The acceleration of a satellite can indeed be derived by equating the universal gravitational force and the centripetal force acting on it. Let's break down the derivation step by step:
Step 1: The gravitational force between two objects can be calculated using Newton's law of universal gravitation:
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.
Step 2: In the case of a satellite orbiting a planet, the gravitational force is responsible for providing the necessary centripetal force to keep the satellite in orbit. The centripetal force is given by:
F_centripetal = m * a
where F_centripetal is the centripetal force, m is the mass of the satellite, and a is the acceleration of the satellite.
Step 3: Equating the gravitational force and the centripetal force, we have:
F_gravity = F_centripetal
G * (m1 * m2) / r^2 = m * a
Step 4: Rearranging the equation to solve for the acceleration, we get:
a = G * (m1 * m2) / (r^2 * m)
Step 5: In the case of a satellite orbiting a planet, the mass of the satellite cancels out with one of the masses in the equation. Assuming m1 is the mass of the planet and m2 is the mass of the satellite, the equation simplifies to:
a = G * m1 / r^2
So, the acceleration of a satellite in orbit around a planet can be calculated using this equation.
the acceleration of a satellite can be derived by equating the universal gravitational force and the centripetal force
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