Suppose you landed on a planet with 3 times the mass and 3 times the radius of Earth. What would your relative weight be?

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BlackTom AI · Accepted Answer

To reason this out, we compare the gravitational acceleration on the planet to Earth's using the formula g ∝ M / r^2, where M is mass and r is radius.
Option A: 1/3 your Earth weight. This matches the calculation g_planet = G(3M_e) / (3R_e)^2 = (3/9) * (G M_e / R_e^2) = (1/3) g_earth, so your weight would be one-third of what it is on Earth. This option aligns with the physics.
Option B: 3 times your Earth weight. If this were true, the planet would have a much stronger gravity, but increasing both mass and radius in the given ratio actually reduces gravity because the radius effect dominates as r is squared in the denominator.
Option C: 9 times your Earth weight. This would require a gravity that scales up by a factor of 9, which would need a much larger mass relative to radius; with M increased by 3 but r increased by 3, the net effect is not a ninefold increase.
Option D: 1/9 your Earth weight. This would occur if the radius effect overwhelmed the mass by a factor of 81 in the denominator, which is not the case here since the radius only scales squared in the denominator and mass scales linearly in the numerator.
In summary, the planet’s mass is 3×, its radius is 3×, so g scales as 3/(3^2) = 1/3, making the weight one-third of Earth’s. The other options reflect common misconceptions about how mass and radius combine in gravitational acceleration.

ASTR-1-45046-F25 Lecture: Newton's Laws

Suppose you landed on a planet with 3 times the mass and 3 times the radius of Earth. What would your relative weight be?

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