Worksheet: Gravitational Forces near Planetary Bodies

In this worksheet, we will practice calculating the acceleration due to gravity for planetary bodies near the surface of such planetary bodies.

Q1:

Find the acceleration due to gravity on the surface of Mars. Use a value of 6 . 4 2 × 1 0 2 3 kg for the mass of Mars and a value of 3 . 3 9 0 × 1 0 6 m for its radius.

Q2:

The acceleration due to gravity on the surface of a planet is three times as large as it is on the surface of Earth. The density of the planet is known to be twice that of the Earth. What is the radius of this planet in terms of Earth’s radius?

  • A 2 3 Earth radius
  • B 1 2 Earth radius
  • C2 Earth radius
  • D 3 2 Earth radius
  • E3 Earth radius

Q3:

The mean diameter of Saturn is 1 2 1 × 1 0 6 m and the acceleration due to gravity at its surface is 9.0 m/s2. Calculate its mass.

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

Q4:

Find the acceleration due to gravity at Saturn’s surface. Use a value of 1 1 6 4 6 0 km for the mean diameter of Saturn and a value of 0.69 g/cm3 for the mean mass density of Saturn.

Q5:

A neutron star is a cold, collapsed star with density comparable to that of an atomic nucleus. A particular neutron star has a mass twice that of Earth’s Sun and a radius of 12.00 km. Determine the weight of an astronaut with a mass of 1 . 0 0 × 1 0 2 kg standing on the surface of this star. Use a value of 1 . 9 8 9 × 1 0 3 0 kg for the mass of the Sun.

  • A 1 . 2 8 × 1 0 1 4 N
  • B 8 . 0 2 × 1 0 1 3 N
  • C 3 . 1 1 × 1 0 1 4 N
  • D 1 . 8 5 × 1 0 1 4 N
  • E 5 . 1 9 × 1 0 1 4 N

Q6:

The value of 𝑔 , the acceleration due to gravity at Earth’s surface, depends on its mass and radius. Use a value of 6 3 7 1 km for the radius of Earth. Taking a value of 5 . 9 7 × 1 0 2 4 kg for Earth’s mass, 𝑔 is 9.82 m/s2.

Find 𝑔 if Earth’s mass is halved and its radius is doubled.

Find 𝑔 if Earth’s density is unchanged and its radius is doubled.

Find 𝑔 if Earth’s density is unchanged and its mass is halved.

Q7:

Jupiter has a radius at its equator of 71 492 km, and the gravitational acceleration at that point is 23.1 m/s2.

Calculate Jupiter’s mass from its radius and the gravitational acceleration at its equator.

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

What is the ratio of the calculated mass of Jupiter to NASA’s Jupiter fact sheet value of 1 8 9 8 × 1 0 2 4 kg?

Q8:

Io is a moon of Jupiter. Find the difference between the magnitudes of the forces on an object of mass 9.00 kg on the near and far sides of Io due to the gravitational force from Jupiter. Use a value of 1 . 8 9 8 × 1 0 2 7 kg for the mass of Jupiter, a value of 1 8 2 1 km for the mean radius of Io, and a value of 4 2 1 7 . 0 0 × 1 0 2 km for the mean orbital radius of Io.

Q9:

A body on the surface of a planet, with the same radius as Earth’s, weighs five times more than it does on Earth. Find the mass of that planet. Use a value of 5 . 9 7 × 1 0 2 4 kg for the mass of Earth and 6 3 7 1 km for its radius.

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

Q10:

Calculate the acceleration due to gravity on the surface of Venus. Use a value of 4 . 8 7 × 1 0 2 4 kg for its mass and 6 0 5 2 km for its radius.

Q11:

On a planet whose radius is 1 5 . 2 0 × 1 0 7 m, the acceleration due to gravity is 36.2 m/s2. What is the mass of that planet?

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

Q12:

The mass of the Moon is 7 . 3 4 × 1 0 2 2 kg, and its mean distance away from Earth is 3 . 8 5 × 1 0 5 km. The mass of the Sun is 1 . 9 9 × 1 0 3 0 kg, and its mean distance from Earth is 1 . 5 0 × 1 0 8 km. The universal gravitational constant has a value of 6 . 6 7 × 1 0 1 1 m3⋅kg−1⋅s−2.

Calculate the magnitude of the acceleration due to gravity on the surface of Earth due to the Moon.

  • A 4 . 9 × 1 0 5 m/s2
  • B 2 . 3 × 1 0 5 m/s2
  • C 2 . 7 × 1 0 5 m/s2
  • D 3 . 3 0 × 1 0 5 m/s2
  • E 1 . 9 × 1 0 5 m/s2

Calculate the magnitude of the acceleration due to gravity at Earth due to the Sun.

  • A 5 . 9 0 × 1 0 3 m/s2
  • B 8 . 4 × 1 0 3 m/s2
  • C 4 . 5 × 1 0 3 m/s2
  • D 7 . 6 × 1 0 3 m/s2
  • E 3 . 9 × 1 0 3 m/s2

What is the ratio of the acceleration due to gravity caused by the Moon to that caused by the Sun?

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

Q13:

A satellite of mass 1 . 0 0 × 1 0 3 kg is in circular orbit about Earth. The radius of the orbit of the satellite is equal to twice the radius of Earth. Use a value of 6 3 7 1 km for the radius of the Earth.

Find the kinetic energy of the satellite.

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

Find the potential energy of the satellite.

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

Find the total energy of the satellite.

  • A 1 . 2 5 × 1 0 1 0 J
  • B 0 . 7 6 7 × 1 0 1 0 J
  • C 1 . 5 6 × 1 0 1 0 J
  • D 0 J
  • E 0 . 5 2 2 × 1 0 1 0 J

Q14:

An asteroid located 5 . 0 × 1 0 7 km from Earth has a mass of 2 . 0 × 1 0 1 3 kg. The asteroid is detected headed directly toward Earth with a relative speed of 2.0 km/s. What will the asteroid’s speed be when it impacts on the Earth’s surface, neglecting any effects of atmospheric drag?

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