You Asked:

Do you weigh more or less when you are 15 floors above the Earth? — Matthew, Milledgeville, Ga.

Marshall Brain Answers:

You weigh very slightly less on the 15th floor of a skyscraper than you do at ground level. The reason is because the acceleration caused by gravity decreases as you move away from the center of the earth. If you look at the equation for the acceleration due to gravity you can see why:

g = G * M / R^2

In this equation, G is the gravitational constant, M is the mass the earth, and R is the distance from earth’s center. So, as you get farther away from the center of the earth, the acceleration of gravity exerted by the earth, g, decreases.

A 15 story skyscraper only puts you 150 feet (50 meters) or so farther away from the center of the earth. That’s not enough to have a noticeable affect, because the radius of the earth is about 4,000 miles (6,378 km). The acceleration caused by earth’s gravity is 9.8 m/sec^2 at sea level. We can plug in some real numbers to see that:

6.673*10^-11 * 5.9742*10^24 / 6,378,000^2 = 9.8 m/sec^2

Where:
- G = 6.673*10^-11 m^3/(kg*sec^2)
- mass of the earth = 5.9742*10^24 kg
- radius of the earth = 6,378,000 meters

If you could build a skyscraper that went 4,000 miles up into space, the force of gravity would drop to 2.45 m/sec^2. You would weigh one quarter of what you weigh at ground level.

Arthur C. Clarke, in his book 3001: The Final Odyssey talks about this effect. In the book, humans have built towers from the earth’s surface up to geostationary orbit. At a certain height in the towers, people can don pterodactyl-size wings and fly like a bird because the force of gravity is so low at that altitude.

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