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 5 . 9 7 × 1 0 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 6 . 4 2 × 1 0 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 1 . 4 8 × 1 0 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 𝑟 from the planet’s center of mass. The planet has a mass 𝑀 . If the object is moved to an orbit 3 𝑟 from the planet’s center of mass, by what factor does the local acceleration due to gravity at its orbital radius change?

  • A 1 9
  • B 1 3
  • C9
  • D1
  • E3

Q5:

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

  • A 𝑎 1 𝑀
  • B 𝑎 1 𝑀
  • C 𝑎 𝑀
  • D 𝑎 𝑀
  • E 𝑎 ( 𝑀 )

Q6:

Europa is the smallest of the four Galilean moons orbiting Jupiter. It has a mass of 4 . 8 0 × 1 0 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, 𝑎 , around a massive object varies with the distance away from the center of mass of that object, 𝑟 ?

  • A 𝑎 1 𝑟
  • B 𝑎 1 𝑟
  • C 𝑎 1 𝑟
  • D 𝑎 ( 𝑟 )
  • E 𝑎 𝑟

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 1 . 2 0 × 1 0 m/s2
  • B 1 . 9 3 × 1 0 m/s2
  • C 3 . 0 2 × 1 0 m/s2
  • D 1 . 2 0 × 1 0 m/s2
  • E 1 . 9 3 × 1 0 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 1 0 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 1 . 1 5 × 1 0 m/s2
  • B 1 . 4 4 × 1 0 m/s2
  • C 2 . 9 1 × 1 0 m/s2
  • D 1 . 2 7 × 1 0 m/s2
  • E 1 . 9 8 × 1 0 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 7 . 8 5 × 1 0 m/s2
  • B 2 . 4 7 × 1 0 m/s2
  • C 6 . 1 6 × 1 0 m/s2
  • D 1 . 9 4 × 1 0 m/s2
  • E 1 . 2 3 × 1 0 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 1 0 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 6 . 6 7 × 1 0 N
  • B 3 3 4 × 1 0 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 6 . 6 7 × 1 0 m/s2
  • C 6.67 m/s2
  • D 9 . 8 1 × 1 0 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 3 3 4 × 1 0 N
  • E 6 . 6 7 × 1 0 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 6 . 6 7 × 1 0 m/s2
  • D 0.667 m/s2
  • E 9 . 8 1 × 1 0 m/s2

Q15:

Geostationary satellites orbit Earth at a height of 35,786 km above the equator. Earth has a mass of 5 . 9 7 × 1 0 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 2 . 7 9 × 1 0
  • D0.0228
  • E6.62

Q16:

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

  • A 𝑎 = 𝐺 𝑀 𝑟
  • B 𝑎 = 𝐺 𝑀 𝑟
  • C 𝑎 = 𝐺 𝑀 𝑟
  • D 𝑎 = 𝐺 𝑀 𝑟
  • E 𝑎 = 𝐺 𝑀 𝑟

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 7 . 3 4 × 1 0 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 9 . 2 9 × 1 0 m/s2
  • E 2 . 8 1 × 1 0 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 1 . 8 7 × 1 0 m/s2
  • B 3 . 7 4 × 1 0 m/s2
  • C 1 . 4 9 × 1 0 m/s2
  • D 2 . 9 9 × 1 0 m/s2
  • E 7 . 4 7 × 1 0 m/s2

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