"A ship in port is safe, but that's not what
ships are built for."

Grace Hopper. (The computer term "bug" is also due
to Grace Hopper)

**Introduction to The Moving Target Laws**

When I talk about the "path of light," I am
really talking about the Moving Target Laws.
It is critical for the reader to have an exact understanding of what the
Moving Target Laws are in order to understand any of my experiments or the
Lunar Laser Ranging experiments. This
chapter will provide that understanding.

Consider an archer who is a perfect shot and always hits the exact center
of the bulls-eye. Now consider the archer and his target as a
three-dimensional coordinate system.
The two-dimensional target is on the X-Z plane. The path of the arrow is the Y axis. The X axis, Y axis and Z axis all meet at a
point that is also the center of the bulls-eye of the target. Suppose further that the archer is 100 feet
from the target.

See graphics on next
page.

Now suppose the archer
aims at the target and that I am holding the target. Suppose that ** after**
the arrow leaves the bow, but

The key to
understanding the Moving Target Laws **( MTLs)**
is to understand the slice of time between:

1) The instant ** after** the arrow leaves the bow
and

2) The instant ** before** the arrow hits the
target.

This slice of time is
the time the arrow is **" in the
air."** "In the
air" means the arrow is no longer attached to the bow, and has not yet hit
the target. While the arrow is "in
the air," what happens to the archer and the bow is irrelevant because the
arrow is no longer attached to the bow.
As I implied above, while the arrow is in the air, the archer can throw
the bow into the trashcan and this act will have absolutely no affect on where
the arrow hits the target. While the
arrow is "in the air" the bow and arrow are totally independent of each
other.

But the same cannot
be said about the target. While the
arrow is in the air, it is headed towards the target. Thus any motion of the target, while the arrow is in the air, has
a direct affect on where the arrow hits the target**!** This is why they are
called the "moving target" laws.

The MTLs basically
study the motion of the **target**
during the slice of time the arrow is in the air. In the example just given,

**More Examples of the MTL**

If I were to move the
target exactly one foot down while the arrow is in the air, the arrow would
land one foot above the (center of the) bulls-eye. If I move the target exactly one foot to **my**
right (while the arrow is in the air), which is to the archer's left, the arrow
would miss the target by exactly one foot to my left. I am behind the target so the arrow would hit to the left of the
bulls-eye from my perspective. But from
the archer's perspective, the arrow would land to the archer's right (i.e. the
archer would see the arrow land one foot to the right of the bulls-eye). And so on.

Now let us do
thousands of these exercises. Suppose
that after the arrow leaves the bow, that I am allowed to move the target
exactly one foot on the two-dimensional X-Z plane, and that I can move the
target in any of the 360 degrees of the plane.
If we were to do this exercise thousands of times there would be up to
360 holes that would form a perfect circle (i.e. the holes would all be on the
outside edge or perimeter of the circle), with the center of the bulls-eye
being the center of the circle. No
holes would be inside or outside of the perimeter of holes.

Now let us construct
an imaginary three-dimensional sphere with the center of the sphere being the
center of the bulls-eye. The imaginary
sphere has a radius of exactly one-foot.
Now let us change the rules. I
can move the target exactly one foot while the arrow is in the air, but I can
move it in any direction in three-dimensions, as long as the center of the
target ends up being on the surface of the imaginary three-dimensional sphere
when the arrow arrives.

In other words, the
center of the bulls-eye will always be on the surface of the imaginary sphere
by the time the arrow arrives. Since
the sphere is in three dimensions, but the target is only in two dimensions, I
can move the target such that the arrow can hit any point within a one-foot
radius of the center of the bulls-eye.

As an example, if I
were to move the target along the Y-Axis, directly towards the archer or
directly away from the archer, ignoring the arch of the arrow, the arrow would
hit the center of the bulls-eye even though I moved the target one-foot. If I were to move the target slightly off of
the Y-Axis, the arrow would just miss the bulls-eye.

Now suppose this
three-dimensional experiment were done thousands of times and I moved the
target randomly. In this case an
imaginary circle of one-foot radius on the target, with the bulls-eye at the
center, would have many arrow holes in it or on its perimeter. In other words, instead of just being on the
perimeter of the circle, the holes would also occupy the inside of the circle.

Now suppose we
studied one specific hole in the target.
Let us suppose that I moved the target one-foot at such an angle on the
sphere that the arrow missed the center of the target by exactly 5 inches. Studying the angle that the hole is from the
bulls-eye, the angle that I moved the target could easily be determined. However, since the target itself has only
two-dimensions, it could not be determined whether I moved the target generally
towards the archer or generally away from the archer (on the Y-Axis). Thus the solution to exactly how I moved the
target in three-dimensions could only be reduced to two possibilities.

If an observer were
standing on the side of the target, she could note whether the target were
moved forward or backwards because she would see the Y-Z axis. Thus she could determine the Y-Axis movement
and narrow the possibilities down to one.

** **

**More Complex Archer Examples**

** **

Now let us suppose
that I am standing on a flatbed car on a moving train. Again, I am holding the target. We will assume the archer is standing on a
train station platform. The flatbed car
is moving with the train (along with the target), but the archer is not
moving. Let the distance between the
archer and the target be 100 feet.

Let us assume that
the train is moving at such a speed that in the time it takes the arrow to
travel to the target the train moves exactly 1 foot (the train is in constant
motion). Now suppose the archer lets go
of the arrow at the exact instant that the bulls-eye passes him. Now suppose that I do not move the target,
but hold it still. The arrow will again
miss the target by 1 foot. If the train
is moving left to right (per the archer), the arrow will land to the left of
the bulls-eye by 1 foot.

If additionally I had
moved the target one-foot in the direction the train is traveling, the arrow
would miss the bulls-eye by 2 feet. It
would miss the bulls-eye by 1 foot because of my moving the target and another
foot because of the moving train.

However, if I moved
the target in the opposite direction the train is traveling, the arrow would
hit the center of the bulls-eye. The
1-foot miss caused by the motion of the train would be offset by the 1-foot
miss caused by my moving the target.

In these cases the **platform** that the target
is standing on (i.e. the flatbed car) is in motion, thus the motion of the
platform has a direct affect on the motion of the target while the arrow is in
the air. The MTLs apply both to my
movement of the target, and to the platform's movement of the target. Anything that moves the target while the
arrow is in the air is significant to where the arrow hits the target.

In the experiments
that are discussed in future chapters, the platform will be the earth, the
archer will be a laser, and the arrow will be a laser beam.

One
of the hardest things for people to grasp about the moving target laws is that
once the arrow or laser beam is "in the air," the motion of the
archer or the motion of the laser is irrelevant. People constantly wonder why the motion of the archer or laser is
irrelevant. Many examples will be given
to make this distinction clear.

The
MTLs will be mentioned many times in this book. They are not only the basis of aberration of starlight, but are
also directly involved with all of my experiments and any experiment that
involves the path of light.