A satellite is in a circular orbit around the Earth. If the radius of the orbit
Practice Questions
Q1
A satellite is in a circular orbit around the Earth. If the radius of the orbit is halved, what happens to the gravitational force acting on the satellite?
It remains the same
It doubles
It quadruples
It decreases by half
Questions & Step-by-Step Solutions
A satellite is in a circular orbit around the Earth. If the radius of the orbit is halved, what happens to the gravitational force acting on the satellite?
Correct Answer: Gravitational force increases by a factor of four.
Step 1: Understand that gravitational force depends on the distance between two objects, in this case, the Earth and the satellite.
Step 2: Remember the formula for gravitational force: F = G * (m1 * m2) / r^2, where F 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 their centers.
Step 3: Note that if the radius of the orbit (r) is halved, the new radius becomes r/2.
Step 4: Substitute the new radius into the formula: F' = G * (m1 * m2) / (r/2)^2.
Step 5: Simplify the equation: (r/2)^2 = r^2 / 4, so F' = G * (m1 * m2) / (r^2 / 4) = 4 * (G * (m1 * m2) / r^2).
Step 6: This shows that the new gravitational force (F') is four times the original gravitational force (F).
Step 7: Conclude that halving the radius increases the gravitational force acting on the satellite by a factor of four.
Gravitational Force – The gravitational force between two masses is given by Newton's law of universal gravitation, which states that the force is inversely proportional to the square of the distance between the centers of the two masses.
Circular Orbits – In a circular orbit, the gravitational force provides the necessary centripetal force to keep the satellite in orbit, and changes in the radius of the orbit affect the gravitational force experienced by the satellite.
