Re: Drake increases estimate to 50K communicating E.T. civilizations

> Rob Dekker wrote: 
"Alfred A. Aburto Jr." <aburto@xxxxxxxxxxxxx> wrote in message news:42E0605F.8010308@xxxxxxxxxxxxxxxx

[....]

Is there a simple formula which expresses the 'tidal-lock-zone' of a
particular star ?
So, can we determine when a stars' HZ is totally within a tidal lock zone ?

The tidal force is inversely proportional to the cube of the distance of the planet from the star (in this case) and it is proportional to the mass of the star.

If we let dMercury be the distance of Mercury from the Sun, and
dHZ be the distance of the HZ from a star, and
Msun & Mstar be the mass of the sun & star, and then let:

a = Mstar/Msun
b = dMercury/dHZ

then c = a * b^3 > 1 will indicate tidal locking is in effect (using Mercury as a reference --- since it is just barely tidally locked with the Sun)

A rule of thumb estimate, but it should work.



Very smooth ! I like it.

So, similarly, the HZ is inversely proportional to the square of
the distance of the planet from the star (assuming a constant-power/m^2 is habitable),
and it is proportional to the power of the star.

Let dEarth be a good reference for a HZ around the sun, and
Psun & Pstar be the power of the sun & star, and then let :

x = Pstar/Psun
y = dEarth/dHZ

then z = x * y^2 == 1 will indicate that the planet receives Earth-like habitable power

Putting both formula's together to get rid of the dHZ, then we will get an
equation for a planet which has Earth-like 'climate' but will be get into tidal lock
like Mercury is around our Sun :

Pstar^2 / Mstar^3 < (Psun^2 / Msun^3 ) * (dMercury / dEarth)^6

The right hand side we can calculate, and is constant.
Voila! There is our boundary for stars for which habitable planets will be tidal-locked.

At constant temperature, the stars' power should roughly scale with square of its radius,
and its mass with the cube of radius, so the radius of the star should not influence the
outcome of this boundary too much.

So I think only temperature is the defining factor. Low temperature (red/brown) stars
should tend get their habitable planets in tidal lock....


Disclaimer: I did not verify any of this, I'm sort of writing as we speak...


I'd better test this with known cases (planets & satellites) :-) 


Me too !


[...]


The Habitable distance is determined by temperature of the star. The star type (O,B,A,F,G,K,M,N ... etc) and subclass number 0,1,2,3,...,9
define the effective temperature of a main sequence star. From this, assuming a simple model, one can determine the distance from the star where the HZ lies using the Stefan-Boltzmann Law ... From the Luminosity of the stars (given type and class effective temperature) one can determine such things as the mass and radius of the star. From this information the tidal locking would fall out. Of course Kasting has a much more complex model of habitable planets and habitable zones, albedo effects and atmospheric effects. Well from his model the neat plots shown on the "solstation" web site fall out. Also Margaret Turnbull's webside is mentioned at the "solstation" site and she has detailed charts of HZ'z (based on Kastings work) and much information about the stars that will be used for the next SETI searches.

Also, she needs help filling in data for her tables and she indicated in one powerpoint paper I read that she could use the volunteer help of amateur astromers using under ultilized 1m optical telescopes to help fill in her table. Nice project for amateur astronomers ...
Al
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