Physics modelling problem.

1. Sep 3, 2008

Spoony

so im tearing my hair out with this one...

the density of the earth's atmostsphere vaires with height r above the earth's surface as

p = p(o) exp(-r/r(o))

where p(o) the density of the air at ground level, is 1.3 kg/m^3 and r(o) the scale height is 8km
use this to estimate an approximate value for the total mass of the atmostsphere, given most of the mass lies within a ddistance above the ground that is much smaller than the radius of the earth

R(earth) = 6.4x10^6

So my attemot at a solution
1) ive got that p = mass/volume so intergrating the expresion with respect to volume gives the total mass of the earth r = v^(1/3).
then R(earth) >> r
but then i get stuck.

2) ive tried to divide the equation through by V but still that leaves me with
r(earth) >> r.

the problem is deailing with the much greater than part of r(earth) >> r, i dont know how to approach it.

thanks guys :)

2. Sep 3, 2008

Spoony

No one even got a clue on how to solve this?

3. Sep 3, 2008

Redbelly98

Staff Emeritus
What is the mass of the air that lies between a height r and a height r+dr?