Question

3 based on the data table, match each planet with the force of gravity you would experience if you could stand on its surface. (assume each planet has the same diameter.)
planet | mass (10²⁴ kg)
x | 4.867
y | 5.972
z | 0.642
blank → 3.71 m/s²
blank → 8.87 m/s²
blank → 9.81 m/s²
planet x planet y planet z

Explanation:

Step1: Recall surface gravity formula

The surface gravity $g$ of a planet is given by $g = \frac{GM}{r^2}$, where $G$ is the gravitational constant, $M$ is the planet's mass, and $r$ is its radius.

Step2: Compare masses (same radius)

Since all planets have the same diameter (so same $r$), $g$ is directly proportional to $M$.

Step3: Rank masses and gravity

Rank masses: $M_Y (5.972) > M_X (4.867) > M_Z (0.642)$. Match to gravity values: highest mass → highest gravity, lowest mass → lowest gravity.

• Planet Y (largest mass) → 9.81 m/s²
• Planet X (middle mass) → 8.87 m/s²
• Planet Z (smallest mass) → 3.71 m/s²

Answer:

Planet X → 8.87 m/s²
Planet Y → 9.81 m/s²
Planet Z → 3.71 m/s²