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/s2 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/s2
• B m/s2
• C m/s2
• D m/s2
• E m/s2

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/s2
• B m/s2
• C m/s2
• D m/s2
• E m/s2

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/s2
• B m/s2
• C m/s2
• D m/s2
• E m/s2

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/s2
• B m/s2
• C 6.67 m/s2
• D m/s2
• E 0.667 m/s2

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/s2
• B 6.67 m/s2
• C m/s2
• D 0.667 m/s2
• E m/s2

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/s2
• B 0.809 m/s2
• C 3.23 m/s2
• D m/s2
• E m/s2

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/s2
• B m/s2
• C m/s2
• D m/s2
• E m/s2