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Lesson Worksheet: Surface Gravity Physics • 9th Grade

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

Q1:

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

Q2:

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

Q3:

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

Q4:

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 two decimal places.

Q5:

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 two decimal places.

Q6:

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 two decimal places.

Q7:

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 two decimal places.

Q8:

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

Q9:

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

Q10:

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 in scientific notation to two decimal places.

  • 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

This lesson includes 25 additional questions for subscribers.

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