Re: [Phys-l] day -> month -> year

["Anthony Lapinski" <Anthony_Lapinski@pds.org>]

Very interesting! The astronomy book I use (Explorations, by Arny) says
this in discussing the tides:

The Moon was once much closer to Earth, and the Earth spun much faster in
the past.
Presently, the Moon is moving away from the Earth at ? 3.8 cm/yr.
Tidal braking lengthens the day by ? 0.0014 sec/century
At this rate, half a billion years ago the Earth day was 22 hours long,
and the year contained 398 days.

Tidal braking also explains why the Moon always keeps the same face toward
the Earth.
Both the Earth and Moon are slowed by tides.
The lunar tides have severely braked the Moon over many years (synchronous
rotation)

Eventually, the Moon braking the Earth will make the Earth rotate in sync
with the Moon’s orbital motion.
Billions of years from now, the Earth and Moon will orbit in such a way
that each will always present the same side toward the other. Thus, the
Moon will be visible from only one side of the Earth!

When this happens, the length of the month (longer than now) = length of
day (much longer than now)
Earth’s “day” (rotation period) will be 47 of our present days, and the
distance to the Moon will be 340,000 miles (550,000 km) or about 43%
larger than at present.

Similar tidal effects have locked some satellites of other planets into
synchronous rotation, but the planets have not been noticeably slowed. For
example, dwarf planet Pluto and Charon orbit with the same side toward
each other.




Forum for Physics Educators <phys-l@carnot.physics.buffalo.edu> writes:
> On 12/05/2011 12:20 AM, Bob Sciamanda wrote:
>
> > Is there any reason to doubt that 
> > the same effect will eventually occur with the earth’s motion –
> eventually 
> > making the day equal to a year?  If so, is there any way to estimate
> the 
> > time rate of advance of this effect?  Just curious.
>
> Long before the day becomes equal to the year, it would
> become equal to the lunar month.  That is, the earth 
> would always turn one fact to the moon, just as the moon 
> always turns one face to the earth.
>
>  I say "would" rather than "will" because the process
>  is very slow;  the sun is expected to turn into a red
>  giant and engulf the earth and moon before the process
>  runs to completion.
>  http://www.astro.uu.nl/~strous/AA/en/antwoorden/getijden.html
>
>       The day becoming equal to the year would take
>       even longer;  far, far longer.
>
> There is no doubt that the day -> month process is under
> way.  The day is getting longer, as angular momentum is 
> transferred from the spin of the earth to its orbital motion 
> around the earth-moon center of mass.  As part of the 
> same process, the earth-moon separation is getting larger,
> in accordance with conservation of angular momentum.
> Among other things, this means that "soon" there will
> be no more total eclipses of the sun;  the moon will
> not subtend a large enough angle.
>
> The mechanism for this process is that the moon sets
> up tides in the earth, and that allows friction to take
> energy out of the system.  The principle of virtual 
> work says the system tends toward the lowest energy 
> configuration.  That is the one with the largest moment 
> of inertia.
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