the acceleration of a satellite can be deprived by equating the universal gravitational force and the centripetal force
true of false
False. The acceleration of a satellite can be derived by equating the gravitational force with the centripetal force, not by depriving it.
True. The acceleration of a satellite can be derived by equating the universal gravitational force with the centripetal force acting on the satellite.
True.
To understand why this statement is true, we need to break it down into its components.
1. Universal Gravitational Force: According to Newton's Law of Universal Gravitation, any two objects with mass will attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them. For two objects, such as a satellite and the Earth, the gravitational force between them can be calculated using the equation:
F_gravity = G * (m1 * m2) / r^2
where F_gravity is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.
2. Centripetal Force: In circular motion, there is a force called the centripetal force that acts towards the center of the circular path, keeping the object in motion. For a satellite in orbit around a planet, the centripetal force is provided by the gravitational force between the satellite and the planet. The centripetal force can be calculated using the equation:
F_centripetal = (m * v^2) / r
where F_centripetal is the centripetal force, m is the mass of the satellite, v is the velocity of the satellite, and r is the distance between the satellite and the planet.
To derive the acceleration of the satellite, we can equate the gravitational force and the centripetal force:
G * (m1 * m2) / r^2 = (m * v^2) / r
By rearranging the equation, we can solve for the acceleration (a):
a = v^2 / r = G * m1 * m2 / (r^2 * m)
In this equation, we can see that the acceleration of the satellite is dependent on the gravitational force between the satellite and the planet, as well as the mass of the satellite and its distance from the planet. Thus, the acceleration of a satellite can be derived by equating the universal gravitational force and the centripetal force. Hence, the statement is true.