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Q & A: Less Gravity on the moon?

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Q:
why is there less gravity on the moon than on the earth
- Anonymous
A:
Newton's equation for the force (in units of "Newtons") of gravity between two objects is:

F = G*m1*m2/d^2

m1 and m2 are masses (in kilograms) and d^2 is the distance (in meters) squared between the centers of the two objects (e.g. you and the center of the earth). G is a constant, the gravitational constant, which is 6.67*10^-11 when these units are used. Since this is a very small number, it means that gravity is a very weak force that you only really notice when there is a very large mass involved (like the earth or the moon).

So, we take our equation and plug and chug.

Mass of the Earth: 5.98 x 10^24 kg
Radius of the Earth: 6378 km
(from http://pds.jpl.nasa.gov/planets/welcome/earth.htm)
Mass of the moon: 7.34*10^22 kg
Radius of the moon: 1737.4 km
(from http://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html)
You: 63.5 (Say you weighed 140 pounds, your mass would be 63.5 kg)

The force of gravity between you and the earth is:

F = (6.67*10^-11) (5.95*10^24 kg)(63.5 kg)
---------------------------------------
(6,378,000 m)^2

F = 620 N

If I redo the equation for the moon, replacing the earth's mass and radius with that of the moon, I get:

F = 103 N

So when Neil Armstrong said "One small step for man, one giant leap for mankind" on the moon in 1969, he was under only 1/6 Earth's gravity!

As you can see, the force of gravity on a person on the earth is greater than the force of gravity on a person on the moon. In a nutshell, this is because the earth has more mass than the moon.

Jason

(republished on 07/19/06)

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