On Sun, Oct 16, 2016 at 08:00:40PM -0400, Christopher Sean Hilton wrote:
> Valles Marineris on Mars is 8km deep. How high would the mean
> surface pressure of Mars have to be to have a surface pressure of
> 75kPa at the base of Valles Marineris?

The scale height for Mars is about 12 km, so the pressure at the
bottom would be about twice the pressure at the top.  However, that
top is rather a lot higher than the mean surface height of Mars, so
that the base is only about 3 km below the mean.  That would put the
mean surface pressure at about 58 kPa to get 75 kPa in the canyon.

The deepest parts of the Martian surface are in the Hellas crater,
largely around 7-8 km below the mean.  The mean pressure could be as
low as 38 kPa to get 75 kPa at the crater floor.

> I'm wondering about the viability of planets like Larry Niven's
> Canyon.

A world with Earthlike gravity is probably better for this sort of
thing than a Mars-like world, since the rate of decrease of pressure
with height is proportional to gravity.

If Earth lost most of its water, then it would have trenches just as
deep as Mars (ignoring any rebound from loss of water pressure).
The Challenger Deep would have air pressure at the bottom more than
three times that at mean surface level, and nearly four times the
pressure at the original "sea level".

- Tim