What causes the perpindicular (to the r vector) velocity of a planet to change?

[carrotstien]

Take earth orbiting the sun. The path that earth takes is an ellipse where the sun is at one of the foci. At one time, earth is the closest to the sun and moving the fastest, while at another time, earth is farther from the sun, and travels slower.

My question is thus:

Lets say you take the velocity at any moment and you seperate it into two components, one parallel to the line connecting earth and the sun (the r vector), and on perpindicular to the r vector. Since the force between earth and the sun is always in the direction parallel to the r vector, and always perpindicular to the perpindicular component of velocity, how does that component of velocity change from the min to the max and so on? I understand the need for it to happen due to conservation laws, but I don't see the forces the cause the effect.

[Klaynos]

When you solve the newtonian differential equations you get a graph that looks like this:

 

http://www.theory.caltech.edu/people/patricia/anims/newton1.gif

 

The different orbit shapes are shown on there...

 

This is explained here:

 

http://en.wikipedia.org/wiki/Elliptic_orbit

 

And a full solution to the 2 body problem can be found here:

 

http://scienceworld.wolfram.com/physics/Two-BodyProblem.html

[Mr Skeptic]

Conservation of energy -- since the orbit is not perfectly circular, you get closer and farther to the sun. The difference in gravitational potential energy gets converted to/from kinetic energy.

[carrotstien]

I understand that from the laws of conservation of momentum and energy the velocity must increase. That, however, doesn't answer my question.

My question is of a lower level than that. Why is the speed of an oject moving in a circular orbit always constant, or why does the speed of a charged particle moving in a magnetic field always constant (not counting radiation losses), because the force is always perpindicular to velocity, so that it can only change the direction but not the magnitude.

In the elliptical case, the force is always perpindicular the perpindicular componant of the velocity, perp to the r vector, so I don't see why by the same logic does the perp velocity change.

Once again I'd like to point out that I understand that it must in order for conservation to work, but that doesn't explain the source of the force.

Maybe i'm just thinking this in a wrong way.

[Mr Skeptic]

No, only in a circular orbit is the force perpendicular to the motion. In the elliptical orbit there is a parallel portion, which changes the speed of the planet as it gets closer or farther from the sun. If the force was only perpendicular, then there could be no change in potential energy (hence, the orbit would have to be circular)

[carrotstien]

thanks Mr Skeptic. I understood that, but for some reason after you said it it all began to make sense. The speed gets changed by the tangential force, while the perpendicular force later takes this increases speed and changes its direction.