Why does your weight change on different planets?

What this question is really asking

You are not changing as a person when you travel to another planet. The key idea is that “weight” depends on gravity, and gravity is not the same everywhere.

Mass vs. weight (the common mix-up)

• Mass is how much matter you have. It does not depend on location and is measured in kilograms (kg).
• Weight is a force caused by gravity pulling on your mass. It is measured in newtons (N).

Mathematically: $$W = mg$$ So if $m$ stays the same but $g$ changes, then $W$ changes.

Why $g$ is different on different planets

A planet’s surface gravity mainly depends on two things:

• the planet’s mass $M$ (more mass usually means stronger gravity),
• the distance from its center, which is basically its radius $R$ (bigger radius means you are farther from the center, which weakens gravity).

A simplified model is: $$g = \frac{GM}{R^2}$$ where $G$ is the gravitational constant.

So:

• A very massive planet can give you a larger $g$ and make you weigh more.
• A planet with a large radius can reduce $g$ at its surface, even if it is massive.

Quick numerical example

If your mass is $m = 60\text{ kg}$:

• On Earth, $g \approx 9.8\text{ m/s}^2$, so $W \approx 60 \cdot 9.8 = 588\text{ N}$.
• On the Moon, $g \approx 1.6\text{ m/s}^2$, so $W \approx 60 \cdot 1.6 = 96\text{ N}$.

Same mass, different $g$, different weight.

Takeaway

Your weight changes on different planets because gravity ($g$) changes due to different planet masses and radii, but your mass stays constant.