The acceleration of a satellite can be derived by equating the universal gravitational force and the centripetal force
true or false
True. The acceleration of a satellite can be derived by equating the universal gravitational force and the centripetal force acting on it.
True. The acceleration of a satellite can be derived by equating the universal gravitational force and the centripetal force.
True.
The acceleration of a satellite can be derived by equating the universal gravitational force and the centripetal force. This is based on the understanding that a satellite performs circular motion around a central body, such as a planet. The centripetal force, which keeps the satellite in orbit, is provided by the gravitational force between the satellite and the central body.
To derive the acceleration of the satellite, we can start by equating these two forces:
Universal gravitational force (Fg) = Centripetal force (Fc)
The universal gravitational force is given by Newton's law of universal gravitation:
Fg = (G * M * m) / r^2
where G is the gravitational constant, M and m are the masses of the central body and satellite respectively, and r is the distance between their centers.
The centripetal force is given by the equation:
Fc = (m * v^2) / r
where v is the velocity of the satellite.
By equating these two forces, we have:
(G * M * m) / r^2 = (m * v^2) / r
We can cancel out the mass of the satellite (m) and rearrange the equation to solve for the acceleration (a):
a = (G * M) / r^2
Therefore, the acceleration of a satellite can be derived by equating the universal gravitational force and the centripetal force.