Our weight change without Moon?

[alpha2cen]

If there were not the Moon, how our body weight would be changed?

These are examples.

* No effect.

* Very small changed.

* Very large changed---above 10%.

If our body weight were changed, which percent would be correct?

And, are there any theory about it?

[D H]

Depends on what you mean by "weight". Colloquially throughout the English-speaking world, and legally in the US, "weight" is a synonym for mass. If you bring a physicians beam scale to the Moon and step on it it will register a very slight increase. (While a beam balance measures mass, it is subject to buoyancy effects.)

 

On the other hand, in much of physics and engineering, "weight" (aka "actual weight") is a synonym for "gravitational force". With this definition in hand, your weight ("actual weight") on the Moon is about 1/6 of your actual weight on the Earth. Ignoring that the Earth and Moon aren't quite round, this is given by Newton's law of gravity: [math]F=G M_p m_b / {r_p}^2[/math]. (G is the universal gravitational constant, M_p is the mass of the planet, m_b is the your body's mass, and r_p is the planet radius.) Since the Moon's mass is 0.0123 Earth masses and its radius about 0.273 Earth radii, your actual weight on the Moon is about 0.123/0.2732=0.165≈1/6 of your Earthbound actual weight.

 

 

On last definition of weight, called "apparent weight" or "scale weight", is that quantity measured by a spring scale. In magnitude this is very close to gravitational force. As a vector, scale weight points away from the planet's surface rather than into it. Unlike gravitational force, scale weight is a measurable quantity. Your scale weight on the Moon is about 1/6 of your scale weight on the Earth.

Edited December 28, 2010 by D H

[alpha2cen]

I mean our Earth grvity effect of the moon.

If there were not the Moon near the Earth, how the Earth's gravity would be changed?

[MrFungus420]

I mean our Earth grvity effect of the moon.

If there were not the Moon near the Earth, how the Earth's gravity would be changed?

 

By far too small an amount for us to feel.

 

Remember, the moon is orbiting the Earth. It can be directly "above" you, it can be on the opposite side of the Earth from you. So it's gravity can be completely against the Earth's (from your point of view) when it is directly above, and it can be adding to the Earth's gravity when it is opposite from you.

[swansont]

It's actually not a simple result. If there was no moon, there would be a reduction in the tides as a result, and tides deform the earth and affect the local value of the gravitational acceleration. The naive answer would be from finding GM/r^2.

 

Its effect on the period of a pendulum clock has been measured, back in the 1930's, when people used really good pendulum clocks. The half-period of oscillation of a 1m pendulum (nominally 1 sec) changed by about 150 microseconds as them moon went from "overhead" to being on the opposite side of the earth.

http://blogs.scienceforums.net/swansont/archives/448