Re: [Phys-L] Moon's orbit

[Paul Nord <paul.nord@valpo.edu>]

Because the sun also pulls on the earth.  Both the earth and the moon are
in freefall around the sun.  By some accident of history, they happen to be
falling together right now.  The orbit for any object at this radius from
the sun will be the same.

The setup for this problem seems to treat it like a simple 3rd Law
summation of forces.  You really must consider the forces on both the earth
and the moon.  Consider this:  What would happen if the sun's suddenly
stopped pulling on the earth, but kept pulling on the moon?  The earth
would move in a straight line tangent to its current orbit.  And the moon
would continue it its orbit around the sun.  (Assuming it didn't crash into
the planet suddenly zipping away from it.)

The Lagrange points and Roche limits are subtleties orbital dynamics that
aren't needed for this problem.

Paul

On Mon, Oct 17, 2016 at 8:58 PM, Anthony Lapinski <alapinski@pds.org> wrote:

> The Sun pulls on the Moon with about twice the force that the Earth pulls
> on it. So why doesn't the Moon get pulled away from the Earth? I realize
> this is complicated. Is there a "simple" explanation I can tell high school
> students?
>
> I searched online. One site said that the Moon's orbital velocity (1 km/s)
> is simply less than the Earth's escape velocity (1.2 km/s) at the Moon's
> distance from the Earth. Not sure how they came up with this 1.2 number.
>
> Several sites mentioned the Hill sphere (never heard of this before). I
> guess if an orbiting object is within a certain distance of a central body
> (e.g., Earth), the gravity dominates that from a more distant body (e.g.,
> Sun). Is this related to the Roche limit?
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