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?
Practice Questions
1 question
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
The gravitational force is inversely proportional to the square of the distance; halving the radius increases the force by a factor of four.
Questions & Step-by-step Solutions
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Q
Q: 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?
Solution: The gravitational force is inversely proportional to the square of the distance; halving the radius increases the force by a factor of four.
Steps: 7
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.
