Newton’s Universal Law of Gravitation

Answer Me!!!

How does the force of gravity affect objects with similar (very large) masses?

Force Due to Gravity

Gravitational Force (FG) is the attractive force between two objects.

Gravitational Force can be determined by:

G is universal gravitational constant (6.67x10-11 N*m2/kg2)

r is radius or distance between centers

221

r

mGmF G

Example: Earth-Moon

Earth Moon

FG from Earth pulls on Moon

FG from Moon pulls on Earth

EQUAL AND OPPOSITE

Calculate the force of gravity between the Earth and the Moon. (Hint: Use your reference Table)

List of Physical Constants

Name Symbol ValueUniversal Gravitational Constant G 6.67 x 10-11 N*m/kg2

Mass of Earth 5.98 x 1024 kg

Mass of Moon 7.35 x 1022 kg

Mean distance: Earth to Moon 3.84 x 108 m

NF

m

kgkgF

r

mGmF

G

kgmN

G

G

20

28

222411

221

100.2

)1084.3(

1035.71098.51067.6 2

2

Practice Problem 1

When a satellite is a distance R from the center of Earth, the force due to gravity on the satellite is F. What is the force due to gravity on the satellite when its distance from the center of Earth is 3R?

Final Thought…

An object weighs 100N on the Earth’s surface. When it is moved to a point one Earth’s radius above the Earth’s surface, what will it weigh?

Answer Me!!!

If there were no nearby objects to feel Earth’s gravity, would there be a gravitational force? Explain.

Gravitational Field Strength

A gravitational field is a region where gravitational force has the potential to exist.

Gravitational Field Strength is a measure of how strong the force due to gravity is at that location.

You know it as the acceleration due to gravity.

Gravitational Field Strength

Remember:

2

objectplanetG

object

G

r

mGmF and

m

Fg

Practice Problem 3

The following graph represents the relationship between gravitational force and mass for objects near the surface of Earth. What does the slope of the graph represent?

Mass

Gra

vita

tio

nal

Fo

rce

Practice Problem 4

A 70kg astronaut has a weight of 560N on the surface of planet Alpha. What is the acceleration due to gravity on planet Alpha?