Gravitational Fields

although Earth and the

Moon do not touch,

they still exert forces on

each other

Michael Faraday

developed the idea of a

field to explain “action

at a distance”

a field is defined as a sphere of influence where one object can exert a force on another without direct contact

all masses are surrounded by a gravitational field

the field exerts a force on any other mass placed in the field

direction of the field is

always to the centre of

the object causing the

field

field direction is indicated

by the use of field lines

the field lines indicate the

direction of the force

acting on another mass

placed in the field

Field lines that are far

apart mean the field is

weaker here

The field is radially

inward

near the surface of Earth, the field lines appear to be at right angles to the surface

The parallel field lines means the direction is the same

Equal spaces between the field lines means the magnitude is the same

gravitational fields are vector fields

(magnitude and direction)

the field extends to infinity

The gravitational field vector at any location

in space is found by placing a test mass m at

that point and measuring the force acting on

it.

g

gF

gm

Gravitational

field strength

Units N/kg

(same as m/s2)

gravitational

force acting

on mass in

field

Mass in gravity field

(‘test mass’)

Magnitude of gravitational field strength

g = field strength N/kg at a

point in space

G= Universal Gravitational Constant

m = mass of object causing field

r = distance from centre of object causing the field

2r

Gmg

the value of g depends on the distance from

the centre of the planet and geology (value of

g is higher close to dense rock such as metal

ore deposits)

Astronauts repair the

Hubble move than 300

km above the coast of

Australia

Yellow and red are regions of high g values

Chicxulub

gravity map

Example

Determine the magnitude of the gravitational

field strength on the surface of Mars (mass =

6.37 x 1023 kg, r = 3.43 x 106 m).

Solution

2

211 236.67 10 6.37 10

2

263.43 10

gGm

r

mN kg

kg

m

g

g = 3.61 N/kg

Example

Determine the

acceleration of gravity

900 km above the

surface of Earth.

Solution

3

2

211 246.67 10 5.97 10

2

266.37 10 900 10

Gm

r

mN kg

kg

m

g

g

m

g = 7.53 N/kg

When many masses are present, each mass

contributes its own field to each point in space.

To find the net field strength, use vector algebra

to find the value and direction.

Example

Two 6.9 x 103 kg objects are arranged as shown.

Determine the net gravitational field at point P.

A B

Solution find the field

caused by each

mass

Ignore mass B, the

field caused by A

will not be

influenced by mass

B.

3

11

2

2116.67 10 6.9 10

2

2130

2.723 10 / left

A

Gm

r

mN kg

kg

g

gm

N kg

Ignore mass

A, find the

field caused

by mass B

3

10

2

2116.67 10 6.9 10

2

250

1.8409 10 / left

B

Gm

r

mN kg

kg

g

gm

N kg

Net |g| = 2.1 x 10-10 N/kg left

Tides

Tides rise and fall because the moon's

gravity pulls the water into a tidal bulge which

the earth rotates under.

On the side of the Earth nearest to the moon, the

pull from the Moon is the strongest. It's clearly

stronger than the pull from the Moon at locations

on Earth further away from the Moon

Because the gravitational pull from the Moon is

less at the farthest-from-the-Moon point than it

is at other locations on the surface of the Earth,

the water at this point is literally left behind.

The sun and

the moon can

make tides

much larger

than usual,

depending on

their position

Inertial & Gravitational Mass

Inertial mass measures the inertial resistance

to acceleration of the body when responding to

all types of force.

𝑎 =𝐹𝑛𝑒𝑡𝑚

Inertial & Gravitational Mass

Gravitational mass is determined by the

strength of the gravitational force experienced

by an object when in the gravitational field g.

𝐹𝑔 = 𝑚𝑔

Inertial mass and gravitational mass are equal

AP Example

A plant’s radius is measured from orbit to be

7.01 x 106 m. An ‘away team’ lands and

measures the gravitational field strength to be

10.4 N/kg.

A) determine the mass of the planet

B)

Determine the average density of the planet.

m

V 34

3V r

C)

If the density of the surface material is 2.7,

what conclusions can you make about the

planet?

Practice

P 219: 1, 2

P 220: 1, 2, 3