Surface gravity across the Solar System
Why a small dense world can out-pull a giant, how the g = GM/r squared formula plays out on real planets, and what the numbers mean.
Mass and radius pull in opposite directions
Surface gravity is a tug of war between two quantities in g = GM/r squared. More mass raises gravity in direct proportion, while a larger radius lowers it as the square. That squared radius term is why size matters so much: a body twice as wide as another of equal mass has only a quarter of its surface gravity. It also explains a surprise, that a small dense world can grip its surface more firmly than a much larger but puffed-up one.
Why Mars and Mercury feel similar
Mars has far more mass than Mercury, yet both sit near 0.38 g at their surfaces. Feeding Mars values of 6.417e23 kg and 3.3895e6 m into the formula gives about 3.73 m/s^2, close to 0.38 g. Mercury lands at almost the same figure despite being smaller and lighter, because its higher density packs that mass into a tighter radius. The lesson is that neither mass nor size alone predicts surface gravity; only their combination in the formula does.
The gas giants and the Sun
Jupiter is more than 300 times Earth's mass, but its enormous radius of about 6.99e7 m spreads that mass out, so its surface gravity is only around 2.64 g rather than hundreds. The Sun, with a mass of 1.989e30 kg and a radius near 6.957e8 m, reaches roughly 274 m/s^2, about 28 g. These bodies have no solid surface, so the figure refers to the visible cloud tops or photosphere rather than solid ground you could stand on.
From surface gravity to weight
Once you know a body's surface gravity you can find what anything would weigh there. Multiply the object's mass in kilograms by the local g in metres per second squared to get its weight in newtons, or simply scale an Earth weight by the relative-to-Earth figure. A 70 kg person weighing about 686 N on Earth would register only around 114 N on the Moon at 0.17 g, and would feel crushingly heavy near 28 g at the Sun's surface.