# 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.

**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?

- A2 Earth radius
- B3 Earth radius
- C Earth radius
- D Earth radius
- E Earth radius

**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
kg
standing on the surface of this star. Use a value of
kg for the mass of
the Sun and a value of
m^{3}⋅kg^{−1}⋅s^{−2}
for the gravitational constant.

- A N
- B N
- C N
- D N
- E N

**Q6: **

The value of , the acceleration due to gravity at Earth’s surface,
depends on its mass and radius. Use a value of 6,371 km for the radius of Earth. Taking
a value of kg for Earth’s mass,
is 9.82 m/s^{2}.

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

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

Find 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/s^{2}.

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

- A kg
- B kg
- C kg
- D kg
- E kg

What is the ratio of the calculated mass of Jupiter to NASA’s Jupiter fact sheet value of 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 kg for the mass of Jupiter, a value of 1,821 km for the mean radius of Io, and a value of km for the mean orbital radius of Io.

**Q12: **

The mass of the Moon is
kg,
and its mean distance away from Earth is
km. The mass of the
Sun is kg,
and its mean distance from Earth is
km.
The universal gravitational constant has
a value of
m^{3}⋅kg^{−1}⋅s^{−2}.

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

- A m/s
^{2} - B m/s
^{2} - C m/s
^{2} - D m/s
^{2} - E m/s
^{2}

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

- A m/s
^{2} - B m/s
^{2} - C m/s
^{2} - D m/s
^{2} - E m/s
^{2}

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

- A
- B
- C
- D
- E

**Q13: **

A satellite of mass 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 6,371 km for the radius of Earth.

Find the kinetic energy of the satellite.

- A J
- B J
- C J
- D J
- E J

Find the potential energy of the satellite.

- A J
- B J
- C J
- D J
- E J

Find the total energy of the satellite.

- A J
- B0 J
- C J
- D J
- E J