Orbital Speed of a Satellite revolving around Earth

To determine the orbital speed of a satellite revolving around Earth, we need to consider the gravitational force acting on the satellite and the centripetal force required to maintain its circular motion.

Gravitational Force:
The gravitational force between Earth and the satellite is given by Newton's law of universal gravitation:
F = G * (m * M) / R^2
where F is the gravitational force, G is the gravitational constant, m is the mass of the satellite, M is the mass of Earth, and R is the radius of Earth.

Centripetal Force:
The centripetal force required to maintain the satellite in its circular orbit is given by:
F = (m * v^2) / R
where F is the centripetal force, m is the mass of the satellite, v is the orbital speed of the satellite, and R is the distance between the satellite and the center of Earth.

Equating the Forces:
Since the gravitational force provides the necessary centripetal force, we can equate the two equations:
G * (m * M) / R^2 = (m * v^2) / R

Canceling the mass:
We can cancel the mass of the satellite from both sides of the equation, resulting in:
G * M / R^2 = v^2 / R

Orbital Speed:
Rearranging the equation, we can solve for v:
v = sqrt(G * M / R)

Explanation:
The orbital speed of a satellite revolving around Earth depends on the gravitational constant (G), the mass of Earth (M), and the distance between the satellite and the center of Earth (R). The equation shows that the orbital speed is independent of the mass of the satellite.

The orbital speed can be calculated using the given values of G, M, and R. The value of G is approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2, the mass of Earth (M) is approximately 5.972 × 10^24 kg, and the distance from the surface of Earth (R) to the satellite is given as x + R.

By substituting these values into the equation, we can calculate the orbital speed of the satellite.