Suppose a spherically symmetric liquid planet of radius R is in hydrostatic equilibrium has a density...

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Suppose a spherically symmetric liquid planet of radius R is in hydrostatic equilibrium has a density profile given by p(r) = { po*(1-a*r) if r R and O if if r > R where pO > 0 and 0 a < 1 are constants. a) Let M = M(r) denote the mass of material enclosed by radius M(r)= { 4pOr^3 ( (1/3) - (a*r/4R)) if r Rand 4r^3 ((1/3) - (a/4)) b) Assume that the planet is in hydrostatic equilibrium (Vp = p g), and is spherically symmetric. Find an expression for p(r) for r R, taking the surface pressure p at r = R to be 0, and show that the pressure at the center of the planet is p(0) = G^2R^2* (2/3 - 7a/9 + (a^2)/4) c) Consider a second planet that has the same total mass and radius as the above planet, but it has a uniform density p. Show that p = po(1 - (3/4) Suppose a spherically symmetric liquid planet of radius R is in hydrostatic equilibrium has a density profile given by p(r) = { po*(1-a*r) if r R and O if if r > R where pO > 0 and 0 a < 1 are constants. a) Let M = M(r) denote the mass of material enclosed by radius M(r)= { 4pOr^3 ( (1/3) - (a*r/4R)) if r Rand 4r^3 ((1/3) - (a/4)) b) Assume that the planet is in hydrostatic equilibrium (Vp = p g), and is spherically symmetric. Find an expression for p(r) for r R, taking the surface pressure p at r = R to be 0, and show that the pressure at the center of the planet is p(0) = G^2R^2* (2/3 - 7a/9 + (a^2)/4) c) Consider a second planet that has the same total mass and radius as the above planet, but it has a uniform density p. Show that p = po(1 - (3/4)

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