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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Beginner moonrise and set question
From: George Huxtable
Date: 2004 Sep 26, 00:21 +0100

```On 22 Sept, Bill followed a question about moonrise with a second question.
I don't remember seeing it answered.

>A more complex question--at least to me:
>
>Regarding the Earth, Moon, and Sun I recently read (if I correctly remember
>and understood it) that the Earth and Moon actually rotate--in relation to
>each other, about a point 800 miles from the Earth's surface.
>
>To draw a 2D analogy, if a 300 lb. person and a 30 lb. person were on a
>see-saw, the fulcrum would have to be much closer to the large person to
>achieve balance.  If we were to spin the pair around the fulcrum, in
>relationship to a nearby post, each person would get nearer then farther
>from the post with each revolution, the 30 lb person more so because of the
>greater distance from the pivot point.
>
>My question:  Ignoring precession and other wobbles, does the Earth's axis
>go smoothly around its elliptical orbit of the Sun; or do the Earth/Moon
>pair spin around some point 800 miles below the Earth's surface between the
>Moon and Earth's centers, held together by gravitational attraction (like
>the pair above held together by the see-saw) with each getting nearer and
>farther from the Sun as they go about their journey?

===============

Here's a shot at an answer, from George.

Bill's analogy of a spinning seesaw with unequal weights on it is a good one.

I wonder if in his last paragraph, which goes " Ignoring precession and
other wobbles, does the Earth's axis go smoothly around its elliptical
orbit of the Sun..." Bill really meant to ask whether the Earth's CENTRE
goes smoothly round... The Earth's  axis is a line; the Earth's centre is a
point.

And the answer is (as Bill suspected, perhaps) ; no, it doesn't. What
happens is better described by the alternative he suggested- "or do the
Earth/Moon
>pair spin around some point 800 miles below the Earth's surface between the
>Moon and Earth's centers, held together by gravitational attraction (like
>the pair above held together by the see-saw) with each getting nearer and
>farther from the Sun as they go about their journey?"

It's the centre-of-mass of the Earth-Moon system that travels rather
smoothly round the Sun in a near-ellipse, and the Earth (and the Moon) go
round that common centre-of-mass, with different radii, once per month. It
happens that for the Earth-Moon pair, the point about which they rotate
happens to be below the Earth's surface.

This is the mechanism behind one of the "perturbation terms", which affect
the Earth's orbit around the Sun, and therefore also affects the position
of the Sun in the sky by an equal and opposite amount.

It's all much more complicated than that of course, because everything in
the solar system attracts (and is attracted by) everything else.

Just as the Moon's pull affects the Earth's centre (as in Bill's spinning
seesaw), so does the Earth's pull on the Sun affect the Sun's centre.
Jupiter and Saturn affect the Sun's position in the same way, but more so.

And the attractions of Jupiter and Saturn on our Moon have quite a major
influence on the orbit of the Moon around the Earth. Not just in causing
deviations in its shape, but speeding and slowing the Moon in its path.

All these are "perturbations" of the simple elliptical Kepler orbits that
would be found if only two bodies were involved. In the case of the Moon
there are literally hundreds of possible perturbation terms that can affect
its orbit and need to be considered when great accuracy is being sought.

George.

================================================================
contact George Huxtable by email at george---.u-net.com, by phone at
01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
================================================================

```
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