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 doubled, what happens to the gravitational force acting on the satellite?
It doubles
It halves
It becomes four times
It becomes one-fourth
Questions & Step-by-Step Solutions
A satellite is in a circular orbit around the Earth. If the radius of the orbit is doubled, what happens to the gravitational force acting on the satellite?
Step 1: Understand that gravitational force depends on the distance from the center of the Earth to the satellite.
Step 2: Know that the formula for gravitational force is inversely proportional to the square of the radius (distance). This means if you double the radius, the force changes based on the square of that change.
Step 3: If the radius is doubled, we can express this as r becomes 2r.
Step 4: Calculate the new gravitational force using the relationship: Gravitational force ∝ 1/r².
Step 5: Substitute the new radius into the formula: 1/(2r)² = 1/(4r²).
Step 6: This shows that the new gravitational force is 1/4 of the original gravitational force.
Gravitational Force – The gravitational force between two masses is inversely proportional to the square of the distance between their centers, as described by Newton's law of universal gravitation.
Circular Orbits – In a circular orbit, the gravitational force provides the necessary centripetal force to keep the satellite in orbit.
