Answer key: Gravity on Other Planets Worksheet
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Goal: Calculate surface gravity, weight and escape speed on other worlds, and explain how mass and radius each affect gravity.
Completed results table
| Setting | Surface gravity | Your weight | Escape speed |
|---|---|---|---|
| Earth | 9.82 m/s² | 687.42 N | 11.19 km/s |
| Moon | 1.62 m/s² | 113.7 N | 2.38 km/s |
| Mars | 3.73 m/s² | 261.1 N | 5.03 km/s |
| Jupiter (317.8 Earth masses, 11.21 Earth radii) | 24.84 m/s² | 1,738.46 N | 59.56 km/s |
| Earth’s mass, twice Earth’s radius | 2.46 m/s² | 171.86 N | 7.91 km/s |
Answers
Your mass is 70 kg everywhere. Use your Moon results to explain the difference between mass and weight.
Mass is the amount of matter in you (70 kg) and does not change. Weight is the force of gravity on that mass: about 114 N on the Moon instead of 687 N on Earth, because the Moon’s surface gravity is only 1.62 m/s².
How many times stronger is gravity on Earth than on Mars? Show your calculation.
About 2.6 times: 9.82 ÷ 3.73 ≈ 2.63.
Jupiter has about 318 times Earth’s mass, yet its surface gravity is only about 2.5 times Earth’s. Why?
Jupiter is also 11.21 times wider. Gravity weakens with the square of the distance from the center, so its larger radius divides the pull by 11.21² ≈ 126. The result is g ≈ 24.8 m/s², about 2.53 times Earth’s.
Predict, then check: if Earth kept its mass but doubled its radius, what would its surface gravity be? Explain with g = GM/R².
One quarter of today’s value, about 2.46 m/s². Doubling R makes R² four times larger, so g = GM/R² falls to 9.82 ÷ 4.
Rank the Moon, Mars, Earth and Jupiter by escape speed. What does this mean for launching rockets?
Moon 2.38 km/s, Mars 5.03 km/s, Earth 11.19 km/s, Jupiter 59.6 km/s. The higher the escape speed, the more energy a rocket needs to leave, so launching from the Moon is far easier than from Earth.
Jupiter has no solid surface. What does “surface gravity” mean for a gas giant?
It is the gravity at the level where the atmospheric pressure is 1 bar (about sea-level pressure on Earth), which astronomers use as the planet’s reference radius.