A satellite has a mass of 6000 kg and is in a circular orbit 4.20 105 m above the surface of a planet. The period of the orbit is two hours. The radius of the planet is 4.20 106 m. What is the true weight of the satellite when it is at rest on the planet's surface?
To find the true weight of the satellite when it is at rest on the planet's surface, we need to first find the gravitational force acting on the satellite at that position. Here's how to do it:
1. Calculate the mass of the planet:
The mass of the planet is not given directly, but we can use the radius and the acceleration due to gravity. The acceleration due to gravity is given by the formula:
g = G * (Mplanet / R^2)
where g is the acceleration due to gravity, G is the gravitational constant (approximately 6.67 x 10^-11 N m^2/kg^2), Mplanet is the mass of the planet, and R is the radius of the planet.
Rearranging the formula, we can solve for Mplanet:
Mplanet = g * (R^2 / G)
Plug in the values of g (9.8 m/s^2), G, and R (4.2 x 10^6 m), and calculate Mplanet.
2. Calculate the gravitational force on the satellite:
The gravitational force acting on the satellite is given by the formula:
F = (G * Mplanet * Msatellite) / r^2
where F is the gravitational force, Msatellite is the mass of the satellite, and r is the distance between the satellite and the center of the planet.
Rearranging the formula, we can solve for F:
F = (G * Mplanet * Msatellite) / r^2
Plug in the values of G, Mplanet, Msatellite (6000 kg), and r (radius of the planet + height above the surface), and calculate F.
3. Calculate the true weight of the satellite:
The true weight of an object is the gravitational force acting on it. In this case, the gravitational force calculated in the previous step is the true weight of the satellite when it is at rest on the planet's surface.
Performing these calculations will give you the true weight of the satellite when it is at rest on the planet's surface.