[extropy-chat] Astronomical question

[spike]

> bounces at lists.extropy.org] On Behalf Of Dan Clemmensen
> Subject: Re: [extropy-chat] Astronomical question
> 
> ... but consider that we won't tide-lock for at least a billion
> years...

Nobody caught my other mistake but I found it as
I was trying to estimate how long it will take for
earth to tidelock.  Before I started I had estimated
~10 billion years, which is why I so confidently 
stated the no-ring notion.  I checked this calc
with a microscope before questioning anything by 
Ian Ridpath, who I admire greatly.  I have read
his stuff since I was a kid (which is a tragically
long time by the way, over 30 years.)

to get my 10 billion year estimate, I first calculated 
the moment of inertia of the earth, then vaguely
recalled that evidence from fossil shellfish 
indicate that a year contained more like 400 days 
than the current 365 about half a billion years 
ago.  Since the process that causes tidelock 
dissipates energy is proportional to the rotation
rate, then 10% decrease in rotation rate is about
a 20% decrease in rotational energy.  20% in half
a billion years in a rate proportional to rotation
extrapolates to about 10 billion years to get to
6 radians per month.

But I made a mistake which caused me to understate
my case.  I used 2/5MR^2, but that assumes a uniform
density, close enough for single digit precision,
usually.  But I goofed this once before about 5
yrs ago when we were discussing drilling holes
in the earth.  The density of the earth increases
dramatically as one goes inward, and since the
MOI increases as the square of the radius, I missed
the MOI by a lot, way more than a factor of 2 methinks.

So since I overestimated the MOI of the earth I
also overestimated the fraction of the rotational
energy of the earth-moon system that is carried in 
the earth's rotation, so I waaay overestimated how 
far the moon will drift out before tidelock.  Now
without going back and hammering those calcs, I
can estimate it wouldnt be more than about 5%
farther out at tidelock than it is now.

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

spike