# Motion in a Central Gravitational Force

1. Feb 26, 2017

### Macykc2

1. The problem statement, all variables and given/known data
Discuss the motion of a particle in a central inverse-square-law force field for a superimposed force whose magnitude is inversely proportional to the cube of the distance from the particle to the force center, that is:
F(r) = -k/r2 - λ/r3 and k,λ>0​
Show that the motion is described by a precessing ellipse.

2. Relevant equations
The one given in the question

3. The attempt at a solution
I honestly don't know where to begin, we derived an equation in class that we could find the force law if a particular known orbit r=r(θ), and I was thinking of using it:
(d2/dθ2)(1/r) + (1/r) = -μr2F(r)/l2
but I don't know what to do with the left hand side, but again it's just a guess as to what to start with.
Sorry for not using the math commands, they didn't want to work for some reason.

2. Feb 26, 2017

### Simon Bridge

You need to solve the differential equation.

For equations, you can type out LaTeX markup directly.

You may want to back up a bit and make sure you understand the motivation for deriving the equation you used in the first place... see if the same approach still applies here.