[ExI] kepler study says 8.8e9 earthlike planets

[Anders Sandberg]

On 2013-11-13 09:32, BillK wrote:
> On Wed, Nov 13, 2013 at 8:32 AM, Kelly Anderson  wrote:
>> So nobody knows NASA's definition of goldilocks planets well enough to know
>> if mars would count as one of the eight billion or not?
> I think the confusion is between 'habitable zone' and 'habitable planet'.
> A goldilocks planet must be in the habitable zone, but for other
> reasons (like being too small) may not be habitable.

Goldilocks is not even a proper scientific term, just a shorthand and 
journa-splaining word.

Whether Mars is too small to be habitable is best phrased as a timing 
issue: Mars-sized worlds will stop continental drift early (crudely: 
total internal energy ~R^3, radiation rate ~R^2, so the time until 
things stop is ~R) and then become dry and lose atmosphere. But once it 
had oceans, and no doubt life could have lived in them (given what 
Earth-life can do). The zone where water can exist also moves somewhat 
across the lifespan of the star (the inner and outer radii scale as 
sqrt(luminosity)) but depends on planet mass and atmosphere.  So we 
might talk about habitability in terms of time and space.

Right now we do not know the number density of small terrestrials. A 
fair guess is some kind of power-law (it works for asteroids, and seem 
to fit the simulations I have seen that people fit to real exoplanet 
data). Their frequency is R^-a where a is some exponent: 0.48 according 
to http://arxiv.org/ftp/arxiv/papers/1305/1305.0542.pdf/. However, there 
may be a plateau below 2 Earth radiuses 
(http://arxiv.org/pdf/1304.0460.pdf) - but this might be mainly about 
the very near star planets. (And a power law with that kind of heavy 
tail will by necessity have a cut-off - or actually have an exponent

If it is a power law all the way down to some limit, the total amount of 
habitable time is the integral of R^(-a+1). This is dominated by the 
smallest worlds if a>2, and by the largest ones if a<2. So if the above 
papers are correct, then most habitable world-moments are on pretty big 
planets.


-- 
Dr Anders Sandberg
Future of Humanity Institute
Oxford Martin School
Oxford University