ORBIT

and

SPECIAL RELATIVITY
Han Erim

February 3, 2010

A few years after writing Alice Law version 5, I began to feel that there was an important deficiency in the subject of Special Relativity. Understanding the source of this deficiency and reaching a solution became possible only after I was able to write the topic Ghost and Spring (Image and Source). This section truly removed the blockage experienced in Special Relativity within Alice Law and opened the way forward. This study of mine brought important results and new expansions. My publications on clock synchronization, space deformation, and perception speed are outcomes of this work. My Ghost and Spring study also revealed the relationship between the Doppler Effect and Special Relativity, which is truly a wonderful result.

The subject of this article is another result of my Ghost and Spring study. Here, I will explain how the orbital calculations of planets and stars should be made by taking Ghost and Spring effects into account. The topic is truly amazing, isn’t it?

About Ghost and Spring (Image and Source)   I would also like to explain here why I chose the words Ghost and Spring instead of Image and Source. In Turkish, the words “Pınar” and “Kaynak” have nearly the same meaning and both refer to a place where water emerges. However, when the word “Pınar” is used, it immediately brings to mind a clean and beautiful water source. The word “Kaynak” is more general. For example, we can speak of a wastewater source, but not of a wastewater spring. A spring is untouched, sparkling, and pure. The word “Pınar” is also mystical and magical. When we want to strengthen emphasis, we usually prefer to say “Spring” instead of “Source.” That is why, in Alice Law, I named the electromagnetic wave source “Spring.” The most appropriate English equivalent of “Pınar” seemed to be “Spring.” Later I learned that in physics the word “spring” can also mean a metal coil or elastic spiral. I used the word “Pınar” in so many places and in so many different works that I was afraid to change it. Besides, I don’t think it is that important. You now know what is meant by spring, and that is what matters. The word “Ghost,” which I chose to describe the images formed due to Special Relativity, came naturally. Ghosts walk, speak, stretch, shrink, shine, fade, and at the same time they are very surprising; they also lack a physical identity. While working on the subject, I was so astonished by what I observed and by the results that emerged that I could not think of any other word to describe this situation. I believe the word “Ghost” is quite consistent in expressing the strangeness and peculiarity of what occurs. Using the distinct terms Ghost and Spring will also be beneficial. When we talk about Ghost and Spring effects, everyone will understand that we are referring to Alice Law and its (c+v)(c-v) mathematics. Expressing this distinction clearly is, in my opinion, especially necessary during the recognition period of Alice Law.

ORBIT

I dedicate this article to astrophysicists, astronomers, and those who deal with the heavens.

As a starting point, let us observe the first animation of the Ghost and Spring study on a figure. If you have not read that study, please read it first.

• There is a planet (Spring) moving in orbit.
• When the planet is at point A, the image packet belonging to the planet sets out. (I)
• While the image packet travels toward the observer, the planet continues its motion along the orbit. (II)
• When the image packet reaches the observer, the observer sees the ghost (image) of the planet at point A. At that moment, the planet (Spring) is at point B. (III)

First of all, we must answer the question of why the observer will see the ghost at point A. The answer to this question is actually very interesting, because it is only possible to give a logical answer. The answer is as follows: apart from point A, there is no other reference point we can propose as the location where the ghost should be seen. Our existing knowledge inevitably directs us toward such an assumption and acceptance. You may not find this answer entirely satisfying, but there is nothing else that can be done except to accept that this assumption is correct. Therefore, let us accept this assumption as correct and call it the first reference point.

If we express the situation at the first reference point mathematically, if the image packet set out from point A at a distance of d = c · t relative to the observer, then the observer will see the ghost again at a distance of d = c · t according to his own reference system. We can also express this situation using a coordinate system. If the image packet set out from position x and y relative to the observer, then the observer will see the ghost again at the same x and y position. (Figure 2)

 

Now, by remaining faithful to the mathematics above, let us observe this part up to here in an animation. In the animation, we will examine where an observer on Earth will see the planet Mercury. (Animation 1)

The planet (Spring) and the Ghost move along the orbital line. Of course, since some time must pass for the image packet to reach the observer, the ghost will follow the planet from a certain distance. In this animation, let us note that the observer is stationary relative to the orbital reference system.

We know that the observer will not see the planet (Spring) itself, but its ghost. The animation shows us the presence of certain effects.

• The larger the value we choose for the speed of light, the smaller the distance between the ghost and the spring becomes. This is because light will cover the distance between them in a shorter time.

• The greater the distance between the observer and the planet (spring), the more the positions of the ghost and the spring will differ. The reason is the same. The longer it takes light to cover the distance between them, the more their positions will differ.

• Although the orbital speed of the planet is constant here, the speed of the ghost is variable. (If you reduce the speed of light, you can observe this effect more clearly.)

I believe you will have no objection regarding what has been explained up to this point. In fact, what I have described so far is merely the mathematical interpretation of a phenomenon you are already familiar with and seeing it through an animation. We can summarize the part up to here as follows.

The observer sees the ghost at a distance d = c · t. (Figure 3)

In our initial example, the planet was moving and the observer was stationary. Now let us consider the opposite. Let the observer move and let the planet remain at point B. In this case as well, the observer will again see the ghost at a distance of d = c · t (at the same x,y coordinates relative to himself), that is, at point A. (Figure 4)

Here, I give a similar answer to the question “why” as above: Without contradicting the first reference point we wrote above, there is no possibility of proposing any location other than point A as the place where the ghost will be seen. The knowledge we have inevitably directs us toward such an assumption. Because whether it is the planet or the observer that is in motion, the same result must be obtained. Let us call this the second reference point.

Thus, based on two reference points, we have obtained a foundation. In the first animation, Earth was stationary relative to Mercury’s orbit. From now on, let us also set Earth in motion in its own orbit and observe the results in a second animation. Let us see what kind of result will emerge. The next animation shows this situation. (Animation 2)

Because the Earth is in motion, the ghost of Mercury is no longer on the orbital line. If you press the "Draw Orbit" button, you can see the path along which the ghost moves.

You might think that the ghost should always be on the orbital line, but this is not possible, because in that case the equality d = c · t would be violated. Such a suggestion would also violate the constant speed of light c. The ghost will always appear at a distance of d = c · t.

You may also think that the calculations here should change due to the Earth’s rotation around its own axis. However, this is not correct. If such a situation existed, when we looked at the sky, the stars would have to change position along with the Earth’s rotation. The rotation of a body around its own axis has no effect on the position of the ghost.

Up to this point, I have not mentioned Alice Law or its (c+v)(c-v) mathematics. In reality, what I have described here are its rules. If you know Alice Law and the rules of its (c+v)(c-v) mathematics, you can interpret what is described here much more easily and see the relationships much more clearly.

Wasn’t an important detail forgotten? Of course, when we look at the Sun, we will not see its Spring but its Ghost. In that case, let us add the ghost of the Sun to the animation and observe the real situation. (Animation 3)

You can download the source codes of the animation as a Flash (.fla) file from here. (Flash CS3, Action Script 3.0)

Download source code.