Where is L3 ?

A number of authors have calculated the exact position of the Third
Lagrange Point (the one more-or-less at the anti-Moon position); a
somewhat larger number have published such calculations, and a
considerably larger number have given verbal or diagrammatic
descriptions.

For all I know, the calculations may all be correct. That cannot, IMHO,
be said of all the descriptions and diagrams.

In the limit of the Moon's size tending to zero, all five points tend to
being on one circle, L1 & L2 being at the Moon.

As the size and mass of the Moon are considered to increase, L1 & L2
lift off rapidly, whereas L3 L4 L5 move much more slowly.

Therefore, a first-approximation diagram can reasonably show the Moon's
orbit as a circle about the centre of the Earth, with L1 & L2 high above
the Moon and L3 L4 L5 on the circle. It should NOT, as some do, show L3
outside the circle.

Exact calculation shows that L3 is slightly further from the barycentre
than the Moon is; it is therefore outside the Moon's orbit. However,
ISTM that, measured from the centre of the Earth, L3 is slightly nearer
than the Moon is (and therefore is within the circle through Moon L4 L5
(which is not a fixed circle)) - but it is commonly stated that L3 is
further from the Earth than the Moon is.

Simple proof, full calculation, diagram, etc., at
<URL:http://www.merlyn.demon.co.uk/gravity4.htm>.

(1) I'd be pleased to have this checked, by those with appropriate
pedagogical and professional interest and/or skilled amateurs.

(2) If I'm right, the situation may serve as a warning not to believe
everything at Web sites, even Wiki or ones linked to NASA.

--
(c) John Stockton, Surrey, UK. ?@merlyn.demon.co.uk Turnpike v6.05 MIME.
Web <URL:http://www.merlyn.demon.co.uk/> - FAQqish topics, acronyms & links;
Astro stuff via astron-1.htm, gravity0.htm ; quotings.htm, pascal.htm, etc.
No Encoding. Quotes before replies. Snip well. Write clearly. Don't Mail News.

	#1
Dr J R Stockton	Where is L3 ? A number of authors have calculated the exact position of the Third Lagrange Point (the one more-or-less at the anti-Moon position); a somewhat larger number have published such calculations, and a considerably larger number have given verbal or diagrammatic descriptions. For all I know, the calculations may all be correct. That cannot, IMHO, be said of all the descriptions and diagrams. In the limit of the Moon's size tending to zero, all five points tend to being on one circle, L1 & L2 being at the Moon. As the size and mass of the Moon are considered to increase, L1 & L2 lift off rapidly, whereas L3 L4 L5 move much more slowly. Therefore, a first-approximation diagram can reasonably show the Moon's orbit as a circle about the centre of the Earth, with L1 & L2 high above the Moon and L3 L4 L5 on the circle. It should NOT, as some do, show L3 outside the circle. Exact calculation shows that L3 is slightly further from the barycentre than the Moon is; it is therefore outside the Moon's orbit. However, ISTM that, measured from the centre of the Earth, L3 is slightly nearer than the Moon is (and therefore is within the circle through Moon L4 L5 (which is not a fixed circle)) - but it is commonly stated that L3 is further from the Earth than the Moon is. Simple proof, full calculation, diagram, etc., at <URL:http://www.merlyn.demon.co.uk/gravity4.htm>. (1) I'd be pleased to have this checked, by those with appropriate pedagogical and professional interest and/or skilled amateurs. (2) If I'm right, the situation may serve as a warning not to believe everything at Web sites, even Wiki or ones linked to NASA. -- (c) John Stockton, Surrey, UK. ?@merlyn.demon.co.uk Turnpike v6.05 MIME. Web <URL:http://www.merlyn.demon.co.uk/> - FAQqish topics, acronyms & links; Astro stuff via astron-1.htm, gravity0.htm ; quotings.htm, pascal.htm, etc. No Encoding. Quotes before replies. Snip well. Write clearly. Don't Mail News.