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.

  • 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

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?

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

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

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

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