Sun and moon distance questions - Feb. 3, 2014

In sci.astro message , Wed, 19 Feb 2014
22:45:27, Steve Willner posted:

In article id,
Dr J R Stockton writes:
I thought it was, considering only circular orbits,

(1) The moon's day is locked to the month, so that the front of the Moon
is always in front as we see it;

(2) As the Earth's day is less than the lunar month, the tides on the
Earth have the effect of pushing the Moon forwards, raising the orbit
and further lengthening the lunar month -

Yes, that's observed.

The other effect is that Earth's rotation is slowing, meaning the day
length is increasing. Once the day is longer than the month, the
tidal effect reverses, and the Moon's orbit starts shrinking.

The reversal would not, I think, occur in a system containing only Earth
and Moon, because there once the month and day become equal the tides on
Earth become static. But the solar tide, which is an appreciable
fraction of the present lunar tide, would continue to increase the day -
eventually, if nothing else interferes.


Did anyone here, yourself not excluded, consider
http://www.merlyn.demon.co.uk/lagrpapr.htm#EP, for which it may be
necessary to look at material higher on the page? A noted mathematician
has agreed that there should be an elegant proof - but has not delivered
one.

--
(c) John Stockton, nr London, UK. Mail via homepage. Turnpike v6.05 MIME.
Web http://www.merlyn.demon.co.uk/ - FAQqish topics, acronyms and links;
Astro stuff via astron-1.htm, gravity0.htm ; quotings.htm, pascal.htm, etc.

In article id,
Dr J R Stockton writes:
The reversal would not, I think, occur in a system containing only Earth
and Moon, because there once the month and day become equal the tides on
Earth become static. But the solar tide, which is an appreciable
fraction of the present lunar tide, would continue to increase the day -
eventually, if nothing else interferes.

Quite right! I'd forgotten the critical role of the solar tide,
which is about 1/2.4 of the lunar tidal force now and of course will
become a smaller fraction as the Moon's orbital radius increases.

Did anyone here, yourself not excluded, consider
http://www.merlyn.demon.co.uk/lagrpapr.htm#EP

Interesting material, but I don't see any obvious elegant proof. I'm
not a mathematician, though.

--
Help keep our newsgroup healthy; please don't feed the trolls.
Steve Willner Phone 617-495-7123
Cambridge, MA 02138 USA

In sci.astro message , Mon, 24 Feb 2014
22:38:14, Steve Willner posted:

In article id,
Dr J R Stockton writes:
The reversal would not, I think, occur in a system containing only Earth
and Moon, because there once the month and day become equal the tides on
Earth become static. But the solar tide, which is an appreciable
fraction of the present lunar tide, would continue to increase the day -
eventually, if nothing else interferes.

Quite right! I'd forgotten the critical role of the solar tide,
which is about 1/2.4 of the lunar tidal force now and of course will
become a smaller fraction as the Moon's orbital radius increases.
larger?

Did anyone here, yourself not excluded, consider
http://www.merlyn.demon.co.uk/lagrpapr.htm#EP

Interesting material, but I don't see any obvious elegant proof. I'm
not a mathematician, though.

I've added :- ", preferably one that astronomers and physicists can
understand".

The tidal field of a (spherical, homogeneous) body is proportional to
its density and the cube of its apparent angular diameter, if the latter
be small. So, when one is drinking one's cup of tea, the tidal
component due to one's head greatly exceeds that from the Moon.

--
(c) John Stockton, nr London, UK. For Mail, see Home Page. Turnpike, WinXP.
Web http://www.merlyn.demon.co.uk/ - FAQ-type topics, acronyms, and links.
Command-prompt MiniTrue is useful for viewing/searching/altering files. Free,
DOS/Win/UNIX now 2.0.6; see my http://www.merlyn.demon.co.uk/pc-links.htm.

In sci.astro message , Mon, 24 Feb 2014
22:38:14, Steve Willner posted:
Quite right! I'd forgotten the critical role of the solar tide,
which is about 1/2.4 of the lunar tidal force now and of course will
become a smaller fraction as the Moon's orbital radius increases.

In article id,
Dr J R Stockton writes:
larger?

Arrghh! Yes, larger of course. The solar tide won't change, but the
lunar tidal force goes down (as the cube of orbital radius) as the
Moon's orbital radius increases.

--
Help keep our newsgroup healthy; please don't feed the trolls.
Steve Willner Phone 617-495-7123
Cambridge, MA 02138 USA