Space/Science — HabitableZone

Space/Science » in reply to Re: Super Earth habitable?

Re: Super Earth habitable?

The gravitational acceleration 'A' at a planet's surface depends on its mass and its size, since the mass acts as if it was all concentrated at the very center. The equation is A = KM / R**2 where M is the mass, R the Radius, and K a constant that makes it all come out in the right units.

So the earth's gravitational acceleration is Ae = K Me/Re**2,
and the planet's gravitational acceleration is Ap = K Mp/Rp**2.

If we set Me = 1 (one earth mass), and Re = 1 (one earth radius), the ratio of the gravitational accelerations of the two planets at their respective surfaces is Ap/Ae = ( K Mp/Rp**2) / (K Me/Re**2).

We know from the article that Mp = 3.6 Me, so if we substitute, cancel and simplify

Ap/Ae = (K 3.6 Me/Rp**2) / (K Me /Re**2) = Ap/Ae = 3.6/Rp**2.

So the gravitational acceleration at the surface of the planet is

Ap = 3.6Ae/Rp**2, where Rp is in terms of Re.

so for the planet to have the same surface gravity as earth, it's radius would have to be almost 1.9 times as large as earth's. Conversely, it the planet were the same size as earth, it's surface gravity would be 3.6 times as large as earth's.

We know Ae from measurement to be 9.8 m/s**2.

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