(see more precisely 8-1, pg. 208-209)
So at the surface of the Mercury the escape speed is 4.2 km/s.
The average speed of a nitrogen molecule in Mercury's atmosphere:
Use the peak temperature of Mercury:
For Nitrogen to remain on Mercury,
,
but currently
, which is greater than
, so nitrogen will escape.
What would Mercury's mass have to be in order for it to still
have a nitrogen atmosphere?
If we increase the Mass of Mercury,
will increase. If
, the nitrogen will
remain on Mercury. The condition for Nitrogen to remain is:
R is fixed, but mass can change. Solve for the new mass:
or