The expression for time period is given as,T=3π/Gd
=(3×22/7)/(6.6×10-11×5.51×10³)
=(66/255.02)×10-8
=0.5×10⁴=5×10³ s

Hope this helps!!!

Given:
Mean density of the planet (ρ) = 5.51 x 10^3 kg/m^3
Gravitational constant (G) = 6.67 x 10^-11 N m^2/kg^2

To find:
Time period of the satellite (T)

Solution:

Step 1: Understanding the problem
We have a satellite revolving in an orbit close to the surface of a planet. We need to calculate the time period of the satellite's orbit.

Step 2: Formulas
1. The gravitational force between two objects can be calculated using the equation:
F = (G * m1 * m2) / r^2
Where F is the force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.

2. The gravitational force provides the centripetal force required for the satellite to stay in orbit. The centripetal force can be calculated using the equation:
F = (m * v^2) / r
Where F is the force, m is the mass of the satellite, v is its velocity, and r is the radius of the orbit.

3. The mass of the satellite can be calculated using the equation:
m = ρ * V
Where m is the mass, ρ is the density of the planet, and V is the volume of the satellite.

4. The volume of the satellite can be calculated using the equation:
V = (4/3) * π * r^3
Where V is the volume and r is the radius of the satellite.

Step 3: Calculations
Let's assume the radius of the satellite's orbit is R, and the mass of the satellite is m.

1. The gravitational force between the planet and the satellite is equal to the centripetal force:
(G * M * m) / R^2 = (m * v^2) / R
Here, M is the mass of the planet.

2. We can cancel out the mass of the satellite and rearrange the equation to solve for the velocity:
v^2 = (G * M) / R
v = sqrt((G * M) / R)

3. The time period of the satellite is the time taken to complete one revolution around the planet:
T = (2 * π * R) / v

Step 4: Substituting values and calculating
We need to find the time period of the satellite's orbit, so we will substitute the given values into the equations and calculate T.

1. First, we need to find the mass of the satellite:
m = ρ * V
Since we don't have the radius of the satellite, let's assume a value of R = 10,000 meters for the radius of the satellite's orbit.

V = (4/3) * π * R^3
= (4/3) * 3.14 * (10,000^3)
= 4.19 x 10^12 m^3

m = (5.51 x 10^3 kg/m^3) * (4.19 x 10^12 m