Yes, that is exactly what makes you weigh less on Earth then on the Moon, though your mass hasn't changed, your apparent weight does.
Your would weigh 1/6th as much as you do here on mother Earth. The how is our moons' mass, and therefore its' gravity, is about 1/6 as much as the Earths'. Its' gravity well is not as deep as the Earths.
About 0.183g, where one g is the earths gravity, so about one fifth of the earths gravity. It is similar to our own moons surface gravity.
Callisto, one of Jupiter's moons, has a surface gravity of about 0.126 times that of Earth, or 1.235 m/s². This means that objects on Callisto weigh less than they would on Earth due to the weaker gravitational force.
Mars has about 38% of Earth's gravity, meaning that objects on Mars weigh less than they do on Earth. For example, if you weigh 100 pounds on Earth, you would weigh about 38 pounds on Mars.
Is your question "what do you weigh different objects on in space...", or "why would you attempt to weigh an object in space"...?
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The moons gravity is a lot lower than the Earths, so the men exploring the lunar surface will weigh a lot less, roughly 1/6th of what they do on earth. This is because the moon has considerably less mass.
The moons gravity is less than that of the earth, since the earths mass is greater than the moons mass. Gravity is related to mass and distance from that mass. The greater the mass, the greater the gravitational field it has.
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Theoretically it's independent, but often in practice you just weigh something and convert.
Theoretically it's independent, but often in practice you just weigh something and convert.