Center of Force: Exploring its Meaning & Location

[pimpalicous]

What exactly is the "center of force"?

For instance, you use reduced mass to make an orbital problem one body. Is the center of force the r "seperation between the bodies"? Or is the center of force at the center of mass? In an ellipse, the center of mass is always at one of the foci, right?

 

[mathman]

When dealing with gravity, a spherically symmetric object can be treated as if the entire mass was at the center of mass, so r in the force of gravity equation is measured from the center of mass.

Your statement about the ellipse is correct.

 

[charng]

The center of force refers to the point where the net force acting on a system is considered to be concentrated. In the case of a two-body system, this point is typically located between the two bodies, but its exact location can vary depending on the arrangement and distribution of mass within the system.

The reduced mass is a concept used to simplify the motion of two bodies by reducing it to a one-body problem. In this case, the center of force would be the point where the reduced mass is located, representing the combined effect of both bodies.

In an elliptical orbit, the center of mass is indeed located at one of the foci, but the center of force may not necessarily be at the same point. This is because the gravitational force exerted by one body on the other is not uniform throughout the elliptical orbit, and therefore the center of force may be slightly shifted from the center of mass.

It is important to note that the center of force is a theoretical concept and may not always have a physical location within a system. It is a useful tool for analyzing and understanding the dynamics of a system, but it does not necessarily correspond to a tangible point in space.