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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.
    
    He asked-
    
    >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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