If the gravitational field of the Earth suddenly doubled, the
eccentricity of the Moon's orbit would dramatically increase.
The eccentricity of the Moon's current orbit is approximately, but not
exactly, zero. If it was exactly zero, then doubling the strength of
the Earth's gravitational field would result in a lunar orbit with an
apogee equal to the radius of the current orbit and a perigee that is
much closer to the Earth.
In a circular orbit, the speed of the Moon is just sufficient to
maintain a constant distance from the Earth. If the gravitational force
becomes stronger, the Moon will not have sufficient speed to maintain a
constant distance, and will move along an elliptical orbit that brings
it closer to the Earth.
Unfortunately, I don't have time right now to calculate the radius at
perigee or to determine what would happen if the change did not occur
suddenly.
Daniel Crowe
Oklahoma School of Science and Mathematics
Ardmore Regional Center
dcrowe@sotc.org
-----Original Message-----
From: Forum for Physics Educators [mailto:PHYS-L@list1.ucc.nau.edu] On
Behalf Of David Abineri
Sent: Wednesday, October 13, 2004 2:48 PM
To: PHYS-L@LISTS.NAU.EDU
Subject: [PHYS-L] Satelite Motion
Can someone give me a way to think about this question?
If the earth's gravity doubled, how would the moon's orbit be affected?
I am getting tangled up in having too many variables and it is not at
all obvious what might happen. Would the results be different if it
happens instantaneously rather than incrementally?
Is there a way to look at this that might make it clear for students?