Unit: Force of Gravity Module: Gravity [page 1 of 2] Newton’s Law of Gravitation www.thinkwell.com [email protected] Copyright 2001, Thinkwell Corp. All Rights Reserved. 1994.doc –rev 04/03/2001 • Newton’s law of gravitation is the general formula for the force of gravity between two objects: 1 2 2 grav GM M F r = . • The force of gravity attracts objects toward one another with equal and opposite force. • The force of gravity decreases rapidly with distance. • Gravity superposes. Newton’s second law applied to any object near the Earth’s surface is F mg = . Although this formula is not exact, it is an excellent approximation. Newton’s law of gravitation is the general formula for the force of gravity between two objects: 1 2 2 grav GM M F r = , where G is a constant of nature, M 1 and M 2 are the masses of two objects, and r is the distance between the objects’ centers of mass. Notice that the force of gravity on the first mass toward the second has the same magnitude as the force gravity on the second mass toward the first. Prof. Pollock stands 2 m from the camera. Prof. Pollock’s mass is 60 kg and the mass of the camera is 10 kg. If there were no other forces, Prof. Pollock and the camera would accelerate toward each other because of the gravitational force between them. The frictional force between Prof. Pollock and the floor prevents his acceleration toward the camera. You can calculate the force of gravity between Prof. Pollock and the camera using Newton’s law of gravitation. The result is 8 1 10 N − × , an extremely small force. The weight of a mosquito is 30,000 times larger than the gravitational force of the camera on Prof. Pollock.

Unit: Force of Gravity Module: Gravity [page Newton’s …notes.… · Unit: Force of Gravity Module: Gravity ... • Newton’s law of gravitation is the general formula for the

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Unit: Force of Gravity Module: Gravity [page 1 of 2]

Newton’s Law of Gravitation

• Newton’s law of gravitation is the general formula for the force of gravity

between two objects: 1 22grav

GM MFr

= .

• The force of gravity attracts objects toward one another with equal and opposite force.

• The force of gravity decreases rapidly with distance.

• Gravity superposes.

Newton’s second law applied to any object near the Earth’s surface is F mg= . Although this formula is not exact, it is an excellent approximation.

Newton’s law of gravitation is the general formula for the force of gravity between two objects:

1 22grav

GM MFr

= , where G is a constant of nature, M1

and M2 are the masses of two objects, and r is the distance between the objects’ centers of mass. Notice that the force of gravity on the first mass toward the second has the same magnitude as the force gravity on the second mass toward the first.

Prof. Pollock stands 2 m from the camera. Prof. Pollock’s mass is 60 kg and the mass of the camera is 10 kg. If there were no other forces, Prof. Pollock and the camera would accelerate toward each other because of the gravitational force between them. The frictional force between Prof. Pollock and the floor prevents his acceleration toward the camera.

You can calculate the force of gravity between Prof. Pollock and the camera using Newton’s law of gravitation. The result is 81 10 N−× , an extremely small force. The weight of a mosquito is 30,000 times larger than the gravitational force of the camera on Prof. Pollock.

Unit: Force of Gravity Module: Gravity [page 2 of 2]

Newton’s Law of Gravitation

According to Newton’s law of gravitation, gravity decreases as the square of the distance between two objects.

If the distance between two objects doubles, the force of gravity is four times smaller.

If the distance between two objects triples, the force of gravity is nine times smaller.

There is a force of gravity between any two objects, however, if r is large enough, the force will be very small.

An object M is a distance r from m. Another object M’ is a distance r’ from m. How do you determine the force of gravity on m?

Gravity superposes, that is, the forces of gravity add like vectors. First determine the force of M on m, which originates at m and points toward M. Then determine the force of M’ on m, which originates at m and points toward M’. Add the two vectors and the resultant is the net force of gravity on m.

Note that Newton’s law of gravitation is not an explanation but instead a description of gravity.