When will the last total solar eclipse occur? Because the moon distance from earth grows, how long will it take, that it is no longer possible to see a total eclipse but only circular eclipses? And does it make a difference if you are on the mount everest or on sea level?
I will take a stab at it.  Assuming 


the last eclipse happens when the moon is at perigee and the earth is at aphelion.
the moon's perigee is increasing by 4 cm per year,
the earth's aphelion does not change with time,
the sun and the moon are perfect spheres,
the radius of the sun and moon don't change, and
a total eclipse occurs when $r_{\mathrm{sun}}/d_{\mathrm{sun}} &lt; r_{\mathrm{moon}}/d_{\mathrm{moon}}$ where $r$ is radius and $d$ is distance,


I get the following results:


The last total eclipse at sea level will occur in 721,587,917 years at sea
level  (obviously too many significant digits).
The last total eclipse at mount Everest will occur in 721,807,917 years.
The difference is 220,000 years = (height_of_Everest) * 25000 years/km.


Mathematica Source Code:

dSun = 152097000; rSun = 695508; dMoonNow = 357347; rMoon = 1737; 
rEarth = 6371; hEverest = 8 + 8/10;
sol2 = Solve[ rMoon/(d + t 4/100/1000) == rSun/(dSun - rEarth), t][[1]];
Print[ t /. sol2 /. d -&gt; dMoonNow - rEarth  // Round];
Print[ t /. sol2 /. d -&gt; dMoonNow - rEarth - hEverest // Round];