9.) A 1 570 kg satellite orbits a planet in a circle of radius 5.94 x 106 m. Relative to zero at infinity the gravitational potential energy of this satellite is -9.32 x 1011 J. What is the mass of the planet?
To find the mass of the planet, we can use the formula for the gravitational potential energy:
Gravitational Potential Energy = (-G * M * m) / r
Where:
- G is the gravitational constant (6.67430 x 10^-11 N m^2/kg^2)
- M is the mass of the planet (what we want to find)
- m is the mass of the satellite (1 570 kg)
- r is the radius of the satellite's orbit (5.94 x 10^6 m)
Rearranging the equation to solve for M:
M = (-Gr) / (GPE * m)
Substituting the given values:
M = (-6.67430 x 10^-11 * 5.94 x 10^6) / (-9.32 x 10^11 * 1 570)
Simplifying the equation:
M = (3.96217 x 10^-4) / (1460.4)
M ≈ 2.71 x 10^(-7) kg
Therefore, the mass of the planet is approximately 2.71 x 10^(-7) kg.