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The rotation of the Moon

Published by Erik Dahlén at Shakespir.

 

Copyright Erik Dahlén.

 

This copy is for your private use only, no distribution is allowed without consent from the

author.

 

The rotation of the Moon

 

Abstract

I will go through the old Newtonian idea which claims that the Moon is rotating around its axis, and then explain why this theory contradict logic. Hence a new theory is needed to explain the movement of the Moon, which I will hand over and it can be explained in one sentence. “An object moving in orbit, or close to a massive object, is moving in a straight path in a curved environment, rather than in a curved path in a flat environment.” I will end up with explaining what impact this will have and how my theory can be falsified and how it can be proven to be better than the old Newtonian view.

 

The old theory

The general theory about the Moons rotation is that the Mrotates around its own axis. The idea is that the Moon most rotate around its axis to be able to show the same side towards earth all the time, which the Moon does. The reason for people to believe this is that the Moon is falling towards earth but misses the earth due to the orbital speed. This idea is an old Newtonian idea that a satellite falls into orbit if it has a perfect speed so that the object always misses the surface of earth when it fall down due to gravity.

 

Most people, and researchers, believe in this old Newtonian theory, but I don’t. So before you continue reading you most know that I am, as far as I know, the only one not believing this, which means that you should not “buy” all my arguments and facts without looking into them by yourself. After all, the chances that I’m right and the rest of the world is wrong is less likely than I have misunderstood something. But if I think that I have a better theory than the general theory I have to argue for it. And remember, the believer of the old Newtonian theory still have to overprove me, or my facts and arguments, just because their theory is older does not give it priority.

 

To explain the old Newtonian theory of orbit one has to start from the beginning. The idea is that if you put a cannon on a hill and fire it, the cannonball will have two speed components. One component will be directed in the same direction as the cannon was pointing and one will point down to earth, due to gravity. (I assume that I don’t have to explain the existence of gravity and how it accelerates an object.) So the idea is that if one fires the cannonball in such high speed that the cannonball will miss the surface of the earth by traveling so fast that it moves toward the horizon equally fast as it falls down towards the ground, the object will fall into orbit.

The left part of the picture above shows a cannon which fires a cannonball perpendicular to the ground. Two velocities working on the cannonball, one is the speed from the fire of the cannon, the red arrow, and other one is the gravity, the blue doted arrow. The speed downward will increase due to gravity works like an acceleration, and the speed forward will decrease due to air resistance. The right picture shows a cannon firing a cannonball in such speed that it misses the ground all the time, and hence fall into orbit.

 

The idea is that the cannonball will always convert the acceleration towards the surface to a new trajectory for the cannonball, so that the velocity of the cannonball will always be perpendicular to the gravity towards the central mass. As the picture below shows, where this transformation of acceleration from the gravity is transformed into speed in a new direction, end hence the cannonball can conserve energy by falling in a fix distance from the central mass. (This assumes an eccentricity of 0, otherwise the cannonball will transform kinetic energy to potential energy and then potential energy back to kinetic energy during its orbit. With a higher potential energy far from the central mass and a higher kinetic energy close to the central mass.) The blue doted arrow is the gravity pulling the cannonball in orbit toward the central mass and the red arrow is the velocity of the cannonball at that position. During the orbit of the cannonball the acceleration from the gravity is turned into a new trajectory for the cannonball so its direction of velocity is shifted.

The old Newtonian theory predicts a non-rotating body to orbit according to the picture below. Where the black triangle is the orbiting object and the blue circle is the massive object, the mass of the triangle is neglectable in compare of the circle. The arrow show in which direction the triangle is orbiting.

With this view of what is going on the answer is obvious, a non-rotating satellite, the black triangle, will show different sides towards the central object, the blue circle, during its orbit. Before I explain why this is not the case and what is really going on I will first explain how this theory will contradict itself. Then it will be obvious that a new theory is needed and I will then hand you one which both explain what is going on and is consistence with the rest of the physics.

 

Now let’s think of a circler object orbiting a central mass. Then let’s think about two circler objects orbiting it after one another, as below.

The only reasonable way for the circler objects to orbit if they are orbiting one after the other is according to the picture above. We do now not know if they are rotating or not or which side they show towards the central mass, but that is not important for now. We still know that they have to move one after the other. Let us move the two small circles closer to each other and see how the old theory predict them to fall.

The old Newtonian theory predict the object to fall according to the left picture, if the object is a non-rotating object. For me this is nonsense, there is no reason at all why the two circles should start orbiting different just because they are so close that they become the same object and not two different objects. (Yes one can “solve” this by move some potential energy to one of them from the other so that one will orbit in a closer orbit and the other in a wider orbit, but this seems to be more ad hoc than reasonable.)

 

The only sensible thing is that each circle is orbiting in its own orbit regardless of if it is connected to any other circle or not. With this argument the only reasonable orbit for the two circles are the right part of the picture. Now imagine a lump of gas orbiting as the picture below, ones again with an old Newtonian theory to the left and a more reasonable theory to the right.

The lump of gas orbiting the blue circle is in the left picture falling in orbit according to the old Newtonian theory, where it shows different sides towards the central mass during its orbit. The right picture show how a lump of gas should fall were every atom falls in its own orbit and will not care about the orbit of the other atoms in the gas. It will show the same side towards the central mass during its orbit. Because the lump of gas in not a rigid body there is no way to move potential energy from one part of the lump to another.

 

There is one even stranger thing with this old Newtonian theory, if you have something inside something else. If one have an object in vacuum inside another object, the inside object will not feel the forces acting on the outside object. So let’s paint this up.

Ones again with the old Newtonian view to the left and my new theory to the right. Remember that the green circle inside the black cube is in vacuum, so the green circle feels no interaction with the black cube. The blue circle is the central mass, the arrow is the direction of orbit and the red-curved part of the black cube is just an indicator of which sides go where and has no other meaning. This means that objects inside another object will start to rotate inside the outer object, and this is for a non-rotating object. Compare that to my new theory which claims that all object will fall in its own orbit, and hence be on the same place inside the outer object.

 

From all pictures above it is clear that every part of an object in orbit will fall in its own orbit regardless of the existence of other part of that same object. And it makes sense, if part of an object is not pushed by something it will continue its path and not move to a new path. It is only when something interacts with it that the part will change its orbit, e.g. when a rigid body rotates around its own axis. For me this is enough for knowing that the old Newtonian theory most be wrong and that it should be replaced by another theory, and here it comes. The newer theory is directly derived from General Relativity and its view on things. We do already know that GR is a better way to explain what happens in gravitational fields, for example the bending of light around massive objects and the shift in planetary orbits called precession, e.g. the orbit of Mercury. So we already know that one should not trust a Newtonian derived theory, and that it is only good for approximation and cannot stand as a correct view on things. I don’t understand why so many holds on to this old and outdated theory, which gives a totally wrong view of how an object orbit in a gravitational field.

 

The new theory

I do not plan to fill this paper with a lot of calculations so I will not write down the orbit of an object in a gravitational field. If you want to find the calculations you can just look them up on internet and there is a lot of good articles about it, which all are derived from Einstein’s theory of general relativity and how it can explain the orbit of planets. (Including the precession.) What I want to focus on is the understanding of what is going on when an object orbits a central mass. But first I will guess what went wrong and why nobody thought of this.

 

When Einstein’s published his work on general theory many people had a hard time to understand it and only accepted it as a model to explain certain phenomenon. So they didn’t bother to update all old theory which stilled seemed to work. Then time passed and no one seemed to care to look into the old theory of how an objects is orbiting a central mass. Notice the difference between how and how. GR has updated the view on how an object is orbiting regarding on where the path of the orbit is, but not how the object in orbit behaves in respect of rotation around its own axis. This is my guess of why nobody looked into this, because according to me it’s obvious that the old theory is wrong and I guess most researcher would have found this if they were looking for it. And at last, I will not start explaining what I think is going on when an object is orbiting a central mass.

 

General relativity claims that a massive object is deforming the fabric of space-time and this curvature is what causing gravity. And this explain why massless particles, e.g. photons, also will feel the effect of gravity. In this perspective the orbit of an object has been updated according to GR. It also suggests that the space-time is curved and not the path of an orbiting object. The object orbiting is not moving in a curved path, it is moving in the only straight path there is. And that all there is to this.

 

Let’s go through this ones more. A non-rotating object traveling in a straight line parallel to a flat surface will always show the same side towards the surface. If the flat surface and the non-rotating object traveling on it were curved so that flat surface were to become the surface of a circle, the path of the non-rotating object will become an orbit around the circle, and still showing the same side towards the surface. This is exactly what is going on. The mass of an object creates a curvature in the fabric of space-time which makes a flat surface circular and an object traveling parallel to this surface going in an orbit around the massive object. What I mean with a “flat surface circular” is like the ocean on earth, they are flat and circular at the same time and that is caused by gravity, or more accurately the curvature of space-time. Another way to think of this is like an ant moving around a tree, it is moving around the center of the tree with the same side towards the center, and is moving along this path because this is the only possible path. (This is not what is really going on since the tree have no attractive force such as gravity but it could be a good way to be able to wrap your head around this.) The bottom line here is, the object in orbit around a central mass is moving in orbit because it is the only possible path and not because it is “falling” in orbit, so it is moving straight forward all the time, in its perspective.

 

Since this is quite, or more accurately, extremely hard to grasp, let us rephrase this in one sentence. “An object moving in orbit, or close to a massive object, is moving in a straight path in a curved environment, rather than in a curved path in a flat environment.” This is my theory of what is going on, everything I suggests is in that sentence, simple and difficult at the same time. So let us go through this ones more.

 

One way to think of this is like a car driving in a straight path on the surface of the earth. Even although it will never turn will it eventually end up in the same spot, after one lap around the world. The reason in this case for this to be possible is that the car is driving on a curved surface. One can think of the same thing for an object traveling close to a massive object, the path of the object is not curved but the environment around the traveling object. (Notice that I don’t claim that this is what is happening, it is only a way to thinking of it which might make it easier. In this car example the car is actually traveling in a third dimension compare to the two-dimensional surface of earth, I do not claim that there is any hidden dimensions close to massive objects.)

 

Conclusion

The old Newtonian theory of an object in orbit is wrong, since it contradict itself. There is no reason for any part of an object to move in any other path then its own unless there is an external force acting on it. There is no reason for two non-rotating objects which travels one after the other to suddenly start to rotate around each other when they connect. Hence we know that a better theory is needed, and there is one to be extracted from general relativity, which we already know to be a better explanation of gravity than the old Newtonian theory.

 

The new theory can be summarized into one sentence. “An object moving in orbit, or close to a massive object, is moving in a straight path in a curved environment, rather than in a curved path in a flat environment.” This means that an object traveling near a central mass is traveling straight forward, in the same manner as it would if it was traveling in a straight line in a flat environment, from its perspective.

 

One interesting point of this theory is that if I’m right, it is not only the rotation of the Moon which is wrong. All rotations calculated for all planets, dwarf planets, Moons and exoplanets has to be recalculated, since they all assume that a non-rotating object is showing different sides towards their central object and not as I have shown, that they will show the same side towards their central mass.

 

Falsifiability

All good theories must both be better than the old ones and be falsifiable, and my theory is of course both. If I find an experiment which the two theories predict different outcomes and if my theory’s prediction is correct, then it is better than the old Newtonian theory.

 

The first experiemnt which predicts different outcomes is when two objects in orbiting showing the same side towards the central mass are connecting to each other. Let’s think of two rectangles orbiting a central mass. They are identically and travels one after the other. Both are showing the same side towards the central mass all the time. The old newtonian theory states that they then have to rotate around their axis to be able to show the same side towards the central mass. My new view of things claims that they are traveling in a straght path so they do not rotate around their axis. Then let them connect to each other.

According to my new theory they will continue to orbit with the same side towards the central mass, as in the right part of the picture. The reason for this is obvious, theywere traveling in a straight path after each other before, there is no reason for them to start to rotate around their common axis now when they are connected. The old newtonian theory claims that they were rotating around their axis and that the angular momentum has to be conserved. Hence will they continue rotate around their commen axis when they are one rigid body instead of two separate bodies. The problem here is that the moment of inertia will not be enough for it to show the same side towards the central mass. The new object now extends twice as long from its center as before, and its mass is now twice as big compare to when it was two separate objects. Accoring to the formula for moment of inertia I=sum(m*r^2), where m is the mass, r the distance to the axis, I is the moment of inertia and then we sum up all elements. (All this can be found on wikipedias atricle “Moment of inertia”.) We also have that the angular velocity is given by this formula, w=L/I, where L is the angular momentum and w is the angular velocity. Since the angular momentum is dubbled, the mass dubbled and the radius is dubbled we have that the angular velocity is decrease by a factor of 4. Hence we have a difference in the two theories which can be tested, which means that my theory is better if it complies with observations, and the other way around.

 

A different way to test this, which should already have been tested, is to send out a setallite from earth into space which has no rotation around its axis and let it pass by a stellar object in our solar system. If the satellite continue moving with the same part of the setallite as the front part, then my theory is correct and if not it is wrong.

 

Thanks

 

I first want to thank you for reading this far, if you have any question you can just email me at [email protected] Then I need to mention the references I used, first of all the main conceptual idea I have directly extracted from general relativity so I guess I have to thank Einstein for that, but he is dead so he doesn’t care. (But someone else might care.) Then I used some different Wikipedia articles to learn about the old Newtonian theory, you can just search the internet to find a lot written about it. (And I also used my knowledge of Newtonian mechanics from my undergraduate studies at Lund University.) But for the new theory I did not use any other source than my understanding of general relativity. (Which I also got at the University.)


The rotation of the Moon

After I have explained the old Newtonian view of the rotation of the Moon around its axis I will continue pointing out some problems with this view. I will then end up with a better way to describe what is going on, which is consistent with the rest of the physics. All my claims will be testable and falsifiable, and I will also explain the impact my view has on different calculated properties.

  • ISBN: 9781311544506
  • Author: Erik Dahlén
  • Published: 2016-03-10 17:40:13
  • Words: 3486
The rotation of the Moon The rotation of the Moon