[Phys-L] earth moon sun

[John Denker <jsd@av8n.com>]

On 12/14/2014 08:33 AM, Anthony Lapinski wrote:
> One more thing. I heard/read once somewhere that
> because the Sun's force on the Moon is about 2x the
> Earth's force on the Moon, the Moon orbits the Sun more
> than it orbits the Earth. In other words, the Moon's true
> orbital path is always concave around the Sun.

It's easy enough to figure out.
 -- What is the monthly component to the moon's velocity?
  (Earth-moon circumference per sidereal month)
 -- What is the annual component?
  (pair-sun circumference per sidereal year)

The latter is 29 times bigger.

> How would the Moon's orbit actually look? Similar
> to the epicycle model to show planetary motion? Would the
> Moon's orbital path ever cross itself? Trying to visualize this...
> Is there an onlne simulation anywhere?

There is now:
  https://www.av8n.com/physics/img48/moon-orbit-x8.png

The dots are spaced one day apart.  The plot covers two
sidereal months.  The X and Y axes are labeled in SI
meters.  The red dots represent the earth+moon barycenter,
while the blue dots represent the moon.

Making such a plot is a few minutes work with a spreadsheet.
It's just sines and cosines.

Here the earth-moon distance is exaggerated by a factor
of 8 for clarity.  Without that, the dots would essentially
sit on top of each other.

Even with exaggeration, the moon never backtracks.  As
seen from the sun, the moon is never "in retrograde".

Bottom line:  The earth and the moon are verrrry close
together.  There is even a name for this:  Double planet.