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 centre of the Milky Way Galaxy, calculate its orbital speed. The mass of the galaxy is equivalent to a single mass that is 1 . 5 × 1 0 1 1 times that of the Sun’s mass, which is 2 . 0 × 1 0 3 0 kg, located at a distance of 3 0 0 0 0 ly from the Sun.

  • A 1 . 4 × 1 0 5 m/s
  • B 9 . 4 × 1 0 4 m/s
  • C 1 . 8 × 1 0 5 m/s
  • D 2 . 7 × 1 0 5 m/s
  • E 2 . 3 × 1 0 5 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 2 𝑣 . (Give your answers to these questions as a decimal if necessary.)

What is the ratio of the orbital radii of the two planets, 𝑟 𝑟 𝐵 𝐴 ?

What is the ratio of the orbital periods of the two planets, 𝑇 𝑇 𝐵 𝐴 ?

Q3:

The asteroid Vesta has a mass of 2 . 6 7 × 1 0 2 0 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 3 s
  • B 7 . 8 0 × 1 0 3 s
  • C 1 . 2 7 × 1 0 4 s
  • D 6 . 2 4 × 1 0 3 s
  • E 1 . 4 6 × 1 0 4 s

Q4:

A small satellite is placed in a circular orbit around a nearby asteroid. The orbital period of the satellite is 1 0 9 0 0 seconds and the orbital radius is 2 . 0 0 0 0 × 1 0 3 km. What is the mass of the asteroid?

  • A 5 . 1 5 × 1 0 1 2 kg
  • B 3 . 2 3 × 1 0 1 1 kg
  • C 1 . 8 7 × 1 0 1 4 kg
  • D 3 . 9 8 × 1 0 1 3 kg
  • E 6 . 1 1 × 1 0 1 4 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 1 2 × 1 0 6 J
  • B 6 . 0 × 1 0 8 J
  • C 5 . 0 × 1 0 7 J
  • D 3 . 0 × 1 0 8 J
  • E 5 . 1 × 1 0 8 J

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