What does motion do to an orbit?

 

Is the equation for an orbit the same when the whole system is in motion?

 

The centripetal force should be greater when the motion of orbit is in the same direction of the motion of the system and less in the reverse direction but the attraction should not change.

 

That is apposed to the orbit being unaffected by the motion of the system.

 

Which is it?

 

Is the equation for an orbit the same when the whole system is in motion?

 

Since you haven't specified an equation, I am guessing that you are confusing reference frames.

 

You need to start by specifying the reference frame and if that frame centre is always the centre of rotation of the orbiting body then why would there be any change to 'The equation' ?

What does motion do to an orbit?

 

Is the equation for an orbit the same when the whole system is in motion?

 

The centripetal force should be greater when the motion of orbit is in the same direction of the motion of the system and less in the reverse direction but the attraction should not change.

 

That is apposed to the orbit being unaffected by the motion of the system.

 

Which is it?

As long as the motion is not an acceleration, the orbit, in respect to its central body, remains unchanged. Remember, there is no preferred frame, so there is no way to distinguish a "moving" frame from a "non-moving" one.

An equation for orbits is:

 

RV^2 = GM

 

where R is the semi-major axis, V IS velocity, G is the gravitational constant and M is the mass of the central body.

 

When the system is in motion the centripetal force changes. That is consistant with the change in the actual path of the satelite but is it equal to the compensation required to keep the distances between the satelite and the central body the same.

 

The actual path of the satelite is:

 

A stationary ellipse for system velocity of zero.

Like a slinky if the system velocity is slower than the satelite's velocity.

Like a spot on a the tread of a rolling tire if the two velocities are equal.

Like a sine wave if the system velocity is greater than the satelite's.

 

This does not involve relativity, It is just everyday effects. There should be a mathemetical solution.

In fact, riding in a convertable and swinging a ball on a rope probably demonstrates that it is the same.

Your equation is true in the frame of the center of mass. You can add translation to it, but that only complicates the equation. The motion itself is unaffected.