Universal Law of

Gravitation

http://ed.ted.com/lessons/jon-bergmann-how-to-think-about-gravity

EQ: What is Newton’s law of universal gravitation and how does the mass and distance between objects affect

the gravitational force?

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)- the gravitational force is affected by mass and

distance.

FGmM

rg 2

FGmM

rg 2

Masses of the 2 objects (kg)

Distance between

the objects from their center (m)

Universal Gravitational Constant-

6.67 x10-11 N

m

kg

2

2

Gravitational force (N)

Example 1: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 mG = 6.67 x 10-11 N

m

kg

2

2

Fg = 2.1 x 1020

Example 2: 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 mG = 6.67 x 10-11 N

m

kg

2

2

Answer:

F = 1.386x1018 N

The sun has a mass of 2.0 x 1030 kg and a radius of 7.0 x 105 km. What mass must be located at the sun’s surface for a gravitational force of 470 N to exist between the mass and the sun?

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?

Answer behind Exit Ticket:

Distance also plays a role in the force of gravity.

-Explain how the force changes with respect to distance.

-Explain how the acceleration between 2 objects changes with respect to distance.

(Hint: think about Newton’s 2nd Law of motion and the relationship between force,

mass, and acceleration )

FGmM

rg 2

Determine the force of gravitational attraction between the earth (m = 5.98 x 1024 kg) and a 70-kg physics student if the student is standing at sea level, a distance

of 6.38 x 106 m from earth's center.

Determine the force of gravitational attraction between the earth (m = 5.98 x 1024 kg) and a 70-kg physics student if the

student is in an airplane at 40000 feet above earth's surface. This would place the

student a distance of 6.39 x 106 m from earth's center.

There is also a way to determine the

gravitational field around one object:

FGmM

rg 2 w

GmM

r 2 mg

GmM

r 2

mgGmM

r 2g

GM

r 2

This is now

the gravitational

Field Strength(GFS)

Example 3: What is the Gravitational Field Strength in

Earth?

• Radius of the Earth – 6.37 x 106 m

Is Gravity Diluted?

The distance d is in the denominator of this relationship, it can be said that the force of gravity

is inversely related to the distance. This mathematical relationship is sometimes referred to

as an inverse square law since one quantity depends inversely upon the square of the other

quantity

Check your understanding

Suppose that two objects attract each other with a gravitational force of 16 units. If the distance between the two objects is doubled, what is the new force of attraction between

the two objects?

Answer: F = 4 units

If the distance is increased by a factor of 2, then force will be decreased by a factor of 4 (22). The new force is then 1/4 of the

original 16 units.

F = (16 N) / 4 = 4 units

Check your understanding

Suppose that two objects attract each other with a gravitational force

of 16 units. If the mass of both objects was doubled, and if the distance between the objects

remained the same, then what would be the new force of attraction

between the two objects?Answer: F = 64 units

If each mass is increased by a factor of 2, then force will be increased by a factor of 4 (2*2). The new force is then 4 times

the original 16 units.

F = (16 units ) • 4 = 64 units

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

¼ re=

2.24 m/s2

1/9 re =

1.09 m/s2

1/16 re =

.61 m/s2

1x

re = 6.4 x 106 m

1 re =

9.81 m/s2