Expanding Spacetime Theory

Do the planets accelerate?

C. Johan Masreliez

Recent findings based on optical observations in the solar system suggest that the planets might accelerate in their orbits. About thirty years ago the first indications of planetary drifts away from their predicted ephemerides appeared in the literature and more recently Kolesnik, 2000, reports that that planetary drifts determined from optical observations actually might be accelerations proportional to their motions. His results agree both qualitatively and quantitatively with the Expanding Spacetime (EST) theory's prediction if the Hubble time is about fourteen billion years.

Verification of planetary accelerations would of course be a dramatic development that would challenge traditional physics including Newton's laws of motion. However, modern astronomical measurements based on radar ranging between the planets and the Earth and laser ranging to the Moon have not revealed any such acceleration. These ranging measurements are far more accurate than optical observations in determining relative positions and are therefore believed to be more reliable. Since the discrepancy between optical observations and the ephemerides now has been confirmed beyond any reasonable doubt and since the agreement between the Post-Newtonian model and the ranging observations is excellent the noted anomaly is puzzling. In what follows I will argue that it might be caused by the use of different coordinate representations.

Modern ephemerides are constructed primarily from ranging measurements by reflecting a radar beam from the surface of the planet, which could give and accuracy in the order of hundreds of meters. Even better accuracy is obtained by using a transponder in a spacecraft orbiting a planet or landed on its surface. In addition lunar laser ranging (LLR) with accuracy in the order of centimeters is used in construction of the ephemerides. On the other hand, optical observations measure angular positions relative to the stellar background with and accuracy of about 0.5 arcseconds, which might be reduced to 0.1 arcseconds by averaging many observations from different observatories (Kolesnik, 2000, 2001). If this angular accuracy is translated into distance the quality of the ranging measurements far exceeds the optical measurements, which explains why modern ephemerides primarily rely on ranging data. However, the optical observations have the advantage of measuring the planetary positions directly relative to the stellar background, while the orientation of the ranging ephemerides relative to the International Celestial Reference System (ICRS) must be done separately.

With these accurate range measurements it has become possible to determine the ephemerides of all four inner planets and the Moon with great accuracy. Using many independent range measurements all parameters that specify the ephemerides may be estimated. This process also automatically defines a time-base for the ephemerides as being the temporal argument, which provides the best fit to the range measurements assuming a Post-Newtonian model for the planetary motions. In this way modern ephemerides of the inner planets and the Moon primarily rely on range measurements and the Post-Newtonian assumption. The time when a particular measurement is made is of secondary importance and may in principle be determined by inverse interpolation after construction of the ephemerides. As mentioned above it is widely recognized that this approach of constructing ephemerides has one major disadvantage compared to optical observations - the orientation of the system of ephemerides relative to ICRS is poorly determined. However, recently it has become possible to tie the ephemerides very accurately to distant radio sources fixed in the cosmological reference frame using VLBI observations.

Another possible disadvantage of the approach is its reliance on the assumption that the planetary orbits are Post-Newtonian. However, since no systematic discrepancies from the Post-Newtonian model have been detected, the ranging observations appear to confirm that the Post-Newtonian assumption is correct. This should mean that the orientation of the dynamic reference system does not change with time. However, in spite of the very accurate ephemerides with errors in the order of one kilometer the predicted planetary positions drift relative to the ICRS and the ephemerides must be updated periodically. It is generally believed that this drift is caused by unmodeled asteroidal influences.

On the other hand, optical observations directly measure the positions of the planets relative to the stellar background and therefore automatically orient the ephemerides. As with the modern ephemerides based on ranging observations the earlier ephemerides based on optical observations were derived so that Newton’s law is satisfied for the planetary motions. In the past this determined a time-base called “ephemeris time” as being the temporal argument for which the planets move in accordance with Newton’s law. It is generally believed that this ephemeris time for the older “optical ephemerides” and the time-base for the modern “ranging ephemerides” are the same and that both these time-bases are proportional to atomic time.

I will challenge this belief by showing that these three time-bases might differ from each other, which might explain the noted discrepancy between the modern ephemerides and optical observations.

In the past all modeling of the planetary motions assume that the underlying spacetime is basically Minkowskian modified by local curvature due to gravitational fields generated by the Sun, planets, moons and the asteroids. However, from the cosmological redshift we know that the universe at large appears to expand. Still we take for granted that spacetime locally is Minkowskian, but this might not be true; there might be some small up till now undetected spacetime curvature of cosmological origin even locally in the solar system.

According to Einstein’s general relativity one can always find a local Minkowskian coordinate system if spacetime is curved. If the cosmological curvature were small and if Newton’s (and Einstein’s) law of gravitation were to hold in this local Minkowskian system, it would be possible to construct Post-Newtonian ephemerides using these locally Minkowskian coordinates. In this coordinate system it might be impossible to detect any deviation from the Post-Newtonian ephemerides. Furthermore, if one relies on ranging measurements and if these measurements are fitted to Post-Newtonian orbits, these “Minkowskian coordinates” would be selected automatically since they are the coordinates that provide the best fit. Thus, the process of constructing ephemerides might implicitly define a Minkowskian coordinate representation that might differ from the cosmological line element.

If spacetime is cosmologically curved the local Minkowskian coordinates might deviate from the “global” cosmological coordinates. For example, it is possible that the local Minkowskian (dynamic) coordinate system might rotate relative to the ICRS causing drift of the ephemerides relative to the cosmological reference frame. Also, the temporal argument for the planetary ephemerides, which is the same as the temporal coordinate of the Minkowskian system, might differ from the temporal coordinate of the cosmological line element. If this were true one might wonder which time-base is the “right” one. Since spectral lines seem to be the same even at huge cosmological distances, we might make the assumption that atomic time represents a true cosmological time-base and look for any discrepancy between atomic time and the ephemerides time-base.

Although this scenario might appear farfetched it should not be dismissed without further investigation since it could explain the mysterious but irrefutable disagreement between optical observations and the planetary ephemerides.

All planets move in the same direction around the Sun; therefore, if there is planetary acceleration only accelerations relative to the Earth might be detected by ranging. The planetary accelerations suggested by Kolesnik, would cause drifts relative to the Earth summarized in Table I.

Table 1

In the process of fitting the ephemerides to the ranging data these relative drifts would be reduced significantly. The resulting deviations are of the same order as the observed drifts, which make it necessary to update the ephemerides repeatedly.

It was mentioned above that the time-base for the ephemerides are implicitly determined in the process of ephemeris construction. However, Oesterwinter and Cohen (Oesterwinter and Cohen, 1972) use atomic time as the time-base of the ephemerides for both the planets and the Moon based on optical observations 1955-1968. Extrapolating these ephemerides backward in time to 1912 they discover that atomic time deviates from traditional ephemeris time and they estimate the deviation to be about seven seconds in fifty years in good agreement with recent results by Kolesnik (Kolesnik, 2000, 2001). At least two other independent investigations estimate the relative accelerations between the planets based on radar ranging data and atomic time (Reasenberg and Shapiro, 1968 and Krasinsky et al. 1986). Both these studies also detect positive acceleration of the planets.

If the planetary accelerations were real it might seems that they should have been discovered a long time ago. At least, they should have been detected when fitting the modern ephemerides to the very precise ranging measurements. However, if the EST theory is correct there is a coordinate representation in which the ephemerides are perfectly post-Newtonian even if the planets were accelerating relative to the ICRS. With this coordinate system the temporal and radial coordinates differ from those of a reference system based on atomic time. Therefore, the discrepancy between optical and ranging measurements methods might be explained by the use of different coordinate representations. The source of the discrepancy would then lie in the presumed post-Newtonian model rather than in any procedural, computational or observational shortcoming.

The question of possible planetary acceleration is of course very controversial since it would invalidate one of the most fundamental laws of nature, Newton's first law of motion, by which freely moving objects in vacuum will continue to move at the same velocity forever. This law has been one of the cornerstones in the foundation of physics since the time of Galileo. If the deviations from this law are very small they will not be detected. The main reason that the planetary accelerations have not been detected in the past is that no independent time reference was available. Only with the introduction of atomic time did it become possible to detect them. However, detection requires that the time base used to fit the ephemerides is independent and not estimated based on the observations. It is unfortunate that the traditional procedure of estimating the ephemerides so efficiently hides the accelerations. They would probably have been detected earlier if atomic time had been used directly in the ephemerides construction process, keeping the time base constant. It is not yet widely recognized that the procedure of estimating the time base when fitting the ephemerides automatically prevents the detection of acceleration.

However, optical observations do not suffer from this problem. They record the locations of the planets relative to background stars with atomic time as the timekeeper. This measures the motion of the planets directly. Discrepancies with the Newtonian ephemerides may be detected by averaging a large number of observations from several observatories. Nowadays, the motions of the background stars are well known in relation to very distant extragalactic sources, which are stationary. The observed planetary accelerations relative to background stars are well above the observational errors and can no longer be ignored.

One of the reasons people resist the idea that the planets might accelerate is that in the past there has been no physical explanation for such acceleration. The EST theory, which predicts it, is not yet well known and is still quite controversial. However, if you take a look at the whole picture you will see that cosmic drag of the EST theory not only explains the planetary accelerations but also the spiral shape of galaxies and their flat velocity curves as well as the spin-down of pulsars. It also explains the Pioneer anomaly and resolves several cosmological puzzles. A revised model for the planetary motions based on the EST theory that takes into account the planetary accelerations will modify the estimated lunar acceleration as well as the estimated spin-down of the Earth. With this new model the enigmatic angular momentum discrepancy between the lunar motion and the spin-down of the Earth disappears. This also changes the estimated drift of the Moon away from the Earth so that the Moon very well could have been formed together with the Earth some five billion years ago.

There is an interesting parallel between the situation today and when Copernicus proposed his heliocentric model. At the time Copernicus proposed that the Earth moves around the Sun, many raised objections since they by definition thought of the Earth as being fixed and at the center of the universe. Today we have a similar situation in that people believe that the pace of (atomic) time is and always has been constant. However, if the pace of time changes with the cosmological expansion, as proposed by the EST theory, the planets will accelerate.


Kolesnik Y. B., 2000, Applied Historical Astronomy, 24th meeting of the IAU, Joint Discussion 6, Manchester, England.

Kolesnik Y. B., 2001a, Journées 2000 “Systèmes de référence spatio-temporels”, J2000, “a fundamental epoch for origins of reference systems and astronomical models”, Paris.

Krasinsky G. A., Pitjeva E.V., Sveshnikov M.L., Chunayeva L.I.,1993, Cel. Mec. Dyn. Astron. 55, 1

Oesterwinter C.and Cohen C.J.: 1972, Cel. Mech. 5,317

Reasenberg R.D, Shapiro I.I.: 1978, “On the measurement of Cosmological Variations of the Gravitational Constant”, ed. L. Halpern (Gainesville:University Press of Florida), p.71.

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