Bob May wrote:
>
> Several things that you don't understand.
Actually, the next sentence shows that there is a lot that you don't
understand.
> First is the centrifigal force is just that, a force which is generated by
> something else. That something else is the gravitational attraction between
> the two objects. You have to remember that the orbiting objects are merely
> falling in the gravitational well, unfortunately, the two objects are
> constantly missing each other because the velocity that they have relative
> to each other is putting them in the same orientation as they were in,
> another way of putting it is that the Moon is going fast enough that when
> it gets the 90deg. of orbit from where it was, it's already traveled the
> radius of difference between them and thus is still in the same relationship
> as they were.
> Second is that these are theories that we are dealing with. There's a whole
> lot of little modifiers that we aren't talking about, including the
> time-space dialation, atmosphere effects and so forth.
> Go do some reading and exploring asking the questions of the books (they
> make books so that you can recover the knowledge of others too, you know!)
> and you will get a lot of interesting answers. Start with a high school
> level physics book and then go on to the different levels of University
> physics. You will understand then why you are being so repeatedly nailed to
> the wall.
>
> --
> Bob May
> Remember that computers do exactly what you tell them to do, not what you
> think you told them to do.
[Like compute the "centrifugal force"...]
Watching this thread has been really interesting so I decided to jump
into the fun.
Newton was sitting under an apple tree one day eating an apple. Another
apple fell on his head. It occurred to him that what must have happened
is that the earth itself had attracted the apple. When he began to get
a bump on his head it occurred to him that the problem was symmetric,
the earth attracted the apple, and the apple attracted the earth, but
since the earth was so much bigger, it had the larger influence.
Besides it really didn't matter what attracted what because his head
still hurt.
[Actually none of that happened. Its JUST A STORY.]
After thinking about it some more and looking at the data for the
observation of objects in the solar system, he decided that a reasonable
fit was that the force of attraction was proportional to the product of
the masses and inversely proportional to the square of the distance
between the two masses. All that was needed was a constant of
proportionality to get the units right. The result was:
F = (G * M1 * M2) / r^2
In addition, it was also discovered that a constant application of a
force to a fixed mass will produce a fixed acceleration:
F = M * A
All this is fine, but useless because you cannot tell where things came
from or where they are going. In order to do this, you have to project
the objects into a coordinate system, say for example, a cartesian
coordinate system (X,Y,Z).
Now you have:
F(X,Y,Z) = (G * M1 * M2 ) * ((x1-x2)^2,(y1-y2)^2,(z1-z2)^2)
and
F(X,Y,Z) = M * A(X,Y,Z)
In other words, you have two vector equations. Now you have something
you can work with and compute trajectories. However, the problem is
that the fundamental equation is only defined for *point* masses, not
large masses such as the earth. This must be true because a little bit
of stuff closer to the moon has a larger gravitational attraction than a
little bit of stuff on the other side.
So what you really need is two triple integrals, one to sum every dV
(delta volume) of earth against every dV of the moon. I won't write
this out because text is a really bad way to enter these equations, but
stick with me.
If you have any doubt that the integrals are actually needed, go sit
with your toes in the surf at low tide. After a while, you will be in
water up to your eyebrows and you will see the light, so to speak.
Now you have a force on one side and two triple integrals on the other,
but this does not help determine where the moon is. So now you need to
plug the force equations into the acceleration equation (and do it
twice, because the earth pulls on the moon and the moon pulls on the
earth).
The MA equation is a differential velocity, so you need to solve the
differential equation to determine what happens to the position. In
order to solve the differential equation, you need initial conditions
for the constants, (so you might as well look out the window and see
where the moon is and where it is going and use those values).
Now, you have something you can use to determine where the moon is going
to go next. (You also know why Newton had to invent calculus).
If I wrote this equation out, it would get lost in all the text, but it
would be general and accurate.
Needless to say, all this math is a pain in the ass, and not necessarily
helpful for someone trying to figure it all out. So normally, some
simplifying assumptions are made.
The first assumption is that there are no special locations so the
location of the (0,0,0) point is not important, so why not set it
equivalent to the center of the earth? Any place is as good as any
other. This means that the motion of the earth has been "nulled out" by
allowing the coordinate system to move. This assumption is reasonable
and supported by data that shows that we cannot seem to measure absolute
motion. There is no special place or preferred direction, and we can
only measure our velocity in reference to something else. So we might
as well drag the coordinate system with us, it simplifies the math.
The second assumption is that since the earth is symmetric and
homogeneous (except at the smallest level) it is OK to assume the earth
is a point mass. The same argument can be made for the moon. This
conveniently removes the triple integrals.
The third assumption is that it is OK to have the coordinate system
ROTATE in conjunction with the moon's orbit. This simplifies the
equations to:
F = G*M1*M2/r^2
F = M*A
Now, we are sitting here on a rotating and moving frame of reference.
It is like we are sitting on a rotating stool with a weight at the end
of a string. We can measure the force we need to apply to the string to
keep the weight a constant distance away, as measured from our eyes,
while sitting on a moving and rotating stool. This is comparable to the
gravitational force between the earth and moon.
Suddenly we let go of the string and notice that the weight moves away
from us AS IF a force had acted on it. We call this force the
"centrifugal" force when we are in elementary school. (When we are in
college, our physics professors are quite clear in stating that there is
no such thing as the "centrifugal force" as it is only an illusion based
on our (moving) frame of reference.) (Um, all you posters did go to
college, no?)
Now all of this makes the math simple, but it is wrong. The only way to
really do it is to setup and solve the differential velocity equation in
three space, and do the full integral.
To do all this correctly all we need is the constant of proportionality,
G. Fortunately, Cavendish measured this and subsequent repetitions of
(essentially) the same experiment have made it more accurate. Once we
have the constant of proportionality, all we need is a detailed
microscopic map of the interior of both the earth and the moon.
Oops. Houston, we have a problem.
Since we cannot measure the earth and the moon without grinding both up
into little pieces, we go back to our equations and SOLVE FOR THE
MASSES. It is a nice trick, actually, we "measure" the mass of the
earth indirectly. But we still do not really have any idea *exactly*
what the earth weighs, we just know that, to within experimental error,
our equations balance with the objects we can see and measure in the
solar system.
But the bottom line is we cheat. And there is no escaping this fact.
Your *only* point of contention can only be not whether we cheat, but
only if it matters.
Since nobody has shown me a differential equation with two triple
integrals, I can only assume that *none* of you know what you are doing,
not just Nancy.
The simplifying assumptions are reasonable and help clarify, and
thinking about a mysterious "centrifugal force" may keep our brains from
exploding, but it is really all wrong. So sorry, guys, Nancy is right,
all your math is wrong, even if hers is too.
Of course none of this takes into account relativistic corrections, so
it is all wrong twice.
Lately it has been released from "respected" researchers in "the
establishment" that the latest measurements of the expansion of the
universe indicate that this expansion is accelerating, not
decelerating. This can only be true if there is a repulsion force
operating.
So the bottom line is the latest thinking among the cosmological and
astronomical community is that, yes, Virginia, there really is a
repulsive force. Now the current explanation is that it only operates
at intergalactic distances, but this is, of course, bull. How can a
force know where to operate and where not to? This is like the other
bit of conventional wisdom about the "expansion of the universe", the
expansion only occurs in space where nobody is looking so we do not have
to confront the fact that the "expansion of the universe" violates the
conservation of energy. (Um, either conservation is a law or it isn't -
you can't have it both ways).
The bottom line is that *all* of the math being thrown around in this
thread is wrong. The other bottom line is that the current thinking
includes a repulsive force. The question is not *if* the repulsive
force is present in the universe, but only what the characteristics of
this force are. These questions include:
- Is this force static ala Einstein's cosmological constant?
- Is this force (directly) related to any other forces such as the
normal attractive gravity? Does this mean that gravity is inherently
bipolar similar to electrostatics and magnetics? Does this bipolar
nature explain *why* gravitation is 10^43 times smaller in magnitude
than the other forces? Is it because the forces are really both
powerful, but ever so slightly out of balance?
- Why do we not observe this force in everyday life? Is it simply
because it is very much smaller than gravity (which is incredibly much
smaller than the other known forces)? How much smaller is it? Why is
it smaller?
- What is this force a function of? Mass? Surface Area? Time? Density?
Composition?
- What is the propagation effect of this force, inverse square like
gravity and the electromagnetic force or some other function (like the
strong force)?
- Can this force be engineered (i.e. manipulated by us, somehow) like
the strong force or electromagnetics?
So you can stop picking on Nancy for her bad math until yours gets MUCH
better and you can also stop discounting the repulsive force because
some very smart people claim to have found it.
