What do you need to know in order to calculate the mass of a planet from observations of a satellite in orbit around that planet?
I read somewhere that you need to know the orbital period and radius of the planet is that correct?
You need the orbital period and the radius of the satellite's orbit (not the planet). That will let you calculate the planet's mass.
To calculate the mass of a planet from observations of a satellite in orbit around it, you need to know the following:
1. Period of the Satellite: The orbital period of the satellite is the time it takes to complete one orbit around the planet. This can be obtained by measuring the time it takes for the satellite to complete a full revolution.
2. Radius of the Satellite's Orbit: The distance between the center of the planet and the satellite's orbit, known as the radius of the orbit, is crucial. This can be measured using techniques such as radar or telescope observations.
3. Gravitational Constant: The gravitational constant, denoted by G, is a fundamental physical constant that relates the strength of the gravitational force between two objects. It is typically given as a value of 6.67430 x 10^-11 cubic meters per kilogram per second squared (m^3/kg/s^2).
Using these pieces of information, you can employ the following formula to calculate the mass of the planet:
M = (4π^2 * r^3) / (G * T^2)
Where:
- M represents the mass of the planet,
- r is the radius of the satellite's orbit,
- G is the gravitational constant, and
- T denotes the period of the satellite.
By substituting the known values into the equation, you can solve for the mass of the planet.