Universal Law of Gravitation

Universal Law of Gravitation

So because of Newton’s 3rd law every body in the universe exerts a force of attraction on

every other body.

• This is Newton’s Universal Law of Gravitation

The force between two objects, due to their masses, is called the gravitational force (Fg)- in this case it’s not Earth specific and is not 9.81 m/s2).

FGmM

rg 2

FGmM

rg 2

Masses of the 2 objects

Distance betweenthe objects

UniversalGravitationalConstant- 6.67 x 10-11 N

m

kg

2

2

What is the gravitational force between the Earth and the Moon?

mEarth = M = 6.0 x 1024 kg

mMoon = m = 7.4 x 1022 kg

r = 3.8 x 108 m

G = 6.67 x 10-11 Nm

kg

2

2

What if the distance between the Earth and the Moon was doubled?

What if the distance between the Earth and the Moon was tripled?

What if the distance between the Earth and the Moon was quadrupled?

What is the gravitational force between the Earth and Venus?

mEarth = M = 6.0 x 1024 kg

mVenus = m = 5.0 x 1024 kg

r = 3.8 x 1010 m

G = 6.67 x 10-11 Nm

kg

2

2

Solving the ULG equation using variables:

FGmM

rg 2

= 100 N

Fg’ = ? If M’ = 3M, and r’ = 2r

F’g = GmM’ r’2

= Gm3M (2r)2

= Gm3M 4r2

= 3 GmM 4 r2

= 3 (100 N) 4

75 N

There is also a way to determine the gravitational field around one object:

FGmM

rg 2

For one object this is weight, so this becomes…

wGmM

r 2

mgGmM

r 2

mg

GmM

r 2g

GM

r 2= =

This is nowthe gravitationalField Strength

For the Earth the gravitational field strength should be 9.81

m/s2…find it.

• Radius of the Earth – 6.37 x 106 m

For the Moon the gravitational field strength should be

1.6 m/s2…find it.• Radius of the Moon – 1.7 x 106 m

Both the ULG and the GFS follow the Inverse square law:

• ULG-If the distance between two objects is doubled the gravitational attraction is (1/4) of the original.

OR

• GFS-If we travel beyond the Earth by a distance that is double it’s radius than we will only feel a quarter of Earth’s gravitational pull (9.81 m/s2/4 = 2.45 m/s2).

2x 3x 4x

1/4 = 2.24

1/9 =1.09

1/16 =.61

1x

r = 6.4 x 106 m

9.81 m/s2

Inverse Square Law

0

2

4

6

8

10

12

0 10000000 20000000 30000000

Distance(m)

Gra

vita

tio

nal

Fie

ld S

tren

gth

GravitationalField Strength

HW:

• The gravitational attraction between the Earth and Mars is 8.7 x 1016 N. The distance between the two planets is 5.5 x 1010m. Earth has a mass of 6.0 x 1024 kg. What’s the mass of Mars?