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

[physio]

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?

 

[A_B]

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).


A_B

 

[ZapperZ]

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.

 

[A_B]

Just found this:
http://nowykurier.com/toys/gravity/gravity.html

Try placing two masses (use the big ones or else its way to slow) near each other at rest. They will collide.

 

[pmacias]

I can provide an explanation for why planets do not smash into each other despite the universal law of gravitation. Firstly, it is important to understand that while the force of gravity is present between all objects in the universe, its strength is affected by the masses and distances of those objects. In the case of planets, their masses are so large and their distances from each other are so vast that the force of gravity between them is relatively weak.

Additionally, planets are in constant motion due to their orbit around the sun. This motion creates a centrifugal force that counteracts the gravitational force, preventing the planets from crashing into each other. This can be compared to a satellite orbiting the Earth - it maintains a constant distance from the Earth due to a balance between the gravitational force pulling it towards the Earth and the centrifugal force pulling it away.

Furthermore, the planets in our solar system also have relatively stable orbits due to the overall balance of gravitational forces between them. Any slight changes in these forces, such as the gravitational pull of a passing asteroid or comet, can cause the orbits to shift slightly but not enough to cause a collision.

In regards to the charge analogy, it is important to note that gravity and electromagnetic forces are fundamentally different. While electromagnetic forces can repel or attract based on the properties of the charges, gravity is always an attractive force. In the case of planets, their masses are not repelling each other, but rather the force of gravity is pulling them towards each other.

In conclusion, the reason why planets do not smash into each other is due to a delicate balance of forces - the gravitational force, centrifugal force, and stable orbits. This balance is maintained by the vast distances and large masses of the planets, as well as the overall stability of our solar system.