You observe an arti�cial satellite orbiting the earth and estimate it is at

an altitude h = [03] km above the earth's surface and has a mass
m = 3500 kg. You wish to calculate when the satellite will be back in the same position. From the second law of
motion and the gravitational force law, calculate the following:
(a) What is the satellite's velocity? (m/s)
(b) What is the period of the satellite's motion?

The only force acting on the satellite is the force of gravity (Fg) right? So by combining the two laws I have Fg = ma. I solved for Fg, but I need some pointers on where to go from there.

mass is m (it will not matter in the end)

if height above earth is h

then radius of orbit = r = Rearth + h

then
Fg = G m Mearth/r^2

a = v^2/r
so Fg = m v2/r

so
G m Mearth/r^2 = m v^2/r
note m cancels, feather drifts right beside the space station

G Mearth/r = v^2
there you go
get v then it goes 2 pi r at v

To calculate the satellite's velocity and period of motion, you're on the right track using the second law of motion (F = ma) and the gravitational force law.

First, let's find the force of gravity (Fg) acting on the satellite:
1. The force of gravity is given by Newton's Law of Universal Gravitation: Fg = G * (m * M) / r^2, where G is the gravitational constant (6.67430 × 10^-11 N m^2/kg^2), m is the mass of the satellite, M is the mass of the Earth (5.972 × 10^24 kg), and r is the distance between the center of the Earth and the satellite.
2. Since the satellite is at an altitude h above the Earth's surface, we need to calculate r as the sum of the Earth's radius and the satellite's altitude: r = R + h, where R is the radius of the Earth (6371 km).
3. Substitute the values into the formula to find Fg in Newtons.

Next, let's find the satellite's velocity:
1. The gravitational force (Fg) provides the necessary centripetal force to keep the satellite in orbit. So we have Fg = (m * v^2) / r, where v is the velocity of the satellite.
2. Substitute the known values of Fg and r into the equation and solve for v.

Finally, we can find the period of the satellite's motion:
1. The period (T) is the time taken for the satellite to complete one orbit.
2. Period is related to velocity and circumference by the equation T = (2πr) / v.
3. Substitute the known values of r and v into the equation to find T in seconds.

Remember to convert the values to the appropriate units. Use a scientific calculator if necessary.