An apple weighs 1 N on the surface of the Earth. What would its weight be on Earth if the planet had the same mass but half of its present radius?

Question

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Answer 1

At the surface of the Earth:

W = GMm/R²

1. W = the apple's weight
2. G = gravitational constant
3. M = Earth's mass
4. m = apple's mass
5. R = Earth's radius

Now let's change R to R/2 and find the new weight:

W_new = GMm/(R/2)² = 4GMm/R² = 4W

It would weigh four times as much (4 N).