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uros
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A spherical mass m with radius r of a known fluid with density ρ floats in the vacuum. Calculate the pressure P at the distance x from the center due its own gravity.
Also... at the distance x from the center due its own gravity.
We are on different wavelengths, here. I'm picturing a sphere of liquid in space where g = 0 and P = ρgh is zero. Looking for the pressure inside the sphere "due its OWN gravity". Remember it "floats in vacuum" whereas if it were at the surface of the Earth, g would pull it down to smash on the bottom of its container.P=ρgh
We are on different wavelengths, here. I'm picturing a sphere of liquid in space where g = 0 and P = ρgh is zero. Looking for the pressure inside the sphere "due its OWN gravity". Remember it "floats in vacuum" whereas if it were at the surface of the Earth, g would pull it down to smash on the bottom of its container.
The mass from the radius x:
V'=4πx³/3
m'=4πx³ρ/3
The pressure at the distance x:
P=ρgh
P=ρGm'(r-x)/x²
P=ρ²G4πx(r-x)/3
P → hydrostatic pressure
P=ρgh
P=ρ²G4πx(r-x)/3
Wouldn't the spherical shell with thickness dR be easier to work with?
A thin "column" would have to be wider at the top than at the bottom, wouldn't it?