[extropy-chat] Astronomical question

[spike]

> bounces at lists.extropy.org] On Behalf Of spike
> Subject: RE: [extropy-chat] Astronomical question
...
> 
> So it will take a loooot longer than 10 billion
> years to tidelock, so the sun will surely go off
> the main sequence onto helium burning, swell and
> boil away any remaining oceans, greatly reducing
> the tide drag...

I calculated that the earth would take closer to
20 billion years to tidelock.  The equations are
kind of a pain in the ass to type into this medium,
but I can kinda describe how I got that number.

I calculated the gravity difference from the sun
and moon on the near side of the earth vs the far
side and found something interesting: the acceleration
difference of the moon on either side of the earth
is about twice the acceleration difference of the
sun on opposite sides of the earth: about 1 micron
per second squared vs 2 microns per second squared.
Then the differences in centrifugal force approximately
doubles those numbers.

Those of you who know from oceans, is a moon tide
about twice as much as a sun tide?  Is a moon tide
about a meter and a sun tide about half a meter?
When a high tide comes at a full moon or new moon,
is that called a neap tide?  Is that about half
again higher and lower than normal?

Using that and estimating a tide as a sort of a
2 dimensional haversine, the mass of a moon tide
comes out to about 3e16 kg.  Model those as a
3e16kg point mass rotated about pi/4 forward of
center and another mass on the opposite side of
earth rotated aft of center with the same 3e16 kg mass.

With these assumptions I get around 20 billion years
to drag the moon up to tidelock with the earth. 

> 
> I have another interesting find I discovered today
> while fiddling with equations, but this post is
> already too long and NOVA is on... spike

NOVA way doesn't suck!

I found an interesting thing that I had never heard
before: the process of tidal drag not only raises the
moon to a higher orbit, it increases the eccentricity
of its orbit.  Kewalll!  {8-]  Someone who knows from 
astronomy, did you already know that?  I have read
stuff for years but never did run across that.  I
found it using the tide-as-mass-concentration model.

Now the insight: the same model shows that the more
eccentric the orbit, the more tidal drag increases
the eccentricity.  So if tidal drag is what caused
the moon's current orbit eccentricity, then it would
have had to start with *some* eccentricity.  A perfectly
round orbit stays perfectly round.

So then, seems like we should be able to run this
process backwards.  We know the moon had to start
its life outside the earth's Roche's limit, so that
forms a hard boundary on the inside.  We should be
able to estimate how long ago it was when the
moon formed and what was its initial eccentricity.

You know, instead of calculating all this, perhaps
someone might point me to websites or papers by
people who know from tides and moon stuff.  Right now
it worries me that my answers are coming up differing
from Ian Ridpath's.  Before 20 billion years have passed,
the sun comes out here to get us, boils away
the oceans.  Then if the earth/moon system manage
to remain in orbit after orbiting inside the tenuous
outer reaches of the sun's atmosphere, the remaining
charred cinders eventually freeze over because the
sun shrinks away as the helium burning stage progresses. 

Probably Amara knows all about this, or if not, she
knows who knows.

spike