Big anaconda orbiting the planet

[paul-g]

Homework Statement

Big anaconda orbiting the planet XYZ-123 in a vertical position (along the radius of the planet and at a constant height). At some point, anaconda folded her in a small bundle. Is its orbit will be circular? He begins to recede from or approach the planet?


2. The attempt at a solution

I know that the anaconda was able to perform the action described in the command have to do some work. It seems to me that it would start by moving away from the planet, but I do not know how to prove it.

 

[WatermelonPig]

Is angular momentum conserved?

 

[paul-g]

There is no information about it, but I think yes.

 

[gneill]

Why not choose some numbers for an example and work out a figure for the angular momentum of the snake stretched out (so going from say, radius r1 to radius r2). Then determine at what radius the compact body would want to orbit with that same angular momentum. Compare this and that.

 

[paul-g]

I thought to write it this way

E_{p}=-\frac{GMm}{r}

F=ma

\frac{GMm}{r^2}=\frac{mv^2}{r}

\frac{mv^2}{2}=\frac{GMm}{2r}

E_{k}=-\frac{E_{p}}{2}

E=E_{k}+E_{p}=\frac{GMm}{2r}-\frac{GMm}{r}

E=-\frac{GMm}{2r}



This applies to the circular orbit, but in our case:

E_{k}=E_{k_{1}}-W

E=E_{k_{1}}-W+E_{p}

How to prove that the orbit is not circular. This is enough? Snake gave up and will be circulated in the orbit of larger radius, or begin to move away from the planet?