Actually, the smaller object exerts the same force on the larger object.
('Same' meaning equal but opposite, of course.)
The gravitational force exerted on body1 by body2 is determined entirely by both their masses, the universal constant G, and the inverse of the square of the distance between them.
It's totally indpendent of which object is bigger (and also independent of which is more massive, if you want to get nitpicky about terms).
For similar and derived laws, see Kepler's Laws, or Newtons.

When I was but a young tyke, I wondered what was the big deal with Newton 'discovering' gravity. I mean, we all knew it was there, right? Surely something was holding us down. What could be so radical about a theory of gravity?

Plenty, it turns out.

As for the formula itself, it was derived from Newton's earlier Laws of Motion, a bit like this. Due to the Second Law of Motion, F = M * A, the force on a falling apple is dependent on its mass, and when the apple hits, the Earth recoils as per the Third Law of Motion (the equal/opposite reaction one). When you combine that with Kepler's previous Laws of Planetary Motions to get distances, you find out that the gravitational strength is inversely proportional to the square of the distance which separates the centers of the Earth and the object, times a constant. It's neat that this came about from his previous laws, but that's just math, really. I bet you could come up with that just by carefully measuring movements and fitting an equation to the data. So what was so great about the law?

The first mindblowing result about the law - it was the first scientific principle to claim action at a distance, where one object affects another invisibly without actually meeting it. As I understand, many thinkers just refused to accept this, and many theologians took the concept and ran with it as proof of God. I mean, realize what was being said here - you can move an object without touching it. That's damn near sorcery.

But that one still wasn't the big breakthrough. Try this on for size - you know the pictures of Newton sitting underneath the apple tree, contemplating both an apple in his hand and the bump on his noggin? What you may not notice is that the moon will usually figure prominently in the background. That's because, in the unabridged story (that I never heard), Newton got bonked by the apple, and then looked at the moon - and questioned if the very same force that caused the apple to drop on his head is keeping the moon floating in the sky.

No one, and I mean no one, ever thought about this before. The laws that existed on the Earth and the laws that existed in the sky were totally seperate, no overlap, no nothing. It made sense - how could you say that the night skies were the same as they were on Earth, the center of the universe? How could they be?

Newton's line of questioning, and later realization that gravity does, in fact, hold the moon over the Earth by the magic of orbits, broke scientific inquiry wide open. People began to look for fundamental truths along those lines - that the physical laws on Earth were the same ones that ruled the night sky. This idea, the so-called 'principle of universiality', is held to be scientific dogma today. Any discovery, to be truly valid, must be true everywhere. No exceptions. And that's why Newton's discovery isn't called the Law of Gravitation, it's called the Law of Universal Gravitation. The equation was the end, but the means to get there has guided scientists in the centuries since.

A postscript, dated August 17, 2000 : You know, action at a distance has since been disproven, I think, first by Einstein, then refined to fit quantum mechanics by others. Somehow, IIRC, gravity moves in that quantum wave/particle duality, carried by gravitons. But that's all I can say, because I don't understand 20th century physics. Maybe once I get beyond 18th century physics, I'll give it a look.

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