Worksheet: Gravitational Potential Energy in Radial Gravitational Fields

In this worksheet, we will practice calculating the kinetic energy, gravitational potential energy, and total energy of objects with orbital trajectories.

Q1:

Assuming a circular orbit for the Sun about the center of the Milky Way Galaxy, calculate its orbital speed. The mass of the galaxy is equivalent to a single mass that is 1.5×10 times that of the Sun’s mass, which is 2.0×10 kg, located at a distance of 30,000 ly from the Sun.

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

Q2:

There are two planets in orbit around a star. Both planets have circular orbits. Planet 𝐴 has a speed of 𝑣, and Planet 𝐵 has a speed of 2𝑣. (Give your answers to these questions as a decimal if necessary.)

What is the ratio of the orbital radii of the two planets, 𝑟𝑟?

What is the ratio of the orbital periods of the two planets, 𝑇𝑇?

Q3:

The asteroid Vesta has a mass of 2.67×10 kg and a radius of 520 km. What would be the orbital period for a space probe in a circular orbit of 10.0 km from Vesta’s surface?

  • A 9 . 2 2 × 1 0 s
  • B 6 . 2 4 × 1 0 s
  • C 7 . 8 0 × 1 0 s
  • D 1 . 2 7 × 1 0 s
  • E 1 . 4 6 × 1 0 s

Q4:

A small satellite is placed in a circular orbit around a nearby asteroid. The orbital period of the satellite is 10,900 seconds and the orbital radius is 2.0000×10 km. What is the mass of the asteroid?

  • A 3 . 9 8 × 1 0 kg
  • B 6 . 3 4 × 1 0 kg
  • C 6 . 3 4 × 1 0 kg
  • D 6 . 9 1 × 1 0 kg
  • E 3 . 9 8 × 1 0 kg

Q5:

What is the gravitational potential energy between two spheres, each of mass 9.5 kg, separated by a center-to-center distance of 20.0 cm?

  • A 5 . 0 × 1 0 J
  • B 3 . 0 × 1 0 J
  • C 6 . 0 × 1 0 J
  • D 5 . 1 × 1 0 J
  • E 1 2 × 1 0 J

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