which the International Space Station orbits? Give your answer to 3 significant figures.

**Q2: **

Mars has a mass of kg
and a radius of 3,390 km.
What is the surface gravity of Mars as a ratio of the surface gravity of Earth?
Use a value of 9.81 m/s^{2}
for the surface gravity of Earth. Give your answer to 3 significant figures.

**Q3: **

Ganymede is the largest moon in the solar system, with a mass of kg and a radius of 2,630 km. What is the surface gravity on Ganymede? Give your answer to 3 significant figures.

**Q4: **

An object orbits a planet at a distance from the planet’s center of mass. The planet has a mass . If the object is moved to an orbit from the planet’s center of mass, by what factor does the local acceleration due to gravity at its orbital radius change?

- A
- B
- C9
- D1
- E3

**Q5: **

Which of the following relations shows how the acceleration due to gravity, , around a massive object varies with the mass of that object, ?

- A
- B
- C
- D
- E

**Q6: **

Europa is the smallest of the four Galilean moons orbiting Jupiter. It has a mass of kg and a radius of 1,560 km. What is the acceleration due to gravity on the surface of Europa? Give your answer to 3 significant figures.

**Q7: **

Which of the following relations shows how the acceleration due to gravity, , around a massive object varies with the distance away from the center of mass of that object, ?

- A
- B
- C
- D
- E

**Q8: **

Which of the lines on the graph shows how the acceleration due to gravity around a massive object varies with the distance away from the center of mass of that object?

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

**Q9: **

Fill in the blank: As the distance between two objects increases, the acceleration due to gravity of each of them .

- Astays the same
- Bincreases
- Cdecreases

**Q10: **

The diagram shows two objects, A and B. What is the initial acceleration of object B due to its gravitational interaction with object A?

- A
m/s
^{2} - B
m/s
^{2} - C
m/s
^{2} - D
m/s
^{2} - E
m/s
^{2}

**Q11: **

Two objects, object A with a mass of 55 kg and object B with a mass of 12 kg, are near an even larger object with a mass of kg. Object A and object B are at an equal distance (1,000 km) away from the center of mass of the very large object. Which of the objects A and B will have the greater acceleration toward the very large object?

- AObject A
- BObject B
- CBoth object A and object B will have the same acceleration.

**Q12: **

The diagram shows two objects, A and B. What is the initial acceleration of object B due to its gravitational interaction with object A?

- A
m/s
^{2} - B
m/s
^{2} - C
m/s
^{2} - D
m/s
^{2} - E
m/s
^{2}

**Q13: **

A 75 kg person jumps off a 1 m high table onto the ground. If Earth has a radius of 6,370 km, what is the acceleration of Earth due to the gravitational force between Earth and the person while they are in the air? Give your answer to 3 significant figures.

- A
m/s
^{2} - B
m/s
^{2} - C
m/s
^{2} - D
m/s
^{2} - E
m/s
^{2}

**Q14: **

Two objects, object A with a mass of 5 kg and object B with a mass of 100 kg, are near an even larger object with a mass of kg. Object A and object B are at an equal distance away, 100 km, from the center of mass of the very large object.

What is the magnitude of the gravitational force experienced by object A due to the very large object? Give your answer to 3 significant figures.

- A N
- B N
- C 5.00 N
- D 66.7 N
- E 3.34 N

What is the acceleration of object A toward the very large object? Give your answer to 3 significant figures.

- A
9.81 m/s
^{2} - B
m/s
^{2} - C
6.67 m/s
^{2} - D
m/s
^{2} - E
0.667 m/s
^{2}

What is the magnitude of the gravitational force experienced by object B due to the very large object? Give your answer to 3 significant figures.

- A 3.34 N
- B 10.0 N
- C 66.7 N
- D N
- E N

What is the acceleration of object B toward the very large object? Give your answer to 3 significant figures.

- A
9.81 m/s
^{2} - B
6.67 m/s
^{2} - C
m/s
^{2} - D
0.667 m/s
^{2} - E
m/s
^{2}

**Q15: **

Geostationary satellites orbit Earth at a height of 35,786 km above the equator. Earth has a mass of kg and a radius of 6,370 km. What is the ratio of the local acceleration due to gravity at the height of a geostationary satellite to that on the surface of Earth? Give your answer to 3 significant figures.

- A43.8
- B0.151
- C
- D0.0228
- E6.62

**Q16: **

Which of the following is the correct formula for the acceleration due to gravity, , at a distance away from the center of mass of an object with mass , where is the universal gravitational constant?

- A
- B
- C
- D
- E

**Q17: **

An astronaut is standing on the surface of the Moon, where he is 1,740 km away from the Moon’s center of mass. The Moon has a mass of kg. What is the acceleration due to gravity on the surface of the Moon? Give your answer to 3 significant figures.

- A
1.62 m/s
^{2} - B
0.809 m/s
^{2} - C
3.23 m/s
^{2} - D
m/s
^{2} - E
m/s
^{2}

**Q18: **

Two objects, A and B, are in deep space. Object A has a mass of 28,000 kg. If the center of mass of object B is at a distance of 50 m away from the center of mass of object A, what is the acceleration of object B toward object A? Give your answer to 3 significant figures.

- A
m/s
^{2} - B
m/s
^{2} - C
m/s
^{2} - D
m/s
^{2} - E
m/s
^{2}