Pressure inside a planet

Finding the pressure inside a spherical planet as a function of radial distance from the centre, by integrating the equation of hydrostatic equilibrium. We assume a uniform density here, but the method can be generalised easily to the non-uniform case.
Deriving the hydrostatic equilibrium condition: • Hydrostatic equilibriu...
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About me: I studied Physics at the University of Cambridge, then stayed on to get a PhD in Astronomy. During my PhD, I also spent four years teaching Physics undergraduates at the university. Now, I'm working as a private tutor, teaching Physics & Maths up to A Level standard.
My website: benyelverton.com/
#physics #mathematics #pressure #gravity #integration #differentialequation #planet #gausslaw #vectorcalculus #gradient #gravitationalfield #density #fluid #fluids #pressuregradient #hydrostaticequilibrium #hydrostatic #equilibrium #forces #balance #vectors #calculus #physicsproblems #maths #math #science #education

[@GauravRaj-zp7hy]

Sir can you bring out something for inpho preparation??

[@SussySusan-lf6fk]

Nice.

[@kimsgeorgspavlovs4286]

Nice follow-up to hydrostatic equilibrium video

[@DrBenYelverton]

Thanks, glad you enjoyed it!

[@shrivatsa8604]

Great video dr ben, thank you.

[@DrBenYelverton]

Thank you!

[@eulerthegreatestofall147]

Excellent!!!

[@DrBenYelverton]

Thanks!

[@desertedgecko1530]

Great, Interesting video as always Dr Ben! Thank you Will you ever consider doing videos on special/general relativity? Id love to see your style of detailed derivations for relativistic physics.

[@DrBenYelverton]

I will probably cover some topics in special relativity at some point, GR is a possibility too but I'd need to spend some time refreshing my own knowledge first!

[@emrekt22]

Nice video as always

[@DrBenYelverton]

Thanks for saying so!

[@press2701]

Nice. I like the simplicity, the thoroughness of explanation, not too fast, not too slow. Thanks. Question: could you explain/discuss how it is that g = 9.8 = mass of the earth/Avogadros number. A "mol of force". I read an article on this, and, well, was astounded, having never been taught anything like that. Is it real physics or math coincidence. I thought avogadro was only for chemistry (mols to mass), nothing to do with physics.

[@DrBenYelverton]

Thanks, glad you enjoyed it. If the numbers do work out that way, it's a complete coincidence! For one thing, it doesn't make sense to compare two quantities with different base units - i.e. g is in m/s² while the right hand side of your equation would be in kg mol. Avogadro's number is useful whenever you need to convert between number of moles and actual number of particles, there are occasions when you want to do this in Physics - things like kinetic theory and thermodynamics come to mind in particular.

[@mingmiao364]

Interesting! Didn’t expect hydrostatics applies to what constitutes as the inside or a planet. Is the relation “grad p = density times g” still valid for solid/lava or whatever the actual material the planet is made of?

[@DrBenYelverton]

Yes, this is actually part of the definition of a planet, or at least one possible definition! See e.g. en.wikipedia.org/wiki/Geophysical_definition_of_planet