A satellite of mass 5700 orbits the Earth and has a period of 6000 .

a) Determine the radius of its circular orbit.

b) Determine the magnitude of the Earth's gravitational force on the satellite.

c) Determine the altitude of the satellite.

To solve this problem, we will use the following equations:

a) The period (T) of an object in circular motion can be related to its radius (r) by the equation:
T = 2π√(r³/GM), where G is the universal gravitational constant and M is the mass of the Earth.

b) The magnitude of the gravitational force (F) between two objects can be calculated using Newton's law of universal gravitation:
F = GMm/r², where m is the mass of the satellite.

c) The altitude (h) of the satellite can be calculated by subtracting the radius of the Earth (R) from the radius of the orbit:
h = r - R

Now let's solve the problem step by step:

a) Determine the radius of its circular orbit:
First, we need to rearrange the equation T = 2π√(r³/GM) to solve for r:
r³ = (GMT²)/(4π²)
r = ∛((GMT²)/(4π²))

Substituting the given values:
r = ∛((6.67430 × 10⁻¹¹ N m²/kg² * 5.98 × 10²⁴ kg * (6000 sec)²)/(4π²))

Calculating this expression will give you the value of r.

b) Determine the magnitude of the Earth's gravitational force on the satellite:
Using the equation F = GMm/r², we can calculate the magnitude of the gravitational force. Substituting the given values, we get:
F = (6.67430 × 10⁻¹¹ N m²/kg² * 5.98 × 10²⁴ kg * (5700 kg))/(r²)

Calculating this expression will give you the magnitude of the gravitational force.

c) Determine the altitude of the satellite:
We can calculate the altitude by subtracting the radius of the Earth (which is approximately 6,371 kilometers or 6.371 × 10⁶ meters) from the radius of the orbit:
h = r - R

Substituting the values of r and R will give you the altitude of the satellite.