Please can someone tell me if my thinking here is right...
I've got a planet with an atmospheric pressure at 6km of 0.5 P_{0} and at 8km of 0.4 P_{0} (P_{0} = pressure at the surface).
I want to work out the scale height of the atmosphere.
Given scale height = λ
and for height above surface = z
P(z)=P(0)e^{(z/λ)}
I could rearrange to show the pressure at the surface as:
P(0)=P(z)/e^{(z/λ)}
I could then use the relative pressure, assume P(0)=1 (as it will cancel out shortly) and height from each of the know quantities and set them equal to each other like this:
0.4/e^{(8000/λ)} = 0.5/e^{(6000/λ)}
A little mutliplication....
0.4 e^{(6000/λ)} = 0.5 e^{(8000/λ)}
Take the Log of both sides....
(6000/λ) log 0.4 = (8000/λ) log 0.5
But know I'm left with the λ cancelling out if I multiply both sides by λ. I'm sure I've gone wrong here somewhere. Probably something very simple. Can anyone advise? Have I made a simple mistake in my working or have I gone completely off the reservation and need to start again? I just need to end up with λ = xxx metres.
Thank you.
