Gravitation - Why don't planets smash into each other?

Gravitation -- Why don't planets smash into each other?

Why don't planets smash into each other? The universal law of gravitation states that everything pulls everything else in the universe. Using this logic shouldn't the Sun move because it should be experiencing the pulling force from so many planets?

Using the charge analogy if a positive charge is kept in the vicinity of a negative charge, there is a force on the charges and both of them accelerate towards each other, why doesn't this apply to the planets?

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An interesting way to see this is Newton's cannonball.
http://en.wikipedia.org/wiki/Newton%27s_cannonball
http://waowen.screaming.net/revision/force&motion/ncananim.htm

In the Feynman Lectures, Feynman talks you through a simple numerical approximation of the motion of a planet which is also very instructive.

For a more technical derivation see any book on classical mechanics (Goldstein for example, or Landau has a very nice exposition as well).

The case of electrically charged particles is completely equivalent, they to do not collide provided their velocities are not along the line joining the particles (and ignoring radiation).

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ZapperZ
Staff Emeritus

Why don't planets smash into each other? The universal law of gravitation states that everything pulls everything else in the universe. Using this logic shouldn't the Sun move because it should be experiencing the pulling force from so many planets?
If I take two planets and place them at a distance apart, and they are stationary to each other, then yes, they will smash into each other.

Now, go back to the situation of planets, etc. What is different here than what I just described? Is the energy of the system ONLY in the attractive potential energy, or is there ANOTHER energy component here that might balance that out?

Secondly, if two bodies are off approximately the same mass, the system will consist not of one body orbiting the other, but both of them moving around some point in between them (the center of mass). So in this case, there is a clear evidence that, yes, they are pulling on each other, and each one is being pulled by the other.

Zz.

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