Escape speed: Ve = (2GM/R)1/2
Average speed of a molecules: Vm = (3kT/m)1/2
k = 1.38 x 10-23J/K
G = 6.67 x 10-11Nm2/kg2
Escape speed of Enceladus:
Ve = (2GM/r)1/2 = ((2 x 6.67 x 10-11 x 8.4 x 1019)/(250 x 103)1/2
Ve = (0.4482 × 105)1/2 = 211.68 m/s
Ve = 0.2117 km/s
Mass of one molecule of water:
m = 18.0152/(6.022 x 1023) = 2.991 x 10-23g
M = 2.991 × 10-26 kg
Average speed of water molecules:
vm = (3KT/m)1/2 = ((3 x 1.38 x 10-23 x 100)/(2.991 x 10-26))1/2
vm = (1.384 × 105)1/2 = 371.9 m/s
vm = 0.372 km/s
Conclusion: vm(H2O) > ve. Therefore, molecules of water can escape from Enceladus.