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.


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.

  • A1.4×10 m/s
  • B9.4×10 m/s
  • C2.3×10 m/s
  • D2.7×10 m/s
  • E1.8×10 m/s


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?


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?

  • A9.22×10 s
  • B6.24×10 s
  • C7.80×10 s
  • D1.27×10 s
  • E1.46×10 s


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?

  • A3.98×10 kg
  • B6.34×10 kg
  • C6.34×10 kg
  • D6.91×10 kg
  • E3.98×10 kg


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?

  • A5.0×10 J
  • B3.0×10 J
  • C6.0×10 J
  • D5.1×10 J
  • E12×10 J

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