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?

- A Earth radius
- B Earth radius
- C2 Earth radius
- D Earth radius
- E3 Earth radius

**Q3: **

The mean diameter of Saturn is m
and the acceleration due to gravity at its surface is 9.0 m/s^{2}.
Calculate its mass.

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

**Q4: **

Find the acceleration due to gravity at Saturn’s surface. Use a value of km for the
mean diameter of Saturn and a value of 0.69 g/cm^{3} 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 kg standing on the surface of this star. Use a value of kg for the mass of the Sun.

- 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 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 km for the mean radius of Io, and a value of 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 kg for the mass of Earth and km for its radius.

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

**Q10: **

Calculate the acceleration due to gravity on the surface of Venus. Use a value of kg for its mass and km for its radius.

**Q11: **

On a planet whose radius is m,
the acceleration due to gravity is
36.2 m/s^{2}.
What is the mass of that planet?

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

**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 km for the radius of the 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
- B J
- C J
- D 0 J
- E J

**Q14: **

An asteroid located km from Earth has a mass of 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?