OTOH, I don't see how it fits into your scheme at all.

The slowing of the Earth over time is very real. The number one reason that we have leap seconds is because the Earth slows, on average, about 2 milliseconds per century. That is, it takes 2 milliseconds longer each day to make a full rotation. Since it has been over a hundred years since the year which is used as the standard (1900), our clocks are off relative to the Earth by 2 more milliseconds each day. After 500 days, that adds up to a full second--and we need a leap second.

However, the Earth does not steadily slow. There are other processes that cause it to speed up and slow down. The seasonal change in atmosphere/water/ice distribution will cause it to speed up and down, noticeably. The movement of material in the mantle will change its moment of inertia, causing it to speed up or down. None of those have a detectable influence on the moon, though.

If we were to use an average day from the year 2000 instead of the average day from 1900, we'd find that we'd have to be subtracting leap seconds once in a while, instead of adding them.

The first one was in June 1972, although it is not on your list. I'm not sure of what you are thinking of--the need for leap seconds is a fairly recent innovation.

There is a complete list at that NIST website. You seem to be missing the ones that occurred June 30, 1972, June 30, 1981, and four more since your last one.

You ask, near the bottom: "The astronomy books use the Earth's center of mass as the "X", or origin for the "r X F"
calculation. Why is that?"

Because the inertial effects act as if they are centered on the center of mass. If a force acts offcenter from the center of mass, a torque will be produced about the center of mass.

That's what we've been trying to say all along.

In your page you write:

It has been argued that a single force can cause a torque in an unsupported or unsuspended mass.
In every example thus far it has been an inertial impulse type force applied to an inertial type mass, such as the hitting, kicking, batting, or shooting: of one mass by another. In every example the mass has been torqued. In addition however the mass has also been given a change in momentum as well, thus making a repeat or sustained application of the force impossible.

This is not true. You were given examples of objects being stabilized by gravity gradients. Remember the barbell in orbit example?

In your drawing you seem to imply that the gravitational field is uniform in all cases. It is not. Remember that gravity fall off as 1/r². This means that the moon pulls harder on the near side of the earth than the far side.

Your torque diagrams need to include the normal force from the inclined plane or table or whatever, when present, not just the gravitational force as drawn.

Also, you can't just pick an arbitrary point for the origin, like "where the handle rests on the table" or whatever: you need to have the vector r point from the center of mass to the point where the force is being applied. The reson for this is simple: these kinds of force diagrams, with just one vector representing a single force on a rigid body, are simplifications of the much more complicated reality, which involved forces on an infinite number of infinitely small mass particles. When you integrate those forces up, you get the net force, and it acts on the center of mass because the center of mass is the result of the unweighted mass integral, whereas the force vector is weighted. If you know calculus, it's easy. If you don't know calculus, you have to take our word for it: torque has to be calculated relative to the center of mass.

I'm sorry, I'm way too tired to be trying to tackle this right now. I'm going to bed. Good night, all. Sleep well.

Don

Don

GrapesOfWrath
Quote:
-------------------------------------------------
The slowing of the Earth over time is very real. The number
one reason that we have leap seconds is because the Earth
slows, on average, about 2 milliseconds per century.
----------------------------------------------------
Please, don't scream!

I disagree. The Earth "appears" to slow. The reason we have the leap second is because the Earth "appears" to slow. You can not prove that it slows, the people who keep the time cannot prove it slows.
They can however show that it "appears" to slow.

There is a vast difference between slowing and "appearing" to slow.

Quote:
----------------------------------------------------
The first one was in June 1972, although it is not on your
list. I'm not sure of what you are thinking of--the need for
leap seconds is a fairly recent innovation.
--------------------------------------------------------
Before the atomic clock was invented the pendulum clocks were showing that the Earth "appeared" to slow. as soon as the atomic clock became real, I think that was about 1956, it then became a fact that the Earth "appeared" to slow.

For some reason it sticks in my mind that the first declared leap second came about before 1960. It may not have been made official until 1972.

I keep saying the Earth "appears" to slow and I must continue to do so.
Because of all the perturbations and the incredibly small time difference, only a yearly reading shows the "Leap Second". A celestial transit at the equator would only show about 1/4 mile in a year.

As I see it, there can always be more than one solution to a problem.

The problem is:
At the end of each year the time keepers look out from the Earth's frame of reference and find that the Earth does not "appear" to be where it should be.

The time keepers wait about 0.68 second, and every thing matches up and "seems" to be correct. The time keepers know the Earth spins on its axis, so they "assume" it is axial rotation that caused the problem. They have written it in books that the Earth is slowing down. Meaning that the axial rotation is slowing down. You have read the books, you "assume" them correct, therefore you "assume" the Earth is slowing on its axis.

I just think there maybe other solutions to the problem. The Earth makes one pass around the Sun and 1/250,000,000 of a trip around the Galaxy, and the Galaxy makes a trip somewhere..., each year.

I just don't see how Newton's first law can be wrong, and gravity can't torque a mass unless the mass is supported or suspended.
The Earth is not supported or suspended so the Moon can not torque the Earth. The Earth can not slow axially. The Earth may be traveling fast or slow in some direction, but it is not slowing around its axis.

The Earth-Moon rotates around the barycenter. That rotation "appears" to slow down one revolution every 18.6, years or about 6000 miles each month.
It does not slow down it only "appears" to slow.
The Earth "appears" to slow 0.68 second per year.
You say the Earth slows, I say the Earth is like the Earth-Moon system, and it only "appears" to slow.

We have been arguing about the 6000 miles and 539 miles with the Earth-Moon. The difference with the Earth-Moon Sun would be about 16 miles in one direction and eight tenths of one mile per year in the other. I'm sure you don't want to go there.

If the one thing doesn't make sense to you the other won't either.

The "Leap Second" is the exact same type motion as the "regression of nodes" motion.

That statement probably doesn't make sense to you either, but that is the way it is.

The Earth-Moon barycenter is traveling around the Galaxy slower than the Sun. The "Leap Second" is not a slowing it is a running slow, which makes it "appear" to be a slowing.

Are you confused?
I will probably go to my grave with this; it is so simple that I just can't explain it to you.

The regression of nodes, and the leap second, are optical illusions. They "appear" to be slowings, but they are running slows.
AAAAAAAAAAAHHHHHHHHHHHHHGGGGGGGGGGGGGGG!!!!!!!!!!!

It always comes out the same way I just can't say it any other way.
When the Moon came into orbit it was going slower than the Earth. The Moon is still going slower than the Earth. Because the Moon is and was going slower than the Earth it has slowed the Earth. Because the Earth is going slow across the Galaxy we have a leap second.


Gary

Karl
Quote:
-------------------------------------------------
This is not true. You were given examples of objects
being stabilized by gravity gradients. Remember the
barbell in orbit example?

-------------------------------------------------
Yes, I remember.

Here in orbits close to Earth, satellites are faced with three major gravitational sources Earth, Moon, Sun. Each of those three, give small objects three separate centers of gravity. At any one instant the shuttle or space station can have three major centers of gravity pulling in different directions. Depending on the mass distribution at that instant, will determine which of the three win out. Most often the Sun and Moon accelerate the far end of the satellite speeding or slowing it to keep it in the stable position.

The Moon keeps one face to the Earth, that is due partly to the Sun and its center of gravity.
The Moon's axial rotation has to speed up and slow down every month. As the Earth goes around the Sun some months are longer than others. It is not the Earth's gravitational gradient that keeps the Moon face on as much as it is the Sun accelerating the other side.

Quote:
-------------------------------------------------
In your drawing you seem to imply that the gravitational
field is uniform in all cases. It is not. Remember that
gravity fall off as 1/r2. This means that the moon pulls
harder on the near side of the earth than the far side.

-------------------------------------------------
I thought I had been very careful to place all the "p" or center of gravitational attraction points toward the gravitational source. I also made a special "Note" saying as how I had exaggerated their location. How could I have implied gravity was uniform?
Perhaps the same sized red arrows?
In my final drawing I placed the big white spot low and to the right of the yellow center of mass to exaggerate the location of "X" and "p". The Moon pulls on or suspends the Earth from a point toward the tidal bulge from the center of mass. That point "p" and that point "X" are one and the same, thus no torque.


Gary

Folks- this thread has been going on for quite some time, and, after perusing it, I don't see much new being discussed. Also, it looks like there are only three or so participants.

It appears to me that this would be best taken to email. Unless there are huge (and well argued) complaints, I'll lock this thread later today. Enough is enough.

No complaints here.

__________________
Jeff Schwarz
__________________________________________________
Argh!! They booby-trapped their sun!!****--Invader ZIM

Thank heavens!

Don

Guess I better get in a cheap shot before this thread closes. Well, actually it won't close, it will only "appear" to be closing. [img]/phpBB/images/smiles/icon_smile.gif[/img]

It's been fun. One last word if I may, Mr. Redmond: please make an effort to learn the mathematics and the physics. It will all make sense afterwards. You can do it, it's never too late.

__________________
Microsoft is over if you want it.

The bar has been lowered for the promotion of ATM ideas; the bar for the acceptance of ATM ideas must remain high.

With great regrets...yeah, kill it. I *HAVE* learned a lot! But real communication, in the sense of a "meeting of minds," has failed.

Still, it set a new record on this BBS for the number of posts!

Silas

Perhaps a Parthian Shot... No. The Moon's tidal lock to the Earth has very, very little to do with the Sun.

Gravitational attraction falls off as the square of the distance between the masses.

But the Tidal effect falls off as the *cube* of the distance. And it is the tidal effect that has caused the Moon to become rotationally locked with the earth.

(I never liked those pesky Parthians...)

Silas