# Elevation of Atmosphere differ?

Does the atmosphere depth (or how high the air molecules from the ground) of Earth or Mars differ gradually or can there be plumes of atmosphere that reaches into space? If I were able to travel a perfect circle around the equator would the atmosphere differ in elevation?

• do you mean variance of atmospheric density with altitude? It's not clear what you are asking. – farrenthorpe Nov 20 '16 at 3:48
• I think they are asking whether the height, and density gradient, of a planet's atmosphere is constant (ish) all over or whether the atmosphere may reach much higher in some places than others. I think the earth / Mars thing is a red herring. But I'm not sufficiently confident that this is the intent to edit the question. @muze, could you clarify please? – Semidiurnal Simon Nov 22 '16 at 8:26
• @SimonW if i were able to travel a perfect circle around the equator would the atmosphere differ in elevation? – Muze Nov 22 '16 at 21:13
• @Muze: You might this question & answer, posted on SE Space Exploration relevant to your question: Is there a calculation for determining the thickness of a planet's atmosphere? – Fred Nov 23 '16 at 1:45

Mathematically, this can be described by $$\frac{dP}{dr}=-\rho g$$ where P is the pressure, $\rho$ is the density, and $g$ is gravity. Using the Ideal Gas Law $$P=\rho R T$$, where $T$ is temperature and $R$ is the gas constant for air. Assuming that the temperature in the height of a column of the atmosphere is averaged ($\bar{T}$) an equation for the average height of the atmosphere can be found $$P(r,\phi,\lambda)=P_0(\phi,\lambda)exp(-\frac{(r-r_0)g}{R\bar{T}(\phi,\lambda)})=P_0(\phi,\lambda)exp(-\frac{gz}{R\bar{T}(\phi,\lambda)})$$ where $r_0$ is the radius of the earth,$P_0$ is the surface pressure, $r=z+r_0$, where $z$ is the height above the earth's surface, $\phi$ is the latitude, and $\lambda$ is the longitude.