I know that the net centripetal force (center seeking) is equal to the gravitational force of the Sun on the Earth, and that this is the only net force in the system. In other words, there are no other forces at work – if there were another force (centrifugal) at work in the system, the Earth would move off in a straight line.
Is the centrifugal force a valid force in the rotating frame of the Earth or is it simply fictitious and invalid?
Is it valid in an inertial frame?
Are there any valid equations for determining centrifugal forces in an orbital system?
Seems to me that you need to sit down with a good physics text.
Newton’s laws hold in inertial reference frames (ignoring relativity). Centripetal force is the term given to any force that causes a body to move in a circle. In the case of the Sun-Earth system, and ignoring all other planets, etc, the centripetal force is their mutual, gravitational attraction, which is what I think you were trying to say.
It is quite possible to rework Newton’s laws for rotating coordinate systems. For example, a coordinate system with it’s origin at the center of the sun and rotating with a period equal to one year. In such a system, all sorts of “fictitious” forces appear. They are not invalid, they are necessary so that motion calculated in a rotating frame agrees with the motion calculated in an inertial frame. Centrifugal and coriolis forces are of this sort.
Any orbiting object and everything on it is in free fall, so there is no centrifugal force (which is the perceived push as your container frame of reference changes direction (ie accelerates) and you don’t).
There will be tidal forces, which are similar: the acceleration of part of the body is too much/too little to match the free fall orbit so it wants to drift away from the centre of gravity.
Thanks guys – I think you did answer my questions but I think I’m still a little unclear. I was looking at this paper, which indicated that centrifugal forces simply do not exist and that if they did, the object in question would not orbit but instead would move in a straight line. Any comments?
In the appropriate (in this case, co-rotating) reference frame, a body in orbit does have a centrifugal force acting on it. But that centrifugal force is exactly cancelled by gravity, so you don’t feel anything (neither the centrifugal force nor gravity). In this reference frame, centripetal force is wrong.
This interpretation is valid if and only if you’re working in the co-rotating reference frame. If you’re working in an inertial reference frame, then centrifugal force is wrong, and you use centripetal force. And if for some reason you’re working in a reference frame which is neither inertial nor co-rotating, then you’ll need to use some combination of centrifugal and centripetal forces, plus possibly yet some other fictitious forces. But one would hope you’re not masochistic enough to do that.