the acceleration of a satellite can be derived by equating the universal gravitational force and the centripetal force.
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True. The acceleration of a satellite can be derived by equating the universal gravitational force and the centripetal force. This is based on the principle that the gravitational force between two objects provides the centripetal force required to keep the satellite in orbit.
The statement is true. The acceleration of a satellite can be derived by equating the universal gravitational force and the centripetal force.
To explain further, let's consider a satellite orbiting around a planet. The gravitational force between the satellite and the planet provides the centripetal force necessary to keep the satellite in its orbit. The centripetal force is directed towards the center of the orbit.
According to Newton's law of universal gravitation, the gravitational force between two objects is given by:
F_gravity = (G * m1 * m2) / r^2
Where:
- F_gravity is the gravitational force
- G is the universal gravitational constant
- m1 and m2 are the masses of the two objects
- r is the distance between the centers of the two objects
Furthermore, the centripetal force required to keep the satellite in orbit is given by:
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
- r is the radius of the satellite's orbit
By equating the two forces, we can solve for the acceleration of the satellite:
(G * m1 * m2) / r^2 = (m * v^2) / r
Simplifying the equation, we can obtain the expression for the acceleration:
a = (G * m1 * m2) / r^2
Therefore, the acceleration of a satellite can be derived by equating the universal gravitational force and the centripetal force.