What is the relationship betweek surface gravity and excape velocity?

 

 

Equate the kinetic energy to the surface gravitational potential to get

 

2      G M m
1/2 m V = ---------
       R

the escape velocity is then

2 2 G M
V = -------
  R

where in gram-cm units G = 6.6 x 10^-8,

R is the radius of the planet in centimeters,

M is the mass of the planet in grams, and

V is the escape velocity in cm/sec.

 

 

from Ask an Astronomer       http://image.gsfc.nasa.gov/poetry/ask/a11012.html