# Homework Help: Circularisation of Orbit

Tags:
1. May 19, 2015

### thespoonftw

1. The problem statement, all variables and given/known data

A body on an orbit with semi-major axis a and eccentricity e undergoes tidal circularisation.

Show that the orbit will circularise at a semi-major axis, acirc, given by

acirc = 2rperi = 2a (1 − e).

2. Relevant equations

No equations given, but I think the following could be useful

E = -GMm/2a
e2 = 1 - b2/a2

3. The attempt at a solution

An earlier part of the question hints at L conservation

Equating centripetal force and grav force for the circular orbit gives:
L = m (GMR)0.5

Finding the velocity at the closest point in orbit r = a(1-e)

E = -GMm/2a = 1/2 mv2 - GMm/a(1-e)

simplifies to
v2 = GM(1+e)/rp

Equating L2
L2 = GMm2 rp (1+e) = GMm2 rc

Finally:
rc = rp (1+e)

This is close to the final answer, but not quite!
Somethings gone wrong somewhere but I'm sure what.. I've checked my working several times.
Sorry a lot of my working lines are missing, it's quite tricky to type them all out.

2. May 19, 2015

### Staff: Mentor

You have to find out which quantities are conserved during the process. Energy, angular momentum, or something else?

That cannot be the final semi-major axis. Consider the trivial case of e=0, for example, where the semi-major axis will certainly not double.
It could be twice the semi-major axis.

3. May 19, 2015

### thespoonftw

Oh, well spotted with the trivial case.
Yea it looks like there's something wrong the question, and i think my method was fine.