Astronomy astrophysics equation

Question

If the sun expanded to a radius 200 times it's present radius, what would it's average density be in g/cm^3

Answer 1

Density is mass divided by volume. Mathematically, ρ = m/V, where the volume (for a sphere) is given as

V = 4/3 * pi * r³ where r is the radius of the sun

Let's let the new radius R = 200 * r so the new volume is V' = 4/3 * pi * R³ = 4/3 * pi * (200*r)³ = (200)³ * 4/3 * pi * r³. So V' = (200)³ * V and the new density is ρ' = m/V' = m/(200³ * V) = 1/200³ * m/V = 1/200³ * ρ

So ρ' = 1/200³ * ρ

The (average) density of the sun is 1.41 g/cm³. So, the new density is 1.41/200³ = 1.76 x 10^-7 g/cm³