If the radius of the Earth were to double, what would happen to the gravitationa

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Question: If the radius of the Earth were to double, what would happen to the gravitational force experienced by a satellite in low Earth orbit?

Options:

Correct Answer: It would decrease to one-fourth

Solution:

The gravitational force is inversely proportional to the square of the distance. If the radius doubles, the force decreases to one-fourth.

If the radius of the Earth were to double, what would happen to the gravitational force experienced by a satellite in low Earth orbit?

If the radius of the Earth were to double, what would happen to the gravitational force experienced by a satellite in low Earth orbit?

Step 1: Understand that gravitational force depends on the mass of the Earth and the distance from the center of the Earth to 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 is the mass of the Earth, m2 is the mass of the satellite, and r is the distance from the center of the Earth to the satellite.
Step 3: If the radius of the Earth doubles, the distance (r) from the center of the Earth to the satellite also doubles.
Step 4: Since the distance is now doubled, we replace r with 2r in the formula: F = G * (m1 * m2) / (2r)^2.
Step 5: Calculate (2r)^2, which equals 4r^2. So, the new formula becomes F = G * (m1 * m2) / 4r^2.
Step 6: This shows that the new gravitational force is one-fourth of the original force because the force is inversely proportional to the square of the distance.

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.
Distance and Force Relationship – Understanding how changes in distance (in this case, the radius of the Earth) affect gravitational force is crucial for solving problems related to orbits.