- #1
thespoonftw
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Homework Statement
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).
Homework Equations
No equations given, but I think the following could be useful
E = -GMm/2a
e2 = 1 - b2/a2
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.