Chapter 10

 

Lunar Laser Ranging Experiments

 

 

"It is easier to find a score of men wise enough to discover the truth than to find one intrepid enough, in the face of opposition, to stand up for it."

A. A. Hodge

 

 

The Tilt of Aberration for the Interior Planets

 

One of the things I really wanted to know was the “tilt of aberration" for light from the interior planets.  It didn’t take long to realize that this determination is impossible because no one really knows the actual or exact location of any planet.  We only know their apparent positions, meaning we only know the direction they appear to be as we look at them.  It is somewhat of a paradox.  If we knew where they were, we would know the tilt of aberration.  Or if we knew the tilt of aberration, we would know where they are.  But we don't know either.

 

Celestial mechanics formulas only predict the apparent positions of planets and are unconcerned with their actual locations.  Because spacecraft make numerous course adjustments during flight, not even NASA or the JPL knows the exact position of any of the planets.  In fact, no one even knows the exact location of the moon because no one knows the tilt of aberration of lunar light, even though humans have walked on its surface.

 

(Note: Actually, it was known prior to the Lunar Laser Ranging experiments that aberration of moonlight was zero, thus they knew the moon was where it appears to be, but this was not common knowledge.  I will not assume a prior knowledge of that fact, I will calculate it anew.)

 

Fortunately, Lunar Laser Ranging experiments, which have been done since 1969, and continue to be done today, provide key information about light and the moon.  Its value, in the context of this book, is that we know exactly where the light from specially designed mirrors on the moon is being aimed.

 

 

Introduction to Lunar Laser Ranging

 

The experiments that that will now be discussed are called: Lunar Laser Ranging ("LLR") experiments and are currently being done at facilities such as the McDonald Laser Ranging Station facility in Texas ("MLRS").[25]  These experiments consist of powerful laser beams being bounced off of special types of mirrors, called “retro-reflectors”, that have been placed on the moon (retro-reflectors will be discussed in a moment).

 

The reason such experiments are important to this book is that we know exactly where these mirrors are located on the moon, and just as importantly, we know exactly where the returning light is "aimed" by the reflected laser beams!

 

In 1969, the Apollo 11 astronauts placed a small box on the moon's surface.  This device was a very special type of mirror: a retro-reflector.  Because it was placed on the moon it is frequently called a "lunar retro-reflector."  What is special about a retro-reflector is that it reflects light back to its point of origin.[26.27.28]

 

To understand this, note that a normal mirror will reflect a 15-degree light ray away from the point of origin, meaning the light will exit the mirror at 15-degrees away from the point of origin.  But a retro-reflector, which actually consists of an array or grid of "corner cubes" or "corner reflectors" of mirrors, returns light back to the point of origin.  The Apollo 11 retro-reflector contained 100 "corner cubes."  To make sure there is no misunderstanding as to what a retro-reflector does, suppose you are standing 15 degrees from a vector that is normal to the surface of a retro-reflector.  If you fired a laser at the retro-reflector, the beam would come back and hit you!  A retro-reflector does not reflect light at an angle, as a normal mirror does, a retro-reflector is specially designed to send light back to where it came from.  That is why we know exactly where a retro-reflector is aiming its reflected light.

 

In total, there were 5 retro-reflectors placed on the moon between 1969 and 1973, but only 4 of them are functional.  The largest of these retro-reflectors, and the one most often used in LLR experiments, was left by the Apollo 15 astronauts in 1971.  Retro-reflectors are generally about the size of a small suitcase.

 

The major purpose of LLR experiments is to determine various facts about the relationship between the moon and the earth and to learn specific facts about the earth.  For example, measuring the time it takes the laser pulse to make the round trip between the earth and moon, at different times of the day, can yield very accurate measurements of the distance between the moon and earth.  This assumes the speed of light is a constant during the trip, which is an assumption that will be discussed much later in this book.

 

In a LLR experiment, a very short pulse of laser light is fired through a telescope at one of the retro-reflectors.  The reason the laser is fired through a telescope is to "collimate" the laser pulse, which will now be explained.  When light normally leaves a laser the angle at which the light leaves the laser is frequently very high, perhaps as high as 30 degrees or more, depending on the laser.  This angle is called “beam divergence

 

Think of a flashlight.  If the angle of light from the flashlight (the angle formed by the two sides or edges of the outside of the main beam) was zero degrees (meaning the edges were parallel), then 100 yards away the width of the flashlight beam would be the width of the flashlight lens.  But that is not the case, the light from flashlights, and some types of lasers, is very broad, meaning at 100 yards away the beam might be 30 yards wide or more.  When the angle of light that leaves a laser is too high, lenses or mirrors can be used to make the beam divergence angle smaller.  When that happens the size of the beam is wider, but the beam divergence is smaller.  That is the trade-off, you can have a narrow beam coming out with high beam divergence or you can use a collimator and have a wide beam coming out, but with small beam divergence.

 

With lasers that are shot at the moon, it is very important that the minimum beam divergence possible be achieved.  This is because only a very, very small percentage of this laser light actually hits the small retro-reflector and is returned to the earth.  Telescopes are used to collimate these laser beams so that the smallest possible beam of light (and thus the most intense beam of light on the moon's surface) hits the moon.  Even though telescopes make the beam very wide at the time the beam is shot, the collimation more than makes up for this wide beam when the beam hits the moon.

 

Shooting through a telescope also provides another benefit.  Telescopes have tracking mechanisms that are very, very accurate.  Thus by shooting a laser through a telescope, the pointing of the laser is very accurate.  When the beam gets to the moon it is about 7 km in diameter and when it returns from the moon it is about 20 km in diameter.[28]  Only a very, very small percentage of the 7 km diameter laser beam actually hits the retro-reflector, thus only a minuscule amount of light actually returns to the earth.  Furthermore, only a minuscule amount of the 20 km wide returning light actually hits the sending telescope.  Needless to say, extremely sensitive detection equipment is needed to detect the returning light.

 

The returning lightwaves are measured by a detection device such as a photo-multiplier or photo-diode, which is coupled to the same telescope that fired the laser.  A telescope is used to capture the returning light because it has a large diameter to gather in more light than other devices.  Nevertheless, considering the ratio of the surface area of a telescope, compared to the 20 km diameter of the returning beam, it is clear than an unbelievably small percentage of the light that is sent is actually detected after returning from the moon.

 

In an LLR, there are three key things to understand:

1) The optical viewing of the moon through the telescope (which is subject to the full 370 kps secular aberration of starlight that all light from all other objects in the sky is subject to - assuming the photon theory),

2) The shooting of the laser through the same telescope that is optically viewing the moon,

3) The receiving of the laser light after hitting the retro-reflector, by the same telescope.

 

In other words, the same telescope does the optical viewing, the firing of the laser and the receiving of any light that returns from the moon.

 

To better understand the significance of LLR experiments, consider this metaphor:

 

 

Two Parallel Car Metaphor

 

Think about two automobiles driving nose-to-nose, 30 feet apart, at the same high velocity down a highway.  Assuming a vacuum, suppose a ball is thrown from one car to the other.  At the instant the ball is released from the first car by one person, a second person in the first car paints a small mark on the pavement underneath the car.  In other words, one person releases the ball and a second person in the same car simultaneously paints a small mark on the pavement.  Suppose that in the time the ball moves from the first car to the second car, both cars travel 100 feet.  Thus, when the ball is received in the second car, both cars are about 100 feet from the mark on the pavement.

 

As soon as the ball arrives at the second car, someone (who is in the second car) catches the ball and immediately throws the ball so that it lands on the mark on the pavement that was painted by the second person in the first car.  In other words, the ball is thrown to where the first car was when the ball was originally released from the first car.  By the time the ball returns to the mark on the pavement, suppose both cars have moved an additional 100 feet away from this mark (this is obviously not accurate, but this is a metaphor).  This means that when the returning ball hits the mark on the pavement, both cars will be about 200 from the ball.

 

Note that when the ball lands on the pavement, both cars, and we are most interested in the first car, are 200 feet from where the ball lands.  This means that no one in the first car is going to catch the ball when it lands after being thrown by someone in the second car.

 

 

Introduction to the Problems Introduced by Lunar Laser Ranging

 

Let us consider an infinitely long imaginary line that passes through the sun and the point in Leo that the sun is currently headed for.  We will define the direction from the sun towards Leo as "north."  We will draw a second line perpendicular to this line that also passes through the center of the sun.  We will further draw this imaginary line on the “ecliptic” plane, which is the two dimensional plane formed by the sun and our orbit plane around the sun.  Actually, we could draw this second imaginary line on the earth-moon 2D plane, which is very close to being on the ecliptic plane.

 

We have timed drawing this second line so that it goes through both the center of the earth and the center of the moon (or as close as possible because the two planes are not the same).  In other words, we waited until the earth and moon were in the correct positions before we drew this line.  The portion of this line to the left of the line to Leo (from our viewpoint from above the north pole with our head pointed towards Leo) will be defined as “west” and the portion of a similar line on the other side of the sun, to the right of the sun, will be defined as “east.”

 

This scenario means that the earth and moon are “nose-to-nose” as they are both headed towards Leo.  (Note: we can ignore the orbit velocity of the moon around the earth and the rotation velocity of the moon because they are so slow).

 

With this scenario, let us visualize what happens when a LLR experiment is done.  First, a laser beam is shot at the moon and retro-reflector.  During the time it takes this laser beam to travel to the moon and back (about 2.5 seconds), both the earth and moon (as part of the solar system) move about 948 km towards Leo (474 km while the beam is headed to the moon and 474 km while the beam is headed back to earth).  Since the retro-reflector sends light back to its point of origin, and because the returning beam is only 20 km wide when it returns, then the returning laser beam should miss the telescope (that shot the laser beam) by at least 928 km (948 km minus 20 km).  This is because both the earth and moon have moved 948 km towards Leo while the laser beam was "in the air."  But in fact the laser beam is detected by the same telescope that shot the laser in the first place!

 

With this scenario, the LLR is a type of experiment virtually identical to the “Two Parallel Car Metaphor.”  The line between the sun and Leo is represented by the path of the two parallel cars.  The person in the first car that throws the ball is represented by the telescope that shoots the laser beam.  The person in the second car, who throws the ball back to the spot on the pavement, represents a retro-reflector that returns light back to where it came from, meaning to where the telescope was when the laser was originally fired.  The returning laser beam should miss the originating telescope by at least 928 km.  I will come back to this example later in much more detail.  For now, I want to present a "big picture" of what is going on.

 

 

More About the LLR Experiments

 

The actual process of doing an LLR experiment begins with an observer "finding" the retro-reflector on the moon.  By "finding" the retro-reflector it is meant that they can detect returning light from the moon after firing the laser and the detected light is not "noise."  I cannot talk about all of their challenges, but I will mention three of the problems they face:

1) The most significant problem is "image motion," caused by hot and cold cells in the earth's atmosphere.  The hot and cold cells cause the image to weave back and forth and up and down.

2) Secondly, "seeing" problems are encountered when a point of light on the moon, or from a star, is "blown-up" or enlarged by either temperature cells or particles in the atmosphere.

3) Third, "dither" problems are jerks in the image caused by the finite mechanical equipment in the telescope drive system.

 

An observer begins by pointing the telescope, as accurately as possible, to where the retro-reflector is located on the moon.  I call this initial pointing of the telescope, whether successful or not, "ground zero."

 

Obviously, no telescope on earth can see an object the size of a suitcase on the moon (not yet anyway), but when the sunlight is hitting the section of the moon where the retro-reflector is located, the observer can see various lunar features in the landscape near the retro-reflector they are going to aim at, thus allowing accurate pointing.

 

When the retro-reflector is in the shadowed part of the moon, the observer must first calibrate the telescope and computer for several well-known reference craters on the moon that are in the sun's light.  But even that is not easy because the shadows cast by the cliffs that are on the sides of the craters vary in length depending on the angle of the sun to the cliffs.  Once these reference craters are used to calibrate the computer, the computer moves the telescope to where it thinks the chosen retro-reflector is in the dark section of the moon.

 

When ground zero is first attempted, either by the observer or the computer, the observer may not have "found" the retro-reflector on the first shot and he or she may need to start "clicking" the telescope controls to "find" the retro-reflector.  Frequently, however, it is not necessary for the observer to "click" the controls because the laser light is returned and is detected in the first laser firing.

 

When "clicking" is necessary, each "click" makes a 1/10 of one arcsecond adjustment (an "arcsecond" is 1/3,600 of a degree, thus a "click" is 1/36,000 of a degree) in where the telescope is pointed.  It is frequently a process of "hunt-and-wait-and-peck" trying to find the retro-reflector.

 

 

Hitting the Retro-Reflector and Looking at "Old Light"

 

Now let's get down to the details.  When a telescope is looking at a galaxy 100,000,000 light years away, it is looking at light that left the galaxy 100,000,000 years ago.  It is also looking at where that galaxy was located in the sky (ignoring aberration, etc.) 100,000,000 years ago.  The same holds true when a telescope is pointed at the moon.

 

When an optical telescope is pointed at the moon, because it takes 1.25 seconds for moonlight to get to the earth, the telescope is really looking at where the moon was located approximately 1.25 seconds earlier.  This means that the telescope is pointed or looking at a spot that is 474 km (i.e. about 1.25 seconds times the average 370 kps motion towards Leo) behind where the moon is actually located when the light arrives at the telescope.  This is based on the assumption that the earth and moon are headed nose-to-nose towards Leo at 370 kps.  In other words, the light the optical telescope is seeing is "old light," meaning that by the time the lunar light arrives at the telescope, the moon has traveled 474 km, meaning the telescope is constantly looking 474 km behind where the moon is when the light arrives.

 

It gets worse, because in the time it takes the laser beam to get to the moon, the moon has moved an additional 474 km.  This means that the laser beam, which is only 7 km wide when it gets to the moon, will miss the retro-reflector by 948 km.  To explain, the telescope (i.e. the laser) is pointed (i.e. aimed) 474 km behind where the retro-reflector is located (because of "old" light) when it fires the laser.  Further, it takes 1.25 seconds for the laser beam to get to the moon.  If this were the case, the observers would never be able to "find" the retro-reflector (this will be discussed in a moment).

 

Now let us consider what would happen if there was a tilt of aberration of the laser/telescope based on 370 kps.  If this were the case, at the instant the laser was fired, the telescope would be pointed directly at where the retro-reflector is located on the moon at the instant the laser is fired.  This is because of two offsetting errors.  The first error is that the light the telescope sees is 1.25 seconds old, meaning the laser is pointed behind where the retro-reflector is located by 474 km.  However, there is a second error in which the "apparent" location of the retro-reflector would be 474 km ahead of its "old" location.  Thus, because the light is 1.25 seconds old, the telescope will point behind the retro-reflector, but because of aberration, it will point ahead of the retro-reflector, meaning there is a net result that at the moment the laser is fired, the telescope is coincidentally pointed exactly at the retro-reflector.

 

However, this does not solve the problem.  By the time the laser beam gets to the moon, the moon has moved 474 km, thus the 7 km wide beam will miss the retro-reflector by 474 km.  Again, if this were the case the observers would never be able to "find" the retro-reflector.  This I will now explain in detail.

 

1) Let T0 be the moment light leaves the moon.  T1, which is 1.25 seconds later, is when the light gets to the earth from the moon, during which time the earth and moon have moved 474 km towards Leo.  T2, which is 1.25 seconds later than T1, is when the laser beam gets to the moon, and between T1 and T2 the earth and moon travel another 474 km towards Leo.

2) Because of "old light," the telescope is actually looking at where the moon was located 1.25 seconds earlier.  However, with tilt of aberration of 370 kps, if the photon theory were correct, the telescope would be tilted so it would point 474 km ahead.  Thus, these two things accidentally offset each other and at T1 the laser is pointed exactly where the moon is located at T1.  However, in the time the laser beam is traveling to the moon, the earth and moon move another 474 km and the laser beam will miss the retro-reflector by 474 km.

3) A "click" (i.e. 1/36,000th of a degree) moves the image in the telescope 186.4 meters (remember that the light pulse is about 7 km wide by the time it gets to the moon).  Note: the simplest way to calculate this is to know that the moon has an angular diameter of 0.5181 degrees (which is 18,652 "clicks") and the diameter of the moon is 3,476 kilometers.

4) The average distance to the moon is 384,400 kilometers.

 

With these statistics in mind, and knowing that the software that drives the computer can also be used for purely optical viewing, the ground-zero shot of an observer would miss the retro-reflector by 2,543 clicks (474,000 divided by 186.4) to the left or right of ground zero (this is the maximum number of clicks needed if the moon happened to be directly "east" or "west" of our path towards Leo).

 

At an average of 1 click every three seconds, it would take an observer up to 127 hours to find the retro-reflector.  This assumes he or she is perfectly efficient at knowing which direction to click.  As mentioned above, observers frequently "find" the retro-reflector without a single click!  Most of the time they find the retro-reflector within 5 minutes.  If they don't find it within 10 minutes, they may take a "coffee break" and then start over.

 

Thus, there is simply no possible way that the laser/telescope could ever hit the retro-reflector with or without secular aberration of moonlight.

 

A person might think that if moonlight had path momentum, that the problem would be solved.  Actually, if moonlight had path momentum, the problem would get worse because the laser/telescope would point even further behind the location of the moon at the time the laser is fired.  We would be back to the 948 km miss, even with aberration.

 

How about path momentum of the laser beam?  My experiment proves that lasers must have path momentum, meaning the light leaves the laser at an angle.  If the laser beam had path momentum, is there a scenario in which the laser beam could hit the retro-reflector?  Actually, yes.  If there was laser path momentum of the laser, and there was aberration of moonlight (i.e. tilt of aberration), and if moonlight did not have path momentum (moonlight is reflected light from the sun, just like retro-reflectors reflects laser beams), then the observer could "find" the retro-reflector in short order, perhaps on the first try.  In summary, because moonlight is "old light" when it gets to the telescope, there is only one combination of events that could explain why observers ever "see" the retro-reflector:

 

1) Path momentum of laser beam light (LPM is true).

2) Aberration of moonlight (tilt of aberration)

3) NO path momentum of reflected sunlight (MPM is false).

 

Without any of these items, and with the photon theory of light, the observer could never "find" the retro-reflector because of the "old" light issue.  I will get back to this issue later in the chapter.

 

 

The Returning Laser Beam

 

So far we have only talked about the observer finding the retro-reflector.  Let us for a moment ignore the problems with actually hitting the retro-reflector.  Let us talk about the returning laser beam hitting the telescope.  We are absolutely certain where the returning laser beam is aimed, it will return the laser beam in the exactly opposite direction it came in at.  That is what a retro-reflector is designed to do.  We don't need to worry about hitting the retro-reflector, we are now assuming the retro-reflector is being hit and our concern is where the retro-reflector is sending its light.

 

If the mirrors in the retro-reflector did not add path momentum to the laser beam, the returning beam would miss the telescope by 948 km per the 2-car example.  The simplest way to comprehend this is to think of the retro-reflector as being the origin of the light beam.  In other words, we don't care about the process of getting the light to the retro-reflector, we are only concerned here with what the retro-reflector does with the light.  We know exactly where the reflected light from the retro-reflector is aimed.  It is aimed at the exact location of where the light source came from (where the telescope was when the beam was fired), without regard to any aberration of earthlight (the retro-reflector is not looking at the earth through a telescope so "aberration of earthlight" is irrelevant), path momentum of laser light, etc.  Consider this scenario:

 

T1) (the same T1 as above) The laser beam is fired.  This instant in time identifies where the laser/telescope is in 3D CMBR space at the instant the laser is fired.  This is the exact location in 3D CMBR space that the retro-reflector will send the returning laser beam.

T2) (1.25 seconds after T1) The laser beam arrives at the moon and is instantly "fired" back by the retro-reflector.  Between T1 and T2, as above, the earth and moon have both moved an additional 474 km towards Leo.  Thus, when the retro-reflector "fires" the laser back to the point in 3D CMBR space where the laser/telescope was at T1 (T2 is the origin of the retro-reflector light), it is aiming the light 474 km behind where the telescope is located at T2.  In other words, T2 is the time the retro-reflector "fires" the returning beam, but at T2 the telescope is already 474 km away from where the retro-reflector is aiming.

T3) (1.25 seconds after T2) The laser beam returns to earth.  Between T2 and T3 the earth and moon travel an additional 474 km.  Thus the returning beam will miss the telescope by a total of 948 km because the retro-reflector is aiming the beam at where the telescope was at T1 (I am ignoring the width of the returning beam because it is insignificant).

 

Because of the fact that the retro-reflector is aiming at where the telescope/laser was at T1, it is clear that the photon theory of light cannot be true.

 

However, now let us look at this scenario.  Suppose the laser light hits exactly two mirrors in each corner cube, and that each of the corner cube mirrors adds one path momentum unit to the light.  In this case the retro-reflector would add two units of path momentum to the laser beam, and the same telescope that fired the laser beam would also be able to receive the laser beam.

 

In other words, because of the Two Parallel Car Metaphor, the light from the retro-reflector to the earth would never hit the sending telescope unless exactly two mirrors in each corner cube added one path momentum unit each (this assumes exactly two mirrors in each corner cube are hit).

 

 

Four More Paradoxes

 

Let us summarize what we have learned, if we assume the photon theory is true:

 

The Observer Trying to Find the Retro-reflector:

1) Path momentum of laser beam light. LPM is true.

2) Aberration of moonlight (tilt of aberration) is true, based on 370 kps.

3) NO path momentum of reflected sunlight. MPM is false.

 

The Returning Light From the Retro-reflector To the Telescope:

1) Path momentum of light bouncing off of mirrors, light must hit two mirrors in each corner cube and each mirror must add one path momentum unit.  MPM is true.

 

My First Experiment:

1) When I used a telescope, I was looking at light reflected from a piece of paper.  This light clearly had to have path momentum in order for me to see a dot, thus MPM is true for reflected light.

 

My Second Experiment:

1) The light from mirrors must not have path momentum, thus MPM is false.

 

 

We thus have four major paradoxes resulting from this analysis.

 

Paradox: Because observers are able to quickly "find" the "retro-reflector" it has been shown that moon dirt (which is reflected light) cannot add path momentum to light.  However, the returning light from the retro-reflector cannot hit the sending telescope unless the reflected light (from the retro-reflector mirrors) adds two path momentum units.  Thus, MPM is false and MPM is true.

 

Paradox: In my second experiment it was evident that MPM was false.  However, the returning light from the retro-reflector cannot hit the sending telescope unless the reflected light (from the retro-reflector mirrors) adds two path momentum units.  Thus, MPM is false and MPM is true.

 

Paradox: In my first experiment, when a telescope was used to look at a paper target, it was clear that because I got a dot, that light being reflected off of a piece of paper does have path momentum.  However, the light being reflected off of the surface of the moon cannot have path momentum.  Thus, MPM is true and MPM is false.

 

Paradox: In my first experiment, as just mentioned, MPM must be true, or else I would not have seen a dot.  In my second experiment, MPM must be false, or else I would not have seen a dot.  Thus, MPM is true and MPM is false.

 

These paradoxes are proof that the "tilt of aberration" of lunar light is actually zero kps.  This means the moon is where it appears to be when we look at it.  This, by itself, is a proof that the photon theory of light is false.

 

These experiments on the "path of light" also prove that the aberration of terrestrial light is also zero.  I could prove this directly if I had the right equipment.  I could also prove that laser light does not have path momentum if I had the right equipment.

 

 

Lunar Laser Ranging and Ether Drag

 

There are actually several scenarios in which the ether theory could easily explain the above paradoxes:

 

1) If the earth's ether drag extends beyond the orbit of the moon around the earth, then both the earth and moon would be in the same ether drag.  In this case it wouldn't matter if the moon had its own ether drag, only "moving target" leads (that apply only to the orbit velocity of the moon around the earth while the laser beam is "in the air") would apply because all light between the earth and moon would be dragged together.  The "moving target" lead is not aberration, it is simply an application of the MTLs within the same ether drag.  The orbit velocity of the moon around the earth is about 1 km per second.  This means that in the time the laser pulse travels between the earth and moon the moon only travels about 1.25 km.  This is still within the 7-km radius of the arriving laser light.

 

The best way to visualize how ether drag works with lunar light is to imagine a string between the retro-reflector and the telescope.  The string is dragged with the earth and moon towards Leo.  The string represents the path of the light beam from the moon (i.e. from the vicinity of the retro-reflector), because everything is dragged together.  Thus this is the direction the telescope thinks the retro-reflector light is coming from, and thus it is also the direction the laser is pointed, and it is the path of the laser beam that travels to the moon.  When the laser beam gets to the moon, this is also the direction the retro-reflector thinks the laser beam is coming from, and thus it is the direction the retro-reflector aims the light, and thus it is the path of the retro-reflector light back to the telescope.

 

2) If the moon had its own ether drag and if the earth's ether drag and the moon's ether drag overlapped, then the earth and moon would essentially be in the same ether drag because all lightwaves during the round trip would be dragged with the earth/moon system towards Leo.  It is very similar to case #1.

 

3) If the earth and moon both had ether drag, and if the ether drag of the earth and the ether drag of the moon did not overlap, but their edges or boundaries were "close" to each other ("close" will be defined in a moment), then the LLR data could be explained.

 

4) If the moon did not have ether drag but the boundary of the earth's ether drag came "close" to the moon, the LLR data could be explained.

 

How "close" does the earth's ether drag need to be to the moon's ether drag (or the moon itself if the moon does not have ether drag)?  It depends on whether the sun's ether drag extends beyond our earth's orbit distance from the sun.  If the ether drag of the sun does not reach the earth's orbit distance, then "close" probably means less than several thousand kilometers, or else the observers would have to "lead" the retro-reflector consistently during certain times of the lunar month (this is simplified).  If the ether drag of the sun does extend beyond our earth's orbit distance (which is highly likely) then there is far more tolerance for how "close" the gap (between the earth's ether drag and the moon or its ether drag) needs to be - perhaps up to a 50,000 kilometer gap.

 

Because LLR observers frequently need to use some "trial and error" when trying to "find" the retro-reflector, their data is not accurate enough (actually for several reasons) to determine an exact number as to how "close" the gap must be.  Also, their data is not accurate enough to determine which of these options is the correct choice.  However, their data is accurate enough to assure that one of these options is the correct choice!

 

The LLR experiments provide critical data as to how large the earth's ether drag must be in order for the LLR experiments to work.  The earth's ether drag probably extends over 330,000 kilometers above the earth and the moon probably has some ether drag of its own.  This height, in fact, is the best evidence that the sun's ether drag does extend beyond the earth's orbit distance.

 

The bottom line to all of this is that because of ether drag, the moon is exactly where we think it is.  In other words, we do know the exact location of a celestial body other than the earth - the moon!  (OK - to be technical lunar light is "old" light, but we can take that into account if we need to.)