What happens to the gravitational force on a satellite if its altitude is doubled?
Practice Questions
1 question
Q1
What happens to the gravitational force on a satellite if its altitude is doubled?
It doubles
It remains the same
It becomes four times weaker
It becomes eight times weaker
The gravitational force decreases with the square of the distance from the center of the Earth. If the altitude is doubled, the distance from the center of the Earth becomes R + 2h, and the force becomes weaker by a factor of four.
Questions & Step-by-step Solutions
1 item
Q
Q: What happens to the gravitational force on a satellite if its altitude is doubled?
Solution: The gravitational force decreases with the square of the distance from the center of the Earth. If the altitude is doubled, the distance from the center of the Earth becomes R + 2h, and the force becomes weaker by a factor of four.
Steps: 6
Step 1: Understand that gravitational force depends on distance from the center of the Earth.
Step 2: Know that the formula for gravitational force is inversely proportional to the square of the distance.
Step 3: If the satellite is at an altitude 'h', the distance from the center of the Earth is 'R + h' (where R is the radius of the Earth).
Step 4: If the altitude is doubled, the new altitude is '2h', making the new distance 'R + 2h'.
Step 5: The new distance is greater than the original distance, which means the gravitational force will be weaker.
Step 6: Since gravitational force decreases with the square of the distance, if the distance is doubled, the force becomes weaker by a factor of four (2 squared).
