The acceleration of a satellite can be derived by equating the universal gravitational force and the centripetal force.
True or False
True.
True.
The acceleration of a satellite can be derived by equating the universal gravitational force and the centripetal force. According to Newton's second law of motion, the net force acting on an object equals the product of its mass and acceleration (F = ma). In the case of a satellite orbiting a larger celestial body, the force of gravity provides the centripetal force required to keep the satellite in its circular orbit. This can be expressed as:
(G * m1 * m2) / r^2 = (m2 * v^2) / r
where G is the gravitational constant, m1 and m2 are the masses of the celestial bodies, r is the distance between their centers of mass, and v is the velocity of the satellite. By rearranging this equation, we can solve for the acceleration of the satellite.
True.
To derive the acceleration of a satellite, we can equate the gravitational force acting on the satellite to the centripetal force required to keep it in orbit.
The gravitational force between two objects can be calculated using Newton's Law of Universal Gravitation, which states that the force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
The equation for gravitational force (Fg) is given by:
Fg = (G * m1 * m2) / r^2
Where G is the universal gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers.
Now, when a satellite is in orbit around a planet, the force acting on it is the gravitational force exerted by the planet. This gravitational force provides the centripetal force necessary to keep the satellite in a circular orbit.
The centripetal force required to keep an object in circular motion is given by the equation:
Fc = (m * v^2) / r
Where m is the mass of the satellite, v is its orbital velocity, and r is the radius of its orbit.
By equating the gravitational force (Fg) and the centripetal force (Fc), we can solve for the satellite's acceleration (a):
(G * m1 * m2) / r^2 = (m * v^2) / r
Simplifying the equation further, we can cancel out the mass of the satellite (m) and rearrange the equation to solve for acceleration (a):
a = (G * m1) / r^2
Therefore, the acceleration of a satellite can be derived by equating the universal gravitational force and the centripetal force, making the statement true.