Pressure Variation in Planetary Atmosphere

[BreakingBad]

1. Show that the variation of pressure with altitude for a planetary atmosphere (assuming constant temperature) is more accurately given by: p = p_oe^k(1/r-1/R), where g is taken to vary as 1/r² (with r being the distance from the centre of the planet), p_o is the pressure at the surface, R is the radius of the planet, and k is a constant.

lower case p = pressure
upper case P = density






2. P/P_o = p/p_o
dP/dy = -pg



3. dP/P = -g(p_o/P_o)dy

 

[JaWiB]

g = k/r^2 and since both dy and dr represent a change in height dr = dy

 

[BreakingBad]

Thank you, makes sense.