Pressure Variation in Planetary Atmosphere

AI Thread Summary
The discussion focuses on the mathematical relationship between pressure and altitude in a planetary atmosphere, assuming constant temperature. It presents the equation p = poek(1/r-1/R) to describe pressure variation, where g varies as 1/r^2. The relationship between density and pressure is established with P/Po = p/po and the differential equation dP/dy = -pg. The participants clarify that changes in height can be represented as dr = dy, reinforcing the connection between pressure and gravitational effects. This analysis emphasizes the importance of understanding atmospheric pressure dynamics in planetary science.
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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
 
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g = k/r^2 and since both dy and dr represent a change in height dr = dy
 
Thank you, makes sense.
 

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