# Here is a puzzle, at least for me:

sonhouse
Posers and Puzzles 11 Mar '06 04:21
1. sonhouse
Fast and Curious
11 Mar '06 04:21
Since all this news about Encaledus I was going over a data sheet
about Saturn and these three lines struck me as odd:
Gravity (eq., 1 bar) (m/s2) 10.44 9.80 1.065
Acceleration (eq., 1 bar) (m/s2) 8.96 9.78 0.916
Escape velocity (km/s) 35.5 11.19 3.172
The first figure is the gravity of Saturn, then earth then the ratio between the two. You see gravity and acceleration as nearly equal to earths but then you look at the escape velocity and you see Saturn has an escape velocity of three times that of earth. How can that be?
2. sonhouse
Fast and Curious
11 Mar '06 05:55
Well I let my rusty neurons grind on it for a while and came to the
conclusion the one bar figure must be the key. It must represent
the gravity at the depth in Saturn's atmosphere that is the same
pressure as earth's at sea level but that point on Saturn would be
way up from the 'surface' but lower down it would be three times
greater gravitation. But if you were at the one bar depth wouldn't the
escape velocity still be about the same as earth? It seems it would
have to be.
3. 12 Mar '06 23:54
I think the grater mass has something to do with it
4. 13 Mar '06 08:39
This is how to calculate the escape velocity
v = sqrt(2*G*M/R
and the gravitation
g = G*M/R^2
where
v = escape velocity [m/s],
g = gravitation [m/s^2],
M = mass of the planet [kg],
R = distance from its center or radius [m] and
G = gravitational constant = 6.673x10^-11

Now you can test different planets and moons and even the sun itself.

If you calculate the density of Saturn by dividing its mass with its volume you'll find that its density is very low - even less than water, and therefore its radius is larger than it should be if it just was a rocky planet like the Earth.