Gravitational Field Examples: 46 Problems with Answers

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Gravitational Field.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

A gravitational field is the region around a mass where another mass experiences a gravitational force.

A planet creates an invisible pull around it. The closer you are, the stronger that pull is.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Gravitational Field asks students to choose the object, list external interactions, and reason from the resulting force or torque pattern.

Common stuck point: Students often know a formula related to gravitational field but skip the recognition step: Have I isolated one system and listed the external forces or torques acting on it before applying a law? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Have I isolated one system and listed the external forces or torques acting on it before applying a law?

Worked Examples

Example 1

medium

Find the height above Earth's surface where

g

drops to

4.9\,\text{N/kg}

. Use

R = 6.4\times 10^6\,\text{m}

g_{surf} = 9.8\,\text{N/kg}

Answer

h \approx 2.65 \times 10^{6} m

First step

g/g_{surf} = (R/r)^2 = 0.5

, so

r/R = \sqrt{2}

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Example 2

hard

Inside a uniform-density planet (mass

M

, radius

R

), the field at radius

r < R

g(r) = GMr/R^3

. Find the depth below the surface where

g

equals half its surface value.

Example 3

hard

At Earth's surface a person weighs

700\,\text{N}

. The same person stands on a tower at altitude

h = 2.0\times 10^6\,\text{m}

. Find their weight there. Use

R_E = 6.4\times 10^6\,\text{m}

Example 4

challenge

Two stars of masses

M

and

2M

separated by distance

L

orbit their common center of mass. At the center of mass, find the magnitude of the total gravitational field.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

2 \text{ kg}

mass feels a gravitational force of

19.6 \text{ N}

. Find the gravitational field strength.

Find the gravitational field strength g = W/m

Example 2

easy

Find the gravitational field at distance

r=2 \times 10^7 \text{ m}

from a planet of mass

M=6 \times 10^{24} \text{ kg}

. (

G=6.67\times10^{-11}

)

Example 3

easy

The gravitational field at a point is

5 \text{ N/kg}

. Find the force on a

3 \text{ kg}

mass there.

Field g

Example 4

easy

If you double your distance from a planet's centre, how does the gravitational field change?

Example 5

easy

Earth's surface field is

9.8 \text{ N/kg}

. What is the weight of a

10 \text{ kg}

object on Earth?

Example 6

easy

The Moon's surface field is about

1.6 \text{ N/kg}

. Find the weight of a

60 \text{ kg}

astronaut on the Moon.

Moon surface field g

Example 7

easy

Distinguish

g

and

G

g = GM/r^2

. Which is the universal constant?

Example 8

easy

A planet has surface field

20 \text{ N/kg}

. Find the acceleration of a freely falling object near its surface.

Example 9

medium

Planet X has twice Earth's mass and the same radius. Compare its surface field to Earth's

9.8 \text{ N/kg}

Example 10

medium

Planet Y has the same mass as Earth but half the radius. Find its surface field relative to Earth's

9.8 \text{ N/kg}

Example 11

medium

Find Earth's surface field given

M=6\times10^{24} \text{ kg}

R=6.4\times10^6 \text{ m}

G=6.67\times10^{-11}

Example 12

medium

At what height above Earth's surface (

R=6.4\times10^6 \text{ m}

) is the field one quarter of the surface value?

Example 13

medium

Two planets have fields

g_1

and

g_2

. Planet 1 has mass

M

, radius

R

; planet 2 has mass

4M

, radius

2R

. Find

g_2/g_1

Example 14

medium

A satellite is at

r = 7\times10^6 \text{ m}

from Earth's centre (

M=6\times10^{24}

G=6.67\times10^{-11}

). Find the field there.

Find the gravitational field g at r

Example 15

medium

An object weighs

50 \text{ N}

on Earth's surface. What does it weigh at a distance

2R

from Earth's centre?

Object at r

Example 16

medium

4 ext{ kg}

mass weighs

24 ext{ N}

on a planet. Find that planet's surface gravitational field strength.

Example 17

medium

Planet Q has

9

times Earth's mass and

3

times its radius. Find its surface field relative to Earth's

9.8 ext{ N/kg}

Example 18

challenge

A planet has surface field

g_s

. A deep mine sits at half the radius. Treating the planet as uniform density (field

\propto r

inside), find the field there.

Example 19

challenge

Two stars of mass

M

each are a distance

d

apart. Find the gravitational field at the midpoint between them.

Gravitational fields from two equal masses M are equal and opposite at the midpoint — net field

Example 20

challenge

On planet Z, a pendulum's period is

\sqrt{2}

times its period on Earth (same length). Find planet Z's surface field given Earth's is

9.8 \text{ N/kg}

Example 21

easy

0.5\,\text{kg}

stone feels a

4.9\,\text{N}

gravitational pull. Find the local field strength.

Example 22

easy

A planet has

M = 3\times 10^{23}\,\text{kg}

and radius

r = 2\times 10^6\,\text{m}

. Find its surface field. (

G = 6.67\times 10^{-11}

)

Example 23

easy

In a field of

g = 3.7\,\text{N/kg}

, what force acts on a

25\,\text{kg}

rover?

Example 24

easy

At distance

r

from a planet,

g = 8\,\text{N/kg}

. Find

g

at distance

2r

Example 25

easy

A satellite weighs

1500\,\text{N}

on Earth's surface (

g = 9.8\,\text{N/kg}

). Find its mass.

Example 26

easy

A satellite orbits at altitude

h = R

above a planet of radius

R

. By what factor is the field weaker than at the surface?

Example 27

medium

Find the gravitational field at Mars's surface:

M = 6.4\times 10^{23}\,\text{kg}

r = 3.4\times 10^6\,\text{m}

Example 28

medium

At what distance from Earth's center is the field

g = 2.45\,\text{N/kg}

? Use

g_{surf} = 9.8\,\text{N/kg}

R = 6.4\times 10^6\,\text{m}

Example 29

medium

A planet has the same density as Earth but twice the radius. Find its surface field relative to Earth.

Example 30

medium

Find Jupiter's surface field:

M = 1.9\times 10^{27}\,\text{kg}

r = 7.0\times 10^7\,\text{m}

Example 31

medium

Two point masses

M

sit at the ends of a

2L

segment. Find the field at the midpoint.

Example 32

medium

A point lies

r_1 = 3\times 10^8\,\text{m}

from Earth (

M_E = 6\times 10^{24}\,\text{kg}

) and

r_2 = 1\times 10^8\,\text{m}

from the Moon (

M_M = 7.3\times 10^{22}\,\text{kg}

) on the line between them. Find the Earth-produced field at that point. (

G = 6.67\times 10^{-11}

)

Example 33

medium

A free-fall accelerometer reads

a = 1.6\,\text{m/s}^2

on a planet. What is the local gravitational field strength?

Example 34

medium

A spring scale shows

W_1 = 600\,\text{N}

on Earth and

W_2 = 100\,\text{N}

on planet P. Find

g_P

Example 35

hard

At what fraction of Earth's radius above the surface is

g

reduced to

1\,\%

of its surface value?

Example 36

hard

Two stars of masses

M

and

4M

are separated by distance

d

. On the line between them, where is the field zero?

Example 37

hard

On the line from Earth (

M_E

) to the Moon (

M_M = M_E/81

), separation

d

, find the distance from Earth to the null point.

Example 38

hard

A geostationary satellite orbits at

r = 4.22\times 10^7\,\text{m}

from Earth's center. Find

g

there. (

GM_E = 4.0\times 10^{14}

)

Example 39

hard

Two equal point masses

M

sit at

(\pm a, 0)

. Find the field magnitude at

(0, a)

Example 40

hard

A spherical asteroid has mass

M = 1.0\times 10^{15}\,\text{kg}

and radius

r = 5\,\text{km}

. Find the surface field.

Example 41

hard

Estimate the gravitational field on the surface of a neutron star:

M = 1.4 M_\odot = 2.8\times 10^{30}\,\text{kg}

r = 1.0\times 10^4\,\text{m}

Example 42

challenge

A thin uniform ring of mass

M

and radius

R

has field

g(x) = GMx/(x^2+R^2)^{3/2}

on its axis at distance

x

. Find the

x

at which the field is maximum.

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Related Concepts

Gravity Mass Orbital Motion Escape Velocity

Background Knowledge

These ideas may be useful before you work through the harder examples.

gravitymass