- #1
ApeXaviour
- 35
- 0
Okay obviously a hypothetical situation, this planet has a radius [tex]R[/tex], uniform density, and it doesn't rotate.
Pressure in a liquid is given by
[tex]p=\rho g d[/tex] where [tex]d[/tex] is the depth.
So the liquid pressure a distance [tex]r[/tex] from the centre of the planet is.
[tex]p=\rho g (R-r)[/tex] (where r<R)
But [tex]g[/tex] is also a function of [tex]r[/tex]. A little bit of fiddling with Newton's gravitation law gives:
[tex]g(r)=GM\frac{r}{R^3}[/tex]
So...
[tex]p=\rho GM\frac{r}{R^3}(R-r)[/tex]
This would mean, at [tex]r=0[/tex] the core of the planet is under zero pressure...! Em, I don't believe this to be correct, so what am I missing? am I slipping up somewhere? Am I putting too much stock in the formula: [tex]p=\rho g d[/tex]?
Pressure in a liquid is given by
[tex]p=\rho g d[/tex] where [tex]d[/tex] is the depth.
So the liquid pressure a distance [tex]r[/tex] from the centre of the planet is.
[tex]p=\rho g (R-r)[/tex] (where r<R)
But [tex]g[/tex] is also a function of [tex]r[/tex]. A little bit of fiddling with Newton's gravitation law gives:
[tex]g(r)=GM\frac{r}{R^3}[/tex]
So...
[tex]p=\rho GM\frac{r}{R^3}(R-r)[/tex]
This would mean, at [tex]r=0[/tex] the core of the planet is under zero pressure...! Em, I don't believe this to be correct, so what am I missing? am I slipping up somewhere? Am I putting too much stock in the formula: [tex]p=\rho g d[/tex]?