# Pressure Variation in Planetary Atmosphere

1. Jan 14, 2010

1. Show that the variation of pressure with altitude for a planetary atmosphere (assuming constant temperature) is more accurately given by: p = poek(1/r-1/R), where g is taken to vary as 1/r2 (with r being the distance from the centre of the planet), po 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/Po = p/po
dP/dy = -pg

3. dP/P = -g(po/Po)dy

2. Jan 14, 2010

### JaWiB

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

3. Jan 15, 2010