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Periodic motion in Universe

Background and actual explanation

The universe is full of movements that repeat themselves over and over in some specific patterns. From ancient times the periodic motion of the Moon and its phases were well known. In our solar system we are now aware of the elliptical motion of planets around Sun although in internet it can be found that, at this moment, there are people who think that Earth is not in motion and is still the center of Universe.

With the rise of astronomy as science, other periodic phenomena outside our Solar system were discovered. The first double star system V1 and V2 Sgr was observed by Ptolemy about two thousand years ago, but the great era of discoveries started with the invention of telescope.

Galileo in 1610 observed the planet Jupiter and its moons. For our topic it is very important the work of Ole Römer regarding the motion of Io – a Jupiter satellite. To date his work is reminded as first proof for a estimating the light speed, but we are interested more in a ,,foundation for a new theory of relativity”.

Actually, Römer found, for several months the eclipses lagged more and more behind the expected time, but then they began to pick up again.  He was further able to predict the time of eclipses based on the relative distance between Earth and Jupiter. The light from Io (actually reflected sunlight) took time to reach the Earth, and took the longest time when the Earth was furthest away.  When the Earth was furthest from Jupiter, there was an extra distance for light to travel equal to the diameter of the Earth’s orbit compared with the point of closest approach. 

From his data, Roemer estimated that when the Earth was nearest to Jupiter (at E1), eclipses of Io would occur about eleven minutes earlier than predicted based on the average orbital period over many years. And 6 months later, when the Earth was farthest from Jupiter (at E2), the eclipses would occur about eleven minutes later than predicted.

Jupiter light speed

Figure 1 Romer estimation of light speed based on relative distance between Earth and Jupiter (picture not at real scale)

Later on other periodic phenomena were observed in Universe starting with binary stars, pulsars and now exoplanets.

To date it is accepted that about half of known stars are part of a double or multiple star systems. Some of these stars are close enough to be observed by a telescope and other are distant stars and they were detected and characterized by spectroscopic methods. The launch of Hipparcos satellite in 1989 has widened a lot our knowledge in this direction and it is estimating that more than 15000 new multiple star systems were discovered.

The search for exoplanets is one of the most exciting fields in astronomy and will perhaps one day answer the question of whether we are alone in the universe.

The first discovery of a planet orbiting a star similar to the sun came in 1995. The Swiss team of Michel Mayor and Didier Queloz of Geneva Observatory announced that they had found a rapidly orbiting world located close to the star 51 Pegasi. As of the 12th January 2014 there have been 1060 exoplanets discovered in 802 different planetary systems, 175 of which are multiple planetary systems (Zolotukhin, I. 2014). The latest updated catalog of exoplanets in 2016, shows more than 2000 exoplanets for which astronomers have made a detailed characterization of their orbits; other about 1000 supposed exoplanets needs further confirmations.

But  quite all exoplanets are very strange for our expectations.  Most exoplanets seem to have walked directly out of the best science fiction moves. For example, we’ve discovered planets consisting purely of water and others consisting mostly of diamond. Some planets nearly scrape their host stars once every orbit, while others exist in darkness without a host star at all.

According to the published data let us see how a hot Jupiter is described:  

HD209458b (sometimes  unofficially called Osiris) is an exoplanet that orbits the solar analog HD 209458 in the constellation Pegasus, some 150 light-years from the Solar System. The radius of the planet's orbit is 7 million kilometres, about 0.047 astronomical units, or one eighth the radius of Mercury's orbit. This small radius results in a year that is 3.5 Earth days long and an estimated surface temperature of about 1,000 °C (about 1,800 °F). Its mass is 220 times that of Earth (0.69 Jupiter masses) and its volume is some 2.5 times greater than that of Jupiter. The high mass and great volume of HD 209458 b indicate that it is a gas giant.

Prediction of actual theory of relativity for periodic motion in Universe…and why they are absurd…

As it is well known the speed of light is considered a ,,fundamental constant of nature” and is invariable and independent of the motion of source or the motion of observer.

If this is the case, even in a layman mind should pop up at least two questions:

1. Why there is a change in perceived time of Io eclipses for an Earth observer, depending on the relative distance up to Jupiter but in case of multiple stars, pulsars and exoplanets there is no such dependency?

2. Are these far away periodic systems having a relative motion relative to Earth or are they stationary? If they move away or come toward Earth, than again their perceived periodicity seen by an Earth observe should have still another second factor of variability .

Let us consider a binary star or an exoplanet with a period of few hours or even few days and explain in detail what should an Earth observer see due to the Earth movement around the Sun.

Periodic motion observed from Earth

Figure 2. Variation of measured period of a far away phenomenon due to Earth orbital motion (picture not at real scale)

When distance between Earth and the place where this periodic phenomenon takes place is minimum, i.e. Earth in E1 point, we should have a minimum time for light to travel up to the observer. As far Earth moves toward E2, the delay time should increase and it would be maximum soon after passing E2 and the cycle will repeat over and over again with each revolution of Earth around Sun.

Why this effect is not observed in measurements? Are all these far away objects plotting a conspiration in order to fool us?

An example: for a planet like PSR J1807-2459 A b, having a period of 0,07 days, i.e. 1,68 hours, it would be impossible to not observe a variation of  about 15 minutes in its period during a terrestrial year …..

But the inquiry goes further: the star which is orbited by such planet is supposed to have a relative motion away or toward Earth. As consequence, with each revolution of the farther away planet around its star, there should be a secondary variation of the eclipses time measured by Earth observer. Even in this case it can be predicted the mathematical form of this variation. 

increase in observede delay for exeoplanets

Figure 3. Variation of measured period of a far away phenomenon due to universe expansion (picture not at real scale)

            Assuming that initial distance between Earth and Star is OS0 =D, and star moves away with speed V, and the period of planet rotation is T, after a period of rotation the star is farther away with an amount:

d = V×T (to date T is considered identical with measured one for the actual relativity and V can be taken from redshit measurements or from other data)

            But, for the Earth observer, light has to travel the distance D+d, and therefore the eclipse of planet will be delayed with a supplementary interval of time d/c after first eclipse; after second eclipse another delay equal with d/c and so on.

            With each eclipse of the planet, there should be a delay proportional with an arithmetic progression given by:

            t= D/c +nd/c where n is the number of eclipses

            In case of a period of planet rotation of 1,68 hours and assuming the star moves away with 1000 km/s, the supplementary delay is apparently very small, i.e.  0.02016 s/period which seems negligible, but for a terrestrial year the delay should be about 1,8 minutes.

            These delays add up and let us assume we come back after a decade and measure again the period of the same planet. The delay is staggering and is about 18 minutes. Any astronomer should look again to the period of exoplanets measured before 2000 and they will see by themselves if their periods are modified or not….

Update 13.04.2016 with examples 

            Observation: we should make a distinction between the real period of an exoplanet and the apparent period of an exoplanet measured by an Earth observer. The example explain how the apparent period of an exoplanet (difference between 2 eclipses )  should modify if the special theory of relativity is correct. 

No astronomer provided me some data for exoplanets and their hosting stars, therefore the exemplification will be made taking into consideration the first planet discovered around Pegasi 51, i.e. Dimidium, with data found here -  (www) -

So, the star Pegasi 51 is receding from us (Solar System) with a speed of 33,7 km/s, previously measured from Doppler shift of absorption lines. The period of hot Jupiter planet – Dimidium, discovered and measured in 1995, orbiting Pegasi 51 was estimated at 4.230785 ± 0.000036 days (101.5388 h); the error in period determination is only 3,11 seconds (0.000036 days converted in seconds).

What should be the period of Dimidium in autumn 1996, after one year from its discovery?

In a terrestrial year, the Star Pegasi 51 gets farther away from Earth with a distance:

D = v×t =33,7×31557600 km =1063491120 km

1 year = 365.25 days = (365.25 days/year) × (24 hours/day) × (3600 seconds/hour) = 31557600 seconds

If light speed is constant, as actual relativity supposes (300 000 km/s), than after a terrestrial year, the period of Dimidium should be increased with an amount of time necessary for light to travel the supplementary distance: 

 t=D/c= 1063491120/300000 = 3545 seconds, i.e. approximately one hour

            By no means this expected variation can be covered by systematic error of measurement which is only 3,11 seconds or by other processes.

Not only this, but there is a pile up of the amounts during each year so in a decade the change is more than significant. Now, in 2016, the period of Dimidium should be increased with more than 20 hours and consequently all data in catalogs should be periodically adjusted. I suppose someone at the International Astronomical Union (IAU) should take care of this problem …. and I am really curios why none has observed this incongruence.

This is only the beginning of a nightmare for actual theoreticians. Let us plot this variation and see what the period of this planet few centuries ago was ……

Time (years) Period (days)
1995 4.230785
1996 4.271815
2006 4.641086
2016 5.051387
2026 5.461688

Dimidium period variation




If we go back in time and for each year we diminish the period of the planet, few centuries ago the period of the planet Dimidium was close to zero, and a little bit earlier it was negative….

This is an undergraduate student task to draw a regression line and extend it a bit, and I suppose there is no need to insist on commenting the consequences…

 A simple concept is unclear to me:  what does it mean in a theoretician mind a negative period for a planet?

Probably we need another mathematical acrobatics to solve this singularity and a new theory has to be proposed…

Or maybe it will better if someone will propose a pop up of planets from dark matter in the right orbit, at the right moment, in order to fit in the observations….

There will be an entire newsletter dedicated to pulsars, therefore here only some simple facts are discussed.

Actual theoreticians should answer to a simple question: If the period of a pulsar is up to few seconds, what was the period few hours or a day ago?

If we assume for pulsars a receding velocity of few decades of km/s, the period diminishes to zero in less then few hours and after that becomes negatives too…..

If the pulsar is approaching us … the situation is the same….

If someone finds an answer, than we have to analyze again the <<procedure of folding>>,  used in pulsar data processing. For those who are not in the field, I will give some hints here: An individual pulse from a pulsar is usually weak and may not rise far enough above the noise. But if the data are ,,folded” at a pulsar’s period, the noise starts to cancel itself out, while the pulses add constructively and pop out more noticeably.

In simple words, folding means to split the received data in chunks of an certain length (let us say a second as in fig. 2) and than these chunks are lined up and added together, so that the strength of the signal at 0.1 seconds is added to the strength of the signal at 1.1 seconds, and that is added to the strength at 2.1 seconds, and so on….

These added pulses are called the “average pulse profile.”

pulsar folding procedure

Fig.2. Pulsar folding procedure

To the desperation of theoreticians, the folding procedure cannot be performed if the pulsar recedes from us, because in this case the signal from 1,1 second will not align perfectly with previous signal from 0,1 second, nor with the signal from 2,1 seconds and so on. Instead of a perfect overlap, after each period, the signal from pulsar will shift toward right if pulsar recedes us…..

I do not want to answer again to a large number of emails, therefore in absence of some reliable data for a specific pulsar, I will provide a simple generic example. Let us consider a pulsar with period of 1 s, having a receding velocity of 50 km/s and the procedure of folding is made over a period of half hour in chunks of 1 s.

In half hour the distance between observer and pulsar has increased with an additional distance equal with:

D=50 ×1800= 90000 km

The signal from pulsar needs a supplementary time to travel this distance so the apparent period is modified with an amount equal with:

t= D/c =90000/300000=0,3 seconds.

Let us say that in the first chunk the pulsar signal is present at 0,1 second from the thick mark. With each subsequent period, the registered pulsar signal shifts toward right, and after half hour- for the last chunk, the signal is present at 0,1+0,3=0,4 seconds from the thick mark.

How could someone line up, add these signals and measure for this pulsar a stable period with eight or nine decimals from a second?

As consequence, if the folding procedure works, either pulsar are stationary relative to Earth or someone has cooked the books here too; but do not worry, this will be the smallest error in science and besides…. who cares !? 


            Proposed explanation

            In a book about relativity published in 2009, I presented a new concept called ,,temporal aberration’’ and I exemplified the effect in case of binary stars.

            In a nutshell the effect is very simple: due to the fact that light has a variable speed, a far away observer measures an apparent period of a phenomenon which can be very different from the real one; in general a far away observer will get like a ,,time compression’’ and if for example the real phenomenon has as a period of a decade, it can appear for the Earth observer as having  only one year periodicity or even less. This ,,apparent time compression” is so consistent that covers all the other effects due to the Earth movement or relative velocity between Earth and far away phenomenon. 

            As consequence, in order to infer the real period of a far away phenomenon a series of parameters are to be known. The ,,rate of time compression” for an far away observer is a topic which deserves an entire chapter and this will be done ,,in extenso” inside  the book.

Astronomer did not bother at all for the fact that two stars orbit one another in few minutes and now they are not bothered for the fact that planets orbit around stars in few hours. In fact these ,,news” are presented like ,,exciting discoveries” and new absurd theories are proposed in order to explain these  facts. Planets at more than 1000 K or hot Jupiters orbiting a star in few days aren’t in this moment a curiosity. They are the rule and only our Solar system seems to be the weirdest thing in the Universe. Science fiction seems more credible than our daily science: I saw a documentary presenting like a proven fact a planet where rain is made out of iron drops …...but I haven’t found yet a science fiction book with such absurd idea …..

How is possible for a planet like Jupiter to migrate in the close vicinity of a star and after this migration to remain stable in such orbits?! Maybe one in a thousand or we can accept even one in a hundred will migrate from different reasons (as example the existence of a interplanetary medium and friction), but by sure such kind of planet will not stop at few millions of km away from its star and it will end up in the mass of the star. This should be a concern for a common sense mind and for a basic science… But who cares….!?

How is possible to have an entire solar system with five or six planets inside Venus orbit and how such solar systems are stable?  And in such solar systems, as a general rule, there is also a hot Jupiter too…

I suppose soon other planets will be discovered in such solar systems and new absurd ideas will be necessary to fit in the observations. For such solar systems scientists should invent a new theory of gravitation too; even with some artifacts and absurd hypothesis, such systems are not stable and either planets are ejected away either they should enter into collision, etc.

Unfortunately, the improvement in analytical instrumentation will soon put an end to some of these speculations …

The infrared measurements of these hot Jupiters will reveal that their temperatures is not thousands degrees or even more. It is impossible to confuse the infrared spectra of a body at thousands degrees with the spectra of a celestial body having few hundreds degrees.

Already analyzing the atmospheric composition of such hot Jupiters, scientists are not able to explain the presence of methane or other gases there which are characteristic for a cold planet….  and therefore in a general state of confusion, they invent new and new absurd hypothesis…

             In fact, because we have assumed light speed is a universal constant, there is also an ,,spatial aberration”, i.e. all distances across universe are crooked but this, Hubble law and dark energy are the topic of the next presentation…

            As I have said in other previous messages the entire astronomy must start again everything from scratch …. and many of  astronomical absurdities are caused by a wrong foundation of science and especially of relativity.

Text added on 22.05.2016

Section 4  Q&A to the previous newsletter

Only two people agreed to publish their correspondence so these emails are grouped in separated pdf documents and a link was created to each of them at the bottom of this page.

Both discussions are worth reading but I will formulate my answer to Mr. A. Chepick as far his first email was very concentrated and punctual. The discussion with Bob Watson is longer and a bit more diluted, having the same essence though.

As a general remark, it is not possible to apply Doppler shift methodology in order to establish the variation of period of an exoplanet. Doppler shift works for physical signals (sound, electromagnetic waves) and not for ,,clocks”; this is a pure relativity problem.

If someone persists in this approach, then please do the calculation for Jupiter moons using Doppler Effect and I will publish the results here.

If someone justifies that Dimidium was discovered by a sort of Doppler effect and it is normal that Doppler shift applies, than again (s)he is wrong. Please redo the measurements for Dimidium period with transit method. Do you see any differences between the results of Dimisium obtained by these two different methods? Of course not! What Doppler shift can someone find in a transit of a planet in front of a star?

The ,,piece of resistence” - Quote from Chepick’s  first email:

,,Undoubtedly, the period TS of the planet Dimidium between the same phases, which observed in the Solar system will depend on the speed of the Pegasi-51 relative to the Sun, but not in such manner, as the Author points out. It is obvious that the data (the period TS=4.230785 ± 0.000036 days and speed v=33.7 km/s) are given relative to the center of mass of the Solar system, and not relative to the Earth. Denote by TP the period of this planet in the system of Pegasi-51. Let's simplify the task by assuming that the Pegasi-51 moves strictly from the Sun. We denote R is the distance between the sun and the Pegasi-51 at some moment. Then after n periods the Pegasi-51 will be away from the Sun at distance R+ Ln, Ln =v*n*TP and last of the observed period will be equal TS, taking into account the time difference of light propagation from the positions of beginning and end of this period (relativistic effects are too small):

TS= TP+(R+Ln)/c -(R+Ln-1)/c = TP+ (Ln- Ln-1)/c = TP+ v(n-(n-1))*TP/с = TP+v*TP/с = TP(1+ v/с).

That is, the period TS does not depend on the period's number. So there is no dependence of the period TS and the observation time. Indeed, we observed that the period TS greater than the period TP in the reference frame of Pegasi-51. And it is more exactly in many times, how many were increased the wavelengths by the Doppler effect. And in the Doppler effect also there is no dependence of wavelength and time. And the conclusion of the Author of this dependence is his logical error. Hence it can bring his other errors in reasoning.”

In a subsequent email I asked Mr. Chepick to provide me a simple calculation not for n periods but after first and second period, in the hope he will discover by himself the error in his math computation.


 ,,I will prepare an answer for you but first I would like to get from you
a simple calculation with change in period of Dimidium after one and two
revolution; Not for n revolutions.

You can use your formula from the newsletter and you will see by
yourself the error.”

As far as he did not answer to the topic, it is necessary to see where the error in his formula is. It is a simple problem of mathematical analysis with an arithmetic series, i.e. level of high school math.   

Of course the entire discussion is in the frame of actual relativity (c = constant).

Let us suppose at a certain moment, one makes a measurement of period of Dimidium. This measurement is only an intermediate term in an arithmetic series; it is not the first and by sure it will not be the last. Let it be this term Ti, and we are interested to see how the next term in the series Ti+1 is related to Ti. The demonstration follows the same steps like the one already presented on site or in emails and one can obtain that:

Ti+1 = Ti +R, where R = approx 40 s

In order to calculate the period of Dimidium after n revolution the right formula is:

Tn = Tn-1  +R

but Tn-1 =Tn-2 +R

and so on until

            T2 = T1 +R

With a simple trick made in elementary math ( adding all these equation left part and right part ) we can get:

Tn = T1 + n×R

When this formula is applied, the same results are obtained like the calculation previously presented on website.

In the formula presented by Mr. Chepick, only the contribution brought by the last revolution is added, when the period of exoplanet after n revolution is calculated.

Furthermore, based on Mr. Chepick formula, something very interesting can be demonstrated: for the same very trip, photons travel with two different speeds; part of trip with speed c and another part of trip with infinite speed. One can deduce this demonstration easily reading the discussion with Mr. Chepick and Watson.

Mr Chepick is right in one direction though. I oversimplified the real situation and only the translation motion of far away Star-exoplanet was taken into consideration. In a previous newsletter two questions were formulated as follows: 

1. Why there is a change in perceived time of Io eclipses for an Earth observer, depending on the relative distance up to Jupiter but in case of multiple stars, pulsars and exoplanets there is no such dependency?

2. Are these far away periodic systems having a relative motion relative to Earth or are they stationary? If they move away or come toward Earth, than again their perceived periodicity seen by an Earth observer should have still another second factor of variability.

 I suppose he did not receive my previous newsletter(s) or the software of his server treated me as spam. I can’t do anything from aprox. 5% of people in distribution list who are not receiving the newsletters because their server refute to allow the email delivery based on some rigid spam protocols.

Coming back to the topic: starting with the first exoplanet discovered in 1995, astronomers should have been questioning any interpretation of the periods of the exoplanets when the component of periodicity, due to the Earth’s motion around the Sun, did not appear.

Let us consider the situation from fig. 4.1 and let us consider the Star-exoplanet system stationary relative to Sun.

Periodic motion observed from Earth

Figure 4.1 Variation of exoplanets period due to Earth motion around Sun

When Earth is in position E1, the observer would have a minimum value for the period of exoplanet. As far Earth moves on orbit, the measured period of exoplanet should steadily increase until a maxim is obtained when Earth is in position E2. The difference between E2 and E1 should be about 17 minutes, the time necessary for light to travel the diameter of Earth orbit.

 If the observer measures a constant period of exoplanet, irrespective on the position of Earth on its orbit, than we have two simple solutions:

  1. Earth is not rotating around Sun;
  2. Someone plays tricks with us and until the limit of the Earth’s orbit light travels with speed c, and after that it travels instantaneously;


Here is the conversation with Mr. A. Chepick

            Here is the conversation with Mr. R. Watson