A satellite has a mass of 5950 kg and is in a circular orbit 3.80 10^5 m above the surface of a planet. The period of the orbit is two hours. The radius of the planet is 4.15 10^6 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 determine the gravitational force acting on it in the given circular orbit, and then convert it to the weight on the planet's surface.

1. Determine the gravitational force acting on the satellite in its orbit:
The gravitational force acting on the satellite is given by the equation: F_gravity = (G * M * m) / r^2
where F_gravity is the gravitational force, G is the gravitational constant (approximately 6.67 × 10^-11 N·m^2/kg^2), M is the mass of the planet, m is the mass of the satellite, and r is the radius of the orbit.

Given:
- Mass of the satellite (m) = 5950 kg
- Radius of the orbit (r) = 3.80 × 10^5 m
- Radius of the planet (R) = 4.15 × 10^6 m

The mass of the planet (M) is not given, but we can calculate it using the radius of the planet.
M = (4/3) * pi * R^3 * density (assuming the planet is spherical with uniform density)

The density can be assumed from the information given or you can research it if necessary.

2. Calculate the mass of the planet:
Let's assume the density of the planet is 5500 kg/m^3. You can adjust this value if needed.
M = (4/3) * pi * R^3 * density
= (4/3) * 3.14 * (4.15 × 10^6 m)^3 * 5500 kg/m^3

Calculate M using the given formula. The result will be in kg.

3. Calculate the gravitational force acting on the satellite:
F_gravity = (G * M * m) / r^2

Substitute the values into the formula and calculate F_gravity in Newtons.

4. Convert the gravitational force to the weight on the planet's surface:
Weight = mass * gravitational acceleration
The gravitational acceleration (g) can be calculated using Newton's law of universal gravitation:
g = G * M / R^2

Substitute the values of G, M, and R into the formula and calculate g in m/s^2.
Note that the weight is equivalent to the gravitational force acting on the satellite when it is at rest on the planet's surface.

5. Calculate the true weight of the satellite when it is at rest on the planet's surface:
Multiply the mass of the satellite by the gravitational acceleration (weight = mass * g) to get the true weight in Newtons.

Follow the steps above, plug in the appropriate values, and calculate to find the true weight of the satellite when it is at rest on the planet's surface.