Universal Gravitation The most abstract topic of first semester

True or False? There is a force of attraction at the earth’s surface. The force of attraction between an object and the earth depends on the mass of the object. The acceleration of a falling object depends on the mass of the object. The force of attraction between an object and the earth is called the weight of the object.

True or False? On a mountaintop, the acceleration of falling objects is less than at the earth’s surface. If you go high enough, the force of attraction becomes zero. There is no gravity in space. Every object attracts every other object. The farther two objects are apart, the less the gravitational force of attraction.

Gravitation Basics M 1 M 2 Force on 1 Force on 2 R

Gravitation Basics The force on object One equals the force on object _ _ _. Recall the _ _ _ _ _ law.

Gravitation Basics The force on object One equals the force on object Two. Recall the third law.

Gravitation Basics The force on object One equals the force on object Two. Recall the third law. The force is proportional to the mass of object _ _ _.

Gravitation Basics The force on object One equals the force on object Two. Recall the third law. The force is proportional to the mass of object One. F  M 1

Gravitation Basics The force on object One equals the force on object Two. Recall the third law. The force is proportional to the mass of object One. F  M 1 The force is also proportional to the mass of object _ _ _.

Gravitation Basics The force on object One equals the force on object Two. Recall the third law. The force is proportional to the mass of object One. F  M 1 The force is also proportional to the mass of object Two. F  M 2

Force varies dramatically with Distance DistanceDist 2 Force /4 = /9 = /16 = 0.04

Gravitation and Distance (R) The farther apart the objects, the _ _ _ _ the attraction.

Gravitation and Distance (R) The farther apart the objects, the less the attraction.

Put all our ideas together

Change the proportionality to an equality by including a constant.

G The universal gravitation constant was measured by Cavendish and Jolly. G is very _ _ _ _ _. G = 6.67 x Nm 2 /kg 2

G The universal gravitation constant was measured by Cavendish and Jolly. G is very small. G = 6.67 x Nm 2 /kg 2

And now, a quiet moment to contemplate what keeps the moon in earth orbit.

Gravity Man, don’t feel so sad. “But with such a small constant, I’m the weakest force (…sob…) in the universe!” Yes, it’s true that for two small charged particles, Gravity is less than the Electrical force. But for uncharged big things like planets and galaxies, the electrical forces cancel out and you, … you rule the Universe!

Two planets are orbiting a star.

One planet is twice as far from the star. Yet the force the star exerts on the two planets is the same. What is different about the two planets?

The more distant planet must have more _ _ _ _.

The more distant planet must have more mass.

A 2 kg object is 6.38 x 10 6 m from a 5.98 x kg object. What is the force of attraction? What is the acceleration of the 2 kg object?

a = _._ m/s 2 !!! Why the familiar result? The large mass given must be the mass of the _ _ _ _ _. The distance given must be the _ _ _ _ _ _ of the _ _ _ _ _.

a = _._ m/s 2 !!! Why the familiar result? The large mass given must be the mass of the EARTH. The distance given must be the _ _ _ _ _ _ of the _ _ _ _ _.

a = _._ m/s 2 !!! Why the familiar result? The large mass given must be the mass of the EARTH. The distance given must be the RADIUS of the EARTH.

Repeat the problem, except replace the 2 kg with 3 kg. What is the new force? What is the new acceleration?

Why is the acceleration of all falling objects the same?

The acceleration of m does not depend on m! (And the acceleration of M does not depend on M)

Horsehead Nebula