The Mysterious Movement of the Moon: What Does It Mean for Our Weight?

[mikebpr]

I watched a show about what if the moon disappeared the other night and it said the moon is moving away from us about an inch and a half per year. Does this mean that the lunar effects such as gravity forces on humans will get weaker and therefore we, along with other items, will get heavier? Is a gram still a gram from when it was first named back in the late 1700's?

 

[russ_watters]

Welcome to PF!

First, a gram is a unit of mass, not weight. So it isn't affected by gravity. But no, the definition of a gram has changed over the years.

For the rest; There are several factors affecting your apparent weight, such as geographic location, altitude and speed. Lunar gravity (tides, actually) have an impact, but they are very small and of course not always in the same direction.

 

[mikebpr]

Did you say that a body of mass is not affected by gravity?

 

[HallsofIvy]

No, you are misinterpreting what he said. What he said was that, while the weight of a body depends upon the gravitational pull on the body, the mass of a body does not depend upon the gravitational pull. A "body of mass" is "influenced" by gravity but its mass does not depend upon the gravitational pull.

 

[russ_watters]

Right: a body of mass is influenced by gravity, but a body's mass is not.

 

[rootone]

Which means that a gram of something on Earth is still a gram on the Moon.
However it's weight as determined by the same weighing scale would be only about 17% of that measured when on Earth.

Yes, the Moon's gravity does have a tiny effect on the measured weight of something on Earth, but it's so small that it makes no difference for any practical purpose.

 

[mgkii]

Hi Mikebpr

If you're already familiar with the following then ignore me - but from the way your question is asked, you may find it useful.

In "real life" day to day conversation, we use grams, kilograms etc to mean weight - and we use "weight" and "mass" interchangeably. And that's not a problem - real life tends to be spent on earth, and there's no confusion for reasons that will become clear. However, mass and weight are two very different - but closely related - things.

Mass is all about how much "stuff" there is in something and it measured in grams or KG. Take a hammer on the Earth and sent the same hammer to the moon - it's the same hammer, and it has the same mass.

Weight is the result of gravity on a mass and is measured in "Newtons". Earth's gravity is pretty much constant wherever you go on the surface of the planet, and it exerts a pull that gives 1KG of mass, a weight of 9.8 Newtons. So a 1Kg hammer weighs more Newtons on Earth that it does on the Moon, because the Moon exerts a weaker gravitational tug on the hammer than the Earth does. You could say in normal conversation that your hammer weighs 9.8 Newtons and you would be accurate - but most people wouldn't have a clue what you meant! When you say your hammer weighs 1Kg, it really means it has a mass of 1Kg - but everyone knows what you mean, as a mass of 1Kg weights the same in anywhere on earth!

If you want to be completely accurate (and it will help in relation to your question), everything that has mass has gravity - so not only is the Earth "pulling" the hammer down towards it (the measured effect being the 9.8 Newtons of weight), the hammer is also pulling the Earth up towards it. But only a little bit :-)

So going back to your original question - if we correct the language so that you're talking about Newtons for Weight, and Grams for Mass then you're pretty much spot on - as the moon recedes from the earth, it's gravitational force lessens in respect of things on earth, and an object of 1 gram will weigh fewer Newtons**. 1 gram will remain 1 gram though.

** When the moon is overhead. Of course - as the Earth spins and the position of the moon appears to move over a 24 hour period, the moon actually makes you heavier at some points of the day and lighter at others. And so does the sun. And all of the other planets as well. But as already said - the effect is really really tiny.

 

[HallsofIvy]

I don't know about you but I'm getting heavier! And next week is thanksgiving!

 

[CWatters]

I watched a show about what if the moon disappeared the other night and it said the moon is moving away from us about an inch and a half per year.

Did they explain why? It's not because gravity is getting weaker, it isn't.

 

[evan-e-cent]

I am not a physicist but his is how I see it. The reason that the moon is moving further away from the Earth is, I believe, caused by the moon's rotation slowing down. The gravitational force between the Earth and the moon is responsible for pulling the moon into its circular orbit. We used to talk about the centrifugal force or its opposite the centripetal force of circular motion (mass . omega squared . radius where omega is the angular velocity in radians per unit time). This must equal the gravitational force in steady state. If the velocity of the moon decreases it moves to a greater distance from Earth where the centripetal force is less and the gravitational force is weaker and the two forces balance again. But gravity on Earth is not significantly affected.

I think they said in the documentary the reason the moon is slowing down is related to the friction of water moving on the Earth's surface with tidal motion. I can see how tides would affect the rotation of the Earth but I cannot see how it affects the moon. Perhaps the bulge of water on the Earth's surface creates a gravitational force on the moon that drags it back slightly, causing it to slow down. But the moon would be pulled towards the center of gravity of the Earth including its oceans, which may not correspond with the geometrical center of the earth. Perhaps someone else can explain this.

A second aspect of this question is whether the gravitational force on an object on the Earth's surface is affected by the position of the moon. In theory it is. If the moon is directly overhead you would weigh slightly less than when the moon is on the opposite side of the earth. But the effect is very small. However next time I weigh myself I will do it at noon when the moon is directly overhead (i.e. new moon).

 

[Drakkith]

The reason that the moon is moving further away from the Earth is, I believe, caused by the moon's rotation slowing down.

I think you mean the Earth's rotation slowing down. The tides transfer angular momentum from the Earth to the Moon, causing it to gradually recede.

 

[jbriggs444]

Perhaps the bulge of water on the Earth's surface creates a gravitational force on the moon that drags it back slightly, causing it to slow down.

This part is correct. Except that the bulges lead the moon. They pull it ahead. This causes the Earth's rotation to slow. All other things being equal, this would cause the moon to speed up. But orbital mechanics is tricky.

If you have an object in circular orbit and you apply a brief thrust to make it move faster, it does move faster. But its orbit becomes elliptical. The ellipse is one that will have a low point where you applied the thrust. It will have a high point 180 degrees away on the opposite side of the object being orbited. In this elliptical orbit, the object's velocity at the low point is higher than it had been in the circular orbit. That is because of the thrust you applied. But at the high point, its velocity is lower than it had been in the circular orbit. That is because its kinetic energy at the low point has been traded for gravitational potential energy at the high point. If you apply a second brief thrust at the high point, increasing the object's velocity, then it can enter a new circular orbit. In this new circular orbit it will be moving more slowly than in the old circular orbit.

You have applied a forward thrust twice, accelerating the object to a higher speed both times. In spite of this, its final speed is lower than its starting speed.

In the case of the moon, the forward thrust is applied continuously, but the end result is the same. You still have the seemingly paradoxical situation where a constant forward thrust results in a decrease in speed over time.

 

[evan-e-cent]

It is amazing how things that we thought were simple, rapidly get complicated. In order to gain some understanding I tend to over-simplify them. That introduces assumptions that may not be valid. But I suppose that is the first step in learning. Thanks for the explanation. I wonder why the tidal bulge leads the moon instead of trailing it.

 

[jbriggs444]

I wonder why the tidal bulge leads the moon instead of trailing it.

The tidal bulge is produced by the moon. The moon pulls the nearer part of the Earth more strongly than the middle. So the nearer part bulges up toward the moon. It pulls the middle of the Earth more strongly than the far side. So the far side bulges up away from the moon. You may have already understood this.

As the Earth rotates relative to the moon, it pulls those bulges in the direction of its rotation. Call it friction, viscosity, rigidity or whatever. The Earth is rotating in the same direction that the moon is revolving and is doing so at a much higher rate [roughly one rotation per day versus roughly one revolution per month]. So the bulges are dragged forward relative to the moon.

 

[rootone]

If the Earth were not rotating the tidal bulge would be directly underneath the moon.
That is where the pull of the Moon's gravity wants the water to go,
but because the Earth IS rotating, and carrying the ocean along with it, the actual flow of water ends up somewhat ahead of the moon.

 

[evan-e-cent]

Ah that explains the bulge of tides leading ahead of the moon. This would tend to speed up the motion of the moon and slow down the, rotation of the Earth until eventually, in many millennia they may be rotating at the same speeds I think. I thought that higher speed of rotation of the moon would be associated with a smaller circular orbit, so the moon would move closer to the earth, but JBRIGGS444 suggests that the opposite occurs paradoxically. No wonder they didn't try to explain it in a TV documentary!

 

[Drakkith]

I thought that higher speed of rotation of the moon would be associated with a smaller circular orbit, so the moon would move closer to the earth, but JBRIGGS444 suggests that the opposite occurs paradoxically. No wonder they didn't try to explain it in a TV documentary!

Indeed!