In the first lesson, I mentioned that the "apple story" isn't 100% accurate in the way it's usually told. First, Newton was not "bonked" by an apple. Second, he didn't "discover" gravity; he simply started thinking about it in a new way.

Newton started thinking about the fact that objects don't necessarily fall perpendicular to the ground. If you're standing on the side of a hill, an object you drop won't fall directly toward the ground. It will fall at a non-perpendicular angle to the ground. That's not a surprising observation; you could have told us the same thing, if you'd stopped to think about it for a minute!

Newton concluded that everything falls toward the center of the earth, not just toward the ground. So he started wondering, "Why would an object fall toward the center of the earth, instead of falling in some other direction?" and also, "Why wouldn't an object fall toward me or toward a house instead of toward the center of the earth?"

His answer was that the more massive an object is, the more gravitational pull it has on other objects. Wait a minute! Newton seems to be suggesting that other objects besides the earth exert gravitational pulls, only those forces are tiny, because other objects are tiny compared to the earth.

Yes, that's exactly right. And that was a novel concept, that everything exerts a gravitational pull on everything else!

Eventually, Newton developed a big old formula to predict how much gravitational force one object exerted on another. Would you like to see the formula? Here it is:

F = Gm₁m₂/r²

G is what we refer to as the gravitational constant, and it is approximately equal to 6.67300 × 10^-11.

m₁ and m₂ are the masses of the two objects.

r is the distance between the centers of the two objects.

Example 1
My mass is 90kg. The mass of the earth is 5.972 × 10²⁴. The radius of the earth is 6,371,000 m. What is the force of gravitational pull between me and planet earth?

Answer 1
F = 6.67300 × 10^-11 × 5.972 × 10²⁴ × 90 / (6,371,000)². You'll want a calculator to grind that out. The result is: 883 Newtons. You know what that is, don't you? It's my weight in Newtons!

Example 2
Jack and Jill are out in space, floating 1 meter apart. Jack's mass is 80 kg, and Jill's mass is 60 kg. What is the pull of gravity between them?

Answer 2
This is kind of a fun problem; most people don't think about two objects as small as human beings exerting a gravitational force on each other, but we can use the same formula as before to calculate the force they exert on each other! Using 80 and 60 for the two m values, and 1 for r, we find that F = 0.0000000320304. It's a very tiny force, but it's a force nonetheless.

Incidentally, depending on Jack and Jill's initial velocities, it is possible that these two people would end up orbiting each other in space!

1.

If the earth is exerting a force of 883 Newtons on me, what is the force I'm exerting on the earth?

2.

If I'm exerting a force of 883 Newtons on the earth, what acceleration does that cause the earth have toward me?

3.

What is the force of attraction between two people floating in space if they have masses of 80 Newtons and 60 Newtons, and the distance between them is 2 meters?

4.

In the previous question, what acceleration will the person with mass 80 Newtons have?