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 5.97×10 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 6.42×10 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 1.48×10 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 3𝑟 from the planet’s center of mass, by what factor does the local acceleration due to gravity at its orbital radius change?

  • A19
  • B9
  • C13
  • D3
  • E1

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?

  • A𝑎1𝑀
  • B𝑎(𝑀)
  • C𝑎𝑀
  • D𝑎1𝑀
  • E𝑎𝑀

Q6:

Europa is the smallest of the four Galilean moons orbiting Jupiter. It has a mass of 4.80×10 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?

  • A𝑎1𝑟
  • B𝑎1𝑟
  • C𝑎𝑟
  • D𝑎(𝑟)
  • E𝑎1𝑟

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 red line
  • BThe green line
  • CThe purple line
  • DThe black 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 .

  • Aincreases
  • Bstays the same
  • 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?

  • A3.02×10 m/s2
  • B1.93×10 m/s2
  • C1.20×10 m/s2
  • D1.93×10 m/s2
  • E1.20×10 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 10 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?

  • ABoth object A and object B will have the same acceleration.
  • BObject A
  • CObject B

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?

  • A1.15×10 m/s2
  • B2.91×10 m/s2
  • C1.44×10 m/s2
  • D1.27×10 m/s2
  • E1.98×10 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.

  • A2.47×10 m/s2
  • B6.16×10 m/s2
  • C7.85×10 m/s2
  • D1.94×10 m/s2
  • E1.23×10 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 10 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.

  • A3.34 N
  • B334×10 N
  • C6.67×10 N
  • D66.7 N
  • E5.00 N

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

  • A9.81 m/s2
  • B9.81×10 m/s2
  • C6.67 m/s2
  • D0.667 m/s2
  • E6.67×10 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.

  • A334×10 N
  • B66.7 N
  • C6.67×10 N
  • D3.34 N
  • E10.0 N

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

  • A9.81 m/s2
  • B9.81×10 m/s2
  • C6.67 m/s2
  • D0.667 m/s2
  • E6.67×10 m/s2

Q15:

Geostationary satellites orbit Earth at a height of 35,786 km above the equator. Earth has a mass of 5.97×10 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.

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?

  • A𝑎=𝐺𝑀𝑟
  • B𝑎=𝐺𝑀𝑟
  • C𝑎=𝐺𝑀𝑟
  • D𝑎=𝐺𝑀𝑟
  • E𝑎=𝐺𝑀𝑟

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 7.34×10 kg. What is the acceleration due to gravity on the surface of the Moon? Give your answer to 3 significant figures.

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.

  • A1.87×10 m/s2
  • B7.47×10 m/s2
  • C3.74×10 m/s2
  • D2.99×10 m/s2
  • E1.49×10 m/s2

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