Recent content by plasehi

If you start from the equation of hydrostatic equilibrium, grad P=-rho*g, sure. I haven't seen a rigorous proof of that though, except by assuming cylindrical or Cartesian geometry in the beginning. That said, for how convenient the proof turns out to be, it seems like there may be a profound...

Below is a write-up I made on the correct derivation. The lateral pressure contribution cancels out conveniently with the area effect, making the usually used equation valid. http://imgur.com/hnP3S

I've researched and found relevant papers. Does the Surface Pressure Equal the Weight per Unit Area of a Hydrostatic Atmosphere? Peter R. Bannon, Craig H. Bishop, and James B. Kerr General relationships between pressure, weight and mass of a hydrostatic fluid Maarten H.P Ambaum To...

So I've realized. But can the lateral contributions of the shells be proved exactly to negate the area effect? Seems pretty convenient at first glance.

I want to derive a formula for pressure at depth in a constant density planet, which sounds pretty simple. Setting up a force balance, d(4∏*r2P) = -4/3∏r3*ρ*4∏ρ*r2*dr*G/r2 I'm too lazy to write down a thorough derivation, but by pretty simple calculus and integrating from the planet surface...