Spoony
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so I am 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) I've 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) I've 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 don't know how to approach it.
thanks guys :)
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) I've 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) I've 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 don't know how to approach it.
thanks guys :)