posted by Cat on .
A satellite has a mass of 6146 kg and is in a circular orbit 4.57 × 105 m above the surface of a planet. The period of the orbit is 1.6 hours. The radius of the planet is 4.44 × 106 m. What would be the true weight of the satellite if it were at rest on the planet’s surface?
What do I use to find the mass of the unknown planet?
The final equation to use is: W=(GmM)/r^2
m=mass of satelite
M=mass of planet
What is the equation to find the mass of the planet?
The weight of the planet in orbit is
W = M V^2/R
where R = 4.57*10^5 m and V is the velocity at that altitude,
V = 2 pi R/(period).
The weight W' of the satellite at the planet's surface is
W'/W = (4.44*10^6/4.57*10^5)^2
because weight is inversely proportional to the square of distance.
The number you want is W'