# PHYS 2211 Module 12.1

## Newton’s Law of Universal Gravitation 12.1 Newton’s Law of Universal Gravitation

### Learning Objectives

By the end of this section, you will be able to:

• List the significant milestones in the history of gravitation
• Calculate the gravitational force between two point masses
• Estimate the gravitational force between collections of mass

### Newton’s Law of Universal Gravitation

Newton’s law of gravitation can be expressed as

where is the force on object 1 exerted by object 2 and is a unit vector that points from object 1 toward object 2. Practice!

She’s in orbit, so she’s in uniform circular motion. She has a large acceleration! We just said F(grav) is almost the same up there, so her acceleration is almost the same as on earth in freefall, namely, nearly g, directed towards the center of the earth. She’s just like a ball that’s been tossed up in the air, accelerating straight down. The only difference is she has such a large sideways speed that when she has fallen 200 km, she’s gone so far to the side that the curved surface of the earth has moved 200 km away from her, so she’s still 200 km above the ground!!!

F(1 on 2) = F(2 on 1) (in magnitude), that’s Newton’s 3rd Law.

(Or, use F = G M1M2/r2, it’s the same if you reverse M1 and M2) Since Fnet = ma, and Fnet is the same for each, the acceleration of the little one must be 10 times bigger than the acceleration of the big one, 10:1.

The only force acting on either one is gravity, F(grav) = GM(earth)m /r2.  The acceleration is then F/m, and that’s the same for both!!

As it approaches, r is getting smaller so GM/r2 is getting bigger. The acceleration is thus getting larger. It’s not constant.

(It’s only approximately constant when you’re NEAR the surface, because r isn’t changing very much as you go from 6000 km + 0 to 6000 km + 20 feet, for example.) Discuss!

Estimate the force that the moon exerts on you when it is directly overhead.