Beyond this first and main wrong, your next problem is the law itself. A multiplication of two masses is meaningless. It's not science. It is a little sciencey, though, when you allow one of the masses to be the gravity field of that mass.
For all your great professors oblivious to the apple hypnotism they work under, we look into your rear view mirror of scientific deduction. One of Sir Isaac's masses has been a considered rate of acceleration towards mass due to a masses inverse square law. And the other mass is mass. And vica versa. When you see this complexity that Sir Isaac built you will also see that his law in full was always unfit for your beautiful planet. The law........ 'Every particle in the universe attracts every other particle in the universe with a force directly proportional to the product of their masses and inversely proportional to the square of their distance apart'.
As a tool, your Sir Isaac's second law of motion works. This law is the acceleration of a body is in proportion of the force causing an acceleration. The acceleration is always in the direction of the force.
First we omit the unknown mechanic of how separate masses combine to create one gravity attracting two ways at once. Then, through a presumed force of attraction within any particle that emanates through the entire universe to every other particle and this second law of motion separately applied to any two particles of the universe, Sir Isaac's mutual formula twice appears.
The problems are the instances are or would be the effect of force. A momentum change. Whatever a mutual force could have been, each instance was not the cause of momentum change that it needed to be. Beyond the life of your wondrous seventeenth century hypnotist, this should explain to you how your hypnotized mathematical physics professors have been making his law cosmetically coherent. The 'law' is being taken back to the large mass half of its origin when it is set equal to the acceleration/weight of a small mass as measured by your second law of motion. And the law of gravity itself just an offbeat cause and effect muddle gaining acceptance through a misread constant between one mass, its inverse square law and a rate of acceleration towards that mass. If an earthling follows your blue italic link below you can see how your own mathematical procedure says to you that the G you have found is not the constant of Sir Isaac's law of gravity. Understandably this has to be stated extra-terrestrially. It's the constant between one mass, its inverse square law and a rate of acceleration towards that mass. Before they wake up in the morning for another lazy hazy hypnotized 24 hour day in our shared solar system, your mathematical physics professors would be well put to understand that the discovered constant is only to do with their larger mass.
Apart from finding a way of making the magnitude of the small mass relevant, the word "fixed" would have to vanish from the large mass for this to become a determination of a mutual gravitation constant for you. In its place you would need a measurement of the movement of the large mass. And that measurement appearing somewhere in your determination of your mutual gravitation constant of G.
Apart from his cause and effect confusion, the thing for an earthling to note is M and m switch from inside to outside the brackets as you go from one instance of Sir Isaac's law of gravity to the other. If this is how the formula has come to appear on your beautiful planet, you should be able to see that it is just an unedifying confusion of two suspected momentum changes. A force of mutual gravitation, your Sir Isaac Newton hoodwinked himself.
Beyond Sir Isaac's life and if you wish to convert momentum change 1 and momentum change 2 into one 'drawing' force, you have no specific but two directions of acceleration. At this point the law is rendered senseless.
Whatever a mutual force could have been, the divergence of mutual magnitudes from 'it must be of proportion of its quantity' always made your law impossible in the product of masses area, anyway. Example M + m = 10
Graphically and according to your junior schoolbook earth - moon dynamics, when you land some of your earthlings upon your moon to look back at yourselves, there is a greater mutual attraction between your planet and its moon than when your same earthlings are living back on your planet. Or, if your joint centre of gravity extension enters your heads, a moving of mass from M to m alters the magnitude of that would be joint centre. Same amount of mass, greater or lesser mutual gravitation depending on which way the mass has been transferred.
AT THE BEGINNING
However your Sir Isaac derived his naughty law of mutual gravitation for the review that your sleeping academics understandably can't even provide yet, he began with a fundamental flaw.
At the beginning of his gravity thought process, he has deduced that all masses have gravity. That was his universal summation of the gravity of the universe.
His mutual idea extends this universal concept into therefore all masses attract all other masses. Sir Isaac's fundamental flaw is his extension of a universal nature of gravity into this unconsidered mutual nature of gravity. And the flaw is as simple as not recognizing or placing vector values on the opposite directions of falling in between the centres of any two particles in the universe.
What you have done since Sir Isaac's hour of direction of fall neglect is expect all inverse square laws to be perfect unhindered arithmetical extensions from their source particle to all other particles in the universe.
Contrary to this, your modern calculations work out where your space shot will leave your earth's inverse square law and enter another. This demonstrates or proves to you that inverse square laws are not perfect vector extensions away from a particular particle of the universe to all other particles in the universe.
What you are doing is presuming these extensions without provided analytical reasoning. For your law to become an original thinkable possibility, you would be required to present rational argument of how a direction of fall rebuilds from termination into further extension. Or, on the hot from a neighbouring planet diagram below, show how your moon's inverse square law rebuilds from zero to reach your beautiful planet and then reach all other particles beyond the far side of your beautiful planet.
On your planet's side of the termination point, anything dropped is not observed to fall towards your moon. The idea that it falls towards your moon a little bit is where your earth scholars need to wake up and slip into normal solar system intelligence. Objects never simultaneously accelerate in opposite directions. Whatever a direction of acceleration is, it is that direction alone. And it is not only us Martians saying that upon our materialization here on your beautiful planet. You say it to yourselves through your very own Sir Isaac Newton's second law.
Acceleratively your space shots do tell you that the direction of acceleration between your beautiful earth and its moon alternates. Because opposing real values are used to find a zero 'value', the precise location of the zero point is only ever approximately calculable. While the zero acceleration point is never an exactly calculable location, through your space shots, the change in direction of acceleration in between your earth and its moon is earth knowable.
According to your Sir Isaac's law of mutual gravitation and tidal analysis, though, both inverse square laws are arithmetically coexisting intact at the change of direction location. If placed at this point, a droplet of ocean would accelerate at a rate of 0.0033 m/s/s towards your moon. The same drop would also accelerate at the same rate towards your beautiful earth and at the same time. Your Sir Isaac really did have an unsophisticated mathematical approach to the inverse square laws of the universe.
If you start to become acquainted with the man your Sir Isaac Newton was, it becomes apparent that he was as much a determined peer conqueror as scientist. "If I have seen further than others, I have stood on the shoulders of giants" he wrote to his peers when he had planetary motion done and dusted. And his peers cheered and he was a happy man.
From the visiting traffic light point of view, he may not have been entirely settled after his imaginary shoulder standing exercise. Not understanding his universal law of gravitation himself was a problem. What he needed was incontrovertible proof of every particle in the universe attracting every other particle in the universe. Sometime after the publication of his law of gravity, your records show that he became of parliament. Statutory law making was not his business, though. His only known earth words in parliament were to do with an open earth window changing atmospheric conditions inside an earth building. As he silently sat, his mind looked for ways to understand his mutual gravitation. One day the parliamentary earth Bible took his fancy. To make simple sense of his formula to himself, a falling apple story began.
You should understand that an errant formula about the universe indicates that your apple story is rhetoric made to convince at least Sir Isaac Newton that he had found the law of gravity that explains the universe. A chance occurrence of seeing an earth apple fall to errantly explain the gravity of the universe should say to you that your Sir Isaac Newton has invented a story. Realistically, if you are into the study of falling objects, you do what one of Sir Isaac's giants did. You drop things. You don't actually need to wait for a fruit falling season to arrive.
Your most addled succeeding theory is Sir Isaac Newton's giants being weight pushing up on Sir Isaac's shoes as he stood upon their shoulders. This weight is not measurable, detectable or necessary sleeping earth academic presumption. The equal and opposite force to one side of your beautiful planet is the weight of the direct opposite side of your beautiful planet. Both Sir Isaac and his giants are part of the weight of one side of your planet. When the terminations of your earth and moon inverse square laws on the earth - moon axis are recognized, to an earth school child your Sir Isaac's mutual summary of the gravity of the universe should be no more. Of the greater significance for you is, when the terminal point on the earth - moon axis is acknowledged, you have your beautiful moment of entering tidal clarity. Whereas your Sir Isaac originally tried to explain your high tides through relative lunar inverse square law magnitudes on the earth moon - axis, your answer lies in relative earth inverse square law magnitudes between that axis and the axis at right angles to that axis. The one that goes through the centre of your beautiful planet.
As it turns on its axis, this is your in principle explanation of why your beautiful earth is experiencing a semidiurnal lunar tidal rhythm. The unanalysed idea of your moon pulling an ocean under your moon was where your scholarship got you off to a bad understanding of the gravity of the universe. Unfortunately, your Sir Isaac Newton or even your Albert Einstein did not seek to question your ancient moon ‘pulls’ ocean idea. Consequently they have left you unsophisticated.
Once your current sleeping academics start waking up and seeing the high tide under your moon through lateral relative terrestrial inverse square law magnitudes (and not any gravitation towards your moon whatsoever), through your future educational standards, things should get enlightened here on your planet.
Parallel, you can easily see both sets of tides as the equal and opposite downward forces of your beautiful planet as those downward forces appear up here on the surface of your beautiful planet. For your earth schoolchildren, if Sir Isaac's equal and opposite force axiom is a true science and if using Sir Isaac's second law of motion to measure weight is also a true science, the tidal status of one side of your earth being an ongoing equal and opposite reaction to the one on the direct opposite side of the core of your earth cannot be wrong. As your beautiful earth turns through its inverse square law, direct opposite sides of your earth alter in force magnitude in accordance with your own Sir Isaac's second and third laws. From one of your Sir Isaac's books of one and half Martian centuries ago, a mutual gravitation declaration in terms of what we (even though your Sir Isaac's penchant for having his portrait painted would indicate he was seeing himself in a historical light, 'we' would mean not you but Sir Isaac's peers of the time) must do. Upon our materialization here on your beautiful earth, we added some pretty colours to Sir Isaac's command.....
Lastly, if it universally appears, by experiments and astronomical observations, that all bodies about the earth, gravitate toward the earth; and that in proportion to the quantity of matter which they severally contain; that the moon likewise, according to the quantity of its matter, gravitates toward the earth; that on the other hand our sea gravitates toward the moon; and all the planets mutually one toward another; and the comets in like manner towards the sun; we must, in consequence of this rule, universally allow, that all bodies whatsoever are endowed with a principle of mutual gravitation.
The declaration of what his peers must do was necessarily vague. By beginning inhope of proof, your Sir Isaac has known he wasn't necessarily dealing in a complete sense. This admission of uncertainty is his honest message to his peers.
They severally contain is addition. Not the product of quantities that appears in your actual law. There isn't evidence to suggest a scientific frame of earth mind when your Sir Isaac declared mass multiplied by mass as the gravity base of the universe. His end of life words of in proportion of its quantity is where he had his head in a happier state.
The moon gravitating towards the earth according to the quantity of its matter is in stark contradiction of your moon gravitates towards your earth in accordance with the product of earth and moon quantities (the M x m of your or his actual law).
Words highlighted in vermillion are where your main problem of academic conscience and character resides. Your sea (under your moon) is notan astronomical observation of a gravitation towards your moon in the slightest. It is impossible for an ocean or anything at all to simultaneously gravitate in opposite directions.
The reality is your sea (under your moon) onlygravitates towards your earth. This gravitation is less because of the interruption caused by your moon's inverse square law to your earth's beautiful inverse square law. A lesser weighting/gravitating in one direction is not a weighting/gravitating in an opposite direction. Once that is understood by your earth schoolchildren, Sir Isaac's command of what "we" must universally allow is by the bye. Conversely, your earth schoolchildren could all just heave a sigh of earth relief and start your education going properly. Because of your Sir Isaac's hypnotic apple story, you are insanely muddling your adult scholarship up with a scantily thought about axiom that has two inverse square laws becoming one and then having the wherewithal to act in two directions at once.
The difference between gravitates towards your beautiful earth less and your fictitious gravitates towards your moon a little bit is significant with respect of further understandings of inverse square laws. And the high tide on the far side of your beautiful planet definitely is not a gravitation towards your moon. If it was a gravitation to do with your moon in the slightest, it would be a gravitation away from your moon.
When an earth professor wakes up, Sir Isaac's use of the word endowed should indicate that Sir Isaac's law of gravity at best was incomplete. Endowed leaves the reasons of how and why physically unexplained and also adrift from a mathematical foundation.
To tune in with the inner dynamics of this beautiful almost round planet of yours, squeezing earth party balloons may help your earth adolescents or any still hypnotized mathematical physics professor or any one of you at all. The analogy is imperfect. But it does place a view of equal and opposite downward earth forces in your hands as your earth vision takes in the changing shape of the earth party balloon.
On our planet, Mars, we have deduced this. The core of a planet or star is weightless.
The evidence supporting weightless cores for you is the rate of acceleration towards the centre of the beautiful planet you are on is measured as diminishing in your underground ore extraction exercises. Meaning not only do inverse square laws conclude / are interrupted where they meet an adjacent one. Inverse square laws break down in side the celestial body that they are causing a descent towards. Going down from the surface of your beautiful earth, you would expect the rate of fall to taper down to zero across its centre. From there you can deduce for yourselves whether or not there could be such things as what your hypnotized mathematical scientists are calling gravity holes in space.
What you do need to understand is this. It's the surface weight that an inverse square law causes that holds a planet to its centre. Not the inverse square law getting bigger and bigger beneath the surface of a planet. And after that and with some consideration of your earthquakes, the implication is that a planet's inverse square law is set at the planet's surface. More precisely at the point where the rate of acceleration towards a planet's centre starts to decrease would be the point where an inverse square law becomes of a reversing arithmetical structure to that of an actual inverse square law. If you can get on top of that, the next step is considerations of how mass actually fixes an inverse square law in the space that surrounds mass. An inverse square law in space says the nature of space is changing with vertical distance. If they can get unhypnotized, post stone age tidal thinking might be ahead for all your beautiful earth professors.
If cleansed just a little bit, from here the waking up big minds of earth professors could take the inverse square law over in proper style. As an ongoing Martian reaction to your heavily hypnotized educational movers and shakers, the next reluctant web page is highly positive about life on earth. But quickly descends further into Martian. So best if the big minds of your earth professors wake up at their earliest convenience.
Incidentally, your modern evidence would show the proportion your Sir Isaac was assuming was between the product of quantity and surface area. Not simply quantity. For example, you now know your moon has 1/6 of the surface gravity of your earth. Whether you accurately know your moon's mass or not, it has about 1/50 of the volume of your earth. You believe your moon has about 1/81 of the mass of your beautiful earth.[(earth's surface area x 9.8)/(moon's surface area x 1.6 = 82.4)]. Whether or not your assessed celestial masses are reliable is your unknown.
Admittedly it isn't really for visiting traffic lights to say terminal and mirror inverse square law magnitudes is where your earth university standard should currently be at if you want your earth school teachers to stop being ongoing apple hypnotists. Your earth professors should be the ones saying that. But, as they have all been hypnotized into the mind of Sir Isaac Newton, drop in traffic lights obviously feel a moral obligation to a neighbour trying to destroy its own beauty through this very rare case of falling apple hypothermia. Or whatever it is in precise earth medical terms.