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Re: [Phys-L] earth moon sun



On 12/14/2014 12:17 PM, Anthony Lapinski wrote:
So the Moon's orbit is always concave toward the Sun?

Yes.

Here's the picture:
https://www.av8n.com/physics/img48/moon-orbit-accel.png

The red dots represent the barycenter (as before). The dots
are one day apart.

The blue vectors are the acceleration vectors (scaled by 1e12).
Note that they always point more-or-less inward, toward the
sun.

You could easily figure it out from the numbers, without
bothering to draw the diagram.
The ratio of distances is 389.
Take out a factor of roughly 13 to get:
The ratio of velocities is 29.
Take out another factor of roughly 13 to get:
The ratio of accelerations is 2.2.

Why a factor of 13? That's the ratio of the angular rates
of motion. There are 13 of those sidereal months per year.
(You lose an entire month per year by counting syzygies
rather than sidereal months.)

That factor of 2.2 is bigger than 1, which means the
acceleration toward the sun always dominates. OTOH
the acceleration toward the earth is nontrivial. At
the time of the new moon, the acceleration toward the
sun is substantially reduced by the pull of the earth.
At the time of the full moon, it is substantially
increased. You can see this in the figure.

Note that exaggerating things by a factor of 8 is not
enough to make a qualitative change in the depiction
of velocity, but is enough to mess up the depiction of
acceleration.