If the radius of a planet is halved, what happens to the gravitational accelerat

If the radius of a planet is halved, what happens to the gravitational acceleration on its surface?

If the radius of a planet is halved, what happens to the gravitational acceleration on its surface?

Step 1: Understand that gravitational acceleration (g) is related to the radius (R) of the planet.
Step 2: Remember the formula that shows this relationship: g is proportional to 1 divided by the square of the radius (g ∝ 1/R²).
Step 3: If the radius (R) is halved, we can express this as R = R/2.
Step 4: Substitute R/2 into the formula: g ∝ 1/(R/2)².
Step 5: Simplify the equation: (R/2)² = R²/4, so g ∝ 1/(R²/4) = 4/R².
Step 6: This means that if the radius is halved, the gravitational acceleration (g) becomes 4 times greater.

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