Worksheet: Escape Velocity

In this worksheet, we will practice calculating the velocity required to escape the pull of a gravitational body given the body's mass and radius.

Q1:

Find the escape velocity from the surface of Mars. Use a value of 6 . 4 × 1 0 kg for the mass of Mars and a value of 3 3 9 0 km for its radius.

Q2:

Find the escape speed of a satellite located at the Moon’s orbit about Earth, assuming the Moon is sufficiently far from the Satellite to not influence its escape speed. Use a value of 3 8 5 × 1 0 km for the Moon’s orbital radius and use a value of 5 . 9 7 × 1 0 kg for the Earth’s mass.

Q3:

The distance from a solar system to the centre of the Milky Way is 27 000 light years. Assume that the mass contained in the sphere of radius 27 000 light years is 100 billion solar masses, taking one solar mass as 1 . 9 9 × 1 0 3 0 kg. What is the escape velocity for the Milky Way from the position of this solar system?

  • A 250 km/s
  • B 216 km/s
  • C 307 km/s
  • D 323 km/s
  • E 348 km/s

Q4:

What is the speed needed to escape from the Earth-Moon system from a point on the surface of Earth? Assume there are no other bodies involved and do not account for the fact that Earth and the Moon are moving in their orbits. Use a value of 3 8 5 . 0 × 1 0 3 km for the distance between the centres of the Moon and Earth, 5 . 9 7 × 1 0 2 4 kg for Earth's mass, and 7 . 3 5 × 1 0 2 2 kg for the Moon's mass.

  • A 1 6 . 4 × 1 0 3 m/s
  • B 1 3 . 5 × 1 0 3 m/s
  • C 2 1 . 1 × 1 0 2 m/s
  • D 1 1 . 2 × 1 0 3 m/s
  • E 9 . 3 6 × 1 0 4 m/s

Q5:

Find the escape speed of a projectile from the surface of Pluto. Use a value of 1 . 5 × 1 0 2 2 kg for the mass of Pluto and 2 3 7 0 km for its diameter.

  • A 5 . 2 × 1 0 3 m/s
  • B 4 1 × 1 0 3 m/s
  • C 6 . 3 × 1 0 2 m/s
  • D 1 3 × 1 0 2 m/s
  • E 9 . 2 × 1 0 2 m/s

Q6:

What is the Schwarzschild radius for the black hole at the centre of our galaxy if it has the mass of 4 . 0 0 × 1 0 6 kg solar masses? Use 1 . 9 9 × 1 0 3 0 kg as the value of the Sun’s mass.

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

Q7:

A planetoid has a mass of 6 3 . 1 × 1 0 2 0 kg and a radius of 963.0 km. Find the magnitude of the escape velocity from the surface of the planetoid, considering it to be spherical.

Q8:

What would the Schwarzschild radius be if our Milky Way galaxy of 120 billion solar mass collapsed into a black hole? Use a value of 1 . 9 9 × 1 0 3 0 kg for the mass of the Sun.

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