What is the Force Generated by a Non-Elliptical Orbit Planet?

[Tom1]

Homework Statement

A planet around a star has an orbit that is not exactly an ellipse. In addition to the dominant Fo \alpha r^-2 term due to gravity from the central star, the planet seems to be responding to a slight additional force which has the form F1 \alpha r^-\alpha where \alpha is some constant.

Homework Equations

Included in 1.

The Attempt at a Solution

Where do I begin?

 

[Kurdt]

I have no idea since I don't know what you're supposed to be doing.

 

[Tom1]

Sorry, part of this seems to have been cut off.

Assuming there is a slight background density of material with spherically symmetric density p1 falling off as p1 (alpha) r^-B

Find the value of B in terms of alpha

 

[Tom1]

Can anyone help me get started please? I don't understand this at all and it's due soon.

 

[Dick]

Near as I can tell you want to assume there is a mass distribution with density rho(r)=p1*(r/r0)^(-B). Now you want to figure out the radial dependence of the force it generates. Compute total mass as a function of r, M(r). Use that to calculate the force.