The leading theory for the origin of the Moon is the giant impact hypothesis, in which the Moon was formed out of the debris left over from the collision of a Marssized body with the Earth.1 Soon after its formation, the orbit of the Moon may have been very different than it is today. We have simulated the phases of the Moon in a model for its formation wherein the Moon develops a highly elliptical orbit with its major axis tangential to the Earth's orbit. This note describes these simulations and their pedagogical value.

1.
Roger A.
Freedman
,
Robert M.
Geller
, and
William J.
Kaufmann
,
Universe
, 9th ed. (
WH. Freeman and Co.
,
New York
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2011
).
2.
Matija
Cuk
and
Sarah
Stewart
,
“Making the Moon from a fast-spinning Earth,”
Sci.
338
,
1047
1052
(Nov.
2012
).
3.
The angular momentum of an object of mass m orbiting one of mass M ≫ m in an orbit with semi-major axis a is mv×r=mGMa for a circular orbit, since v=GM/a in that case, and mv×r=mGMa(1e2) for an elliptical orbit.
4.
It is important to note that the times used here are specific to one simulation from Cuk and Stewart. Changing the parameters of the simulation could change the times by a factor of a few.
5.
Cuk and Stewart found an equal probability of perigee being locked at first quarter or third quarter. We have arbitrarily chosen perigee to be locked at third quarter. If perigee was in fact locked at first quarter, we would have instead seen the time span from new Moon to full Moon be significantly shorter than that from full to new.
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