Your weight is a measure of the amount of gravity exerted on your body by the planet Earth. If you travel to a different planet or celestial body, such as the moon, your weight changes if the gravity is different. Because the moon has about one-sixth of the gravity that Earth does, you’d weigh less standing on it.
Comparing Objects’ Gravity
Gravity is based on an object’s mass and your distance from the center. When you’re on the surface of a planet, you can use the planet’s radius to calculate your distance from the center.
If you compare the mass of the moon to the earth’s, you will find that the moon’s mass is 0.0123 of the earth. The moon’s radius is 0.273 of the Earth’s. To see what the moon’s gravity is compared to the earth, divide the ratio of the masses by the ratio of the radii squared.
(x=frac{text{ratio of masses}}{text{ratio of radii}^2}=frac{0.0123}{0.273^2}=frac{0.0123}{0.074529}=0.165)
Calculating Your Weight on the Moon
1. Weight Yourself on Earth
Write down your weight in pounds or kilograms. For example, suppose that you weigh 135 pounds.
2. Multiply
Multiply your weight by the moon’s gravity relative to earth’s, which is 0.165.
3. Find Your Weight on the Moon
Solve the equation. In the example, you would obtain the product 22.28 lbs. So a person weighing 135 pounds on Earth would weigh just over 22 pounds on the moon. Remember, however that your mass has not changed.
