The formula for gravitational acceleration is:
g = (G*M)/R^2, with
G being the universal gravitational constant.
For a planet with ten-times Earth's gravity, the equation is:
(G*M)/R^2 = 10*((G*Mᴇ)/Rᴇ^2).
The formula for mass is
ρV or density x volume, and formula for volume of a sphere is: (4/3)π*R^3.
- G is a like term and is cancelled out; the equation becomes: M/R^2 = 10*(Mᴇ/Rᴇ^2).
- Factoring in the formula for spherical volume, the equation becomes: (ρ * (4/3)πR^3)/R^2 = 10((ρᴇ * (4/3)π*Rᴇ^3)/Rᴇ^2).
- (4/3)*π is a like term and is cancelled out; simplified, the equation becomes: 10 * (ρᴇ * Rᴇ) = ρR.
- Rearranging for R, the radius, the equation becomes: R = (10 * ρᴇ * Rᴇ) / ρ.
- Assuming Planet Vegeta shares a density with Earth, then the equation becomes: R = 10Rᴇ.
The radius of Earth (
Rᴇ) is
6,371 km, therefore, the radius of Vegeta (
R) is
63,371 km.
As for mass,
- Given the radius of Vegeta is 10Rᴇ, the equation becomes: M = ρᴇ * (4/3) * π * (10Rᴇ)^3.
- By cubing the parentheses, the equation becomes: M = 1,000 * ρᴇ * (4/3) * π * Rᴇ^3.
ρᴇ * (4/3) * π * Rᴇ^3 is the equation for calculating Earth's mass.
Therefore, the mass of Vegeta is:
1,000 * Mᴇ or
5.97200e+27 kg.