TRANSITS OF VENUS vs. NASA's ASTRONOMICAL DATA

The following analysis of the Venus transits will show that the Earth must go around the Sun 360 degrees in a tropical year, contrary to current lunisolar precession theory.

If we take a look at the transit dates of Venus in the table below, it becomes immediately apparent that in the various years they all occur during the month of June, and that the days of a transit shift back and forth by about 2 days. What is the reason for such a difference in time?

Astronomers say that both Earth's precession and the movement of the nodes of Venus effect the timing of the transits of Venus. As we know, a transit can only occur when Earth and Venus are not only in direct conjunction with the Sun, but Venus also crosses at the same time the Earth-Sun plane. The moment when Venus and Earth are in direct conjunction with the Sun depends on the so-called synodic period. Therefore, if the synodic period matches with the 360° orbit period of Venus (same node to same node) while Venus is crossing the Earth-Sun plane, a transit can be seen from Earth as long as the periods match within a certain degree.

It is also important to remember that this celestial mechanical phenomenon is completely independent of the orientation of the Earth's axis in space, and that the Earth can only have one true 360° orbit period around the Sun. This period does either consist of 365.242198 days or 365.256361 days. The same principle applies to Venus, either its smaller 360° orbit period consists of 224.695 days or its larger orbit consists of 224.701 days. The term "day" refers to a mean solar day of 86400 seconds.

A mathematical analysis of the data will show that an accurate prediction of transits not only depends upon the correct synodic cycle, but also on the actual 360-degree orbital period of both Venus and the Earth around the Sun.

Assuming the accuracy of the transit data below, we shall consider the recorded and observed transit of June 6, 1761 as the "first" transit, or starting point for all calculation purposes. Furthermore, we will assume for now that the node line of Venus remains stationary; i.e. it does not move by roughly 20" per tropical year.

Transits of Venus [Greatest Transit Contact Time (UT)] *

June 6, 1761 at 05:19 to June 3, 1769 at 22:25 = 2919.7 days

June 8, 2004 at 08:20 to June 6, 2012 at 01:29 = 2919.7 days

June 6, 1761 at 05:19 to June 8, 2004 at 08:20 = 88756.1 days

June 6, 1761 at 05:19 to June 6, 2012 at 01:29 = 91675.8 days

*(Source: GSFC-NASA, F. Espenak, "Transits of Venus Catalog", updated Feb.11, 2004)

http://sunearth.gsfc.nasa.gov/eclipse/transit/catalog/VenusCatalog.html

http://nssdc.gsfc.nasa.gov/planetary/factsheet/venusfact.html

Editor's Note: In March 2003, Mr. Espenak's calculations of the transit times of Venus have shown that the 2012 transit should occur on June 5, basically around the same contact times (given in UT). In September 2003, the author of this article informed Mr. Espenak that he had posted a comment on Mr. Espenak's "Transit of Venus - Six Millennium Catalog". It appears that by February 2004 Mr. Espenak did make some corrections to his catalog and changed, for instance, the day of June 5 to June 6. According to his calculations the "First Contact" of the transit in 1769 occurred of June 3, while the "Third Contact" occurred on June 4. It remains unclear whether or not Mr. Espenak considers the date of June 6, 2012 as the day of the "First Contact", or still the date of June 5, 2012. There appears to be an inconsistency in his transit calculations.

Please, see also: Correspondence with Dr. Fred Espenak regarding his "Transits of Venus Catalog"

TROPICAL YEAR SCENARIO

If the synodic cycle is based on the shorter 360° tropical orbit periods of Venus (224.695 days) and Earth (365.2421988 days), then every 583.9184 days Earth and Venus are in conjunction.

1/224.695 minus 1/365.242198 = 0.001712568 (reciprocal of 583.9184)

5 synodic periods = 2919.592 days

152 synodic periods = 88755.597 days

157 synodic periods = 91675.189 days

13 Venus orbits = 2921.035 days

395 Venus orbits = 88754.525 days

408 Venus orbits = 91675.560 days

From these figure it can be concluded that the most accurate match between the synodic and the node cycle occurs every 251 tropical years. It seems like a remarkable coincidence that the Venus nodes are in such a close resonance with Earth's equinoctial year. In other words, the orbital relationship between Venus and Earth of 408 to 251 reflects are better resonance than the 395 to 243, or the common 13 to 8 relationship. However, it will become clear that this resonance does not apply to a longer sidereal period; i.e. a wider or larger 360° orbit.

SIDEREAL YEAR SCENARIO

If the synodic cycle is based on the longer 360° sidereal orbit periods of Venus (224.701 days) and Earth (365.256361 days), then every 583.9227 days Earth and Venus are in conjunction.

1/224.701 minus 1/365.256361 = 0.001712555 (reciprocal of 583.9227)

5 synodic periods = 2919.614 days

152 synodic periods = 88756.254 days

157 synodic periods = 91675.868 days

13 Venus orbits = 2921.113 days

395 Venus orbits = 88756.895 days

408 Venus orbits = 91678.008 days

As the sidereal data shows, after 408 Venus orbits and 157 synodic periods a time difference of 2.14 days occurs (91678.008 minus 91675.868). Evidently, these periods do not match. In order to observe the actual transit of Venus (e.g. on June 6, 2012), it appears that somehow a correction has to be made.

Astronomers assert that this time difference is due to the combined effect of Earth's precession and the slow backward movement of the nodes of Venus.

According to the theory of lunisolar precession, Earth is supposed to "slip back" in its 360° orbit around the Sun, thus arriving each year about 20 minutes (or 22000 miles) earlier with respect to a fixed orbital position and also in relation to the 360° sidereal orbit of Venus. Hence, only a correction of about 2 days for precession and node movement would make a transit on the predicted date possible after a period of 157 synodic cycles.

If this is true, then why does it not already require a similar correction of about 2 days after a period of 395 Venus orbits and 152 synodic cycles?

According to the sidereal orbit periods of Venus and Earth, which astronomers assume to be 360 degrees, 395 Venus orbits and 152 synodic cycles represent a very close resonance [88756.895 minus 88756.254 = 0.641 (days)]. Yet a correction for precession and node movement would imply that the actual transit could not be observed on the predicted date.

The crux of the matter is that there can only be one synodic period that reflects the actual 360° orbits of the planets Venus and Earth around the Sun. Although we have seen that in both scenarios (tropical vs. sidereal) the resonance of the synodic cycle and the position of the nodes still produces a match after the 243-year period, the 251-year period seems to create a problem with the "sidereal year".

Remember that we used for the calculations the date of June 6, 1761 as the first transit or starting point. Let us assume that the nodes of Venus move forward relative to the equinox at the rate of about 20" per tropical year. Hence, after 8 synodic periods the nodes have advanced by about 0.07 days, 1.37 days after 152 periods and after 157 periods 1.42 days. This shifting of the nodes would make the prediction of the June 8, 2004 transit fairly accurate, but not the one of June 6, 2012.

The situation for the sidereal year is reversed. Since the nodes would have to shift backward by about 30" per sidereal year, the nodes regress by about 0.11 days after 8 synodic periods, 2.06 days after 152 periods and after 157 periods 2.13 days. This would make the prediction of the June 6, 2012 quite accurate, but not the one of June 8, 2004. Obviously, we can't have it both ways. The transit cycle of Venus does not stop after 243 years only to begin anew. It would be an illusion to think that the 8-year, the 243-year and the 251-year period are separate cycles in the linear progression of time.

Here it is interesting to note how the time discrepancy between the synodic period and the node line increases if the node line of Venus were to remain fixed with respect to the equinox. For instance, after a period of about 20,000 years or 360° revolutions of the Earth around the Sun (or 12510 synodic periods and 32510 Venus orbits) the difference is 15 days based on Earth's 360° tropical year and 156 days based on Earth's 360° sidereal year. In fact, a fixed node line would imply that Venus has a 360° orbit period of 224.69557 days. However, by taking a year of 365.256361 days as Earth's 360-degree orbit period, the synodic cycle would be reduced to 583.887 days.

So in order to observe the 2004 and the 2012 transit on the predicted date and times, we cannot use sidereal time for 2004 and revert back to tropical time about 8 years later, or vice versa. It seems the only way to make the various cycles fit with each other, would be to consider an orbit period of 224.6974 days for Venus to move from same node to same node. This figure is based upon the following calculation:

224.695 + [(224.701 - 224.695) × (20" ÷ 50")]

395 Venus orbits = 88755.473 days

408 Venus orbits = 91676.539 days

If we compare these figures to the previously calculated synodic periods (152 vs. 157) based on the 360° tropical year and the 360° sidereal year, the time difference after 395 and 408 orbits of Venus is:

Tropical: plus 0.124 days and minus 1.35 days respectively ( 88755.597 vs. 91675.189 )

Sidereal: plus 0.781 days and minus 0.671 days respectively ( 88756.254 vs. 91675.868 )

The accumulted time difference in calendar days, according to NASA's Venus Transit Catalog starting from June 6, 1761 is:

June 6, 1761 to June 8, 2004: ......88756.1 days

June 6, 1761 to June 6, 2012: ......91675.8 days

Although these predicted times appear to be a fairly close match with the above synodic periods, there is a noticeable difference in the transit times based on the tropical period. This difference appears to be averaged out with the sidereal periods. Evidently, the calculations of the transit cycle of Venus in relation to the various orbital periods show a pattern of deviation. It seems only precise observations of the actual transits of Venus are going to tell us whether or not there will be a difference.

BUT WAIT....

We forgot to examine the transit period of 2919.7 days from June 6, 1761 to June 3, 1769. If we look at the synodic period it appears to be almost the same, whether in tropical time or sidereal time. But obviously, there is a time difference of more than 1.4 days (2919.6 days synodic vs. 2921 days node cycle). In other words, it should not have been possible to observe a transit in 1769. Yet historical observations prove otherwise.

So what is the problem? Remember that we used June 6, 1761 as the starting point, or point "0". However, when the transit occurred in 1761, Venus did not EXACTLY go through the node as the Earth and Venus were in direct conjunction with the Sun. The descending node occurred a little earlier, but still in resonance for a transit to be visible.

Let's say the difference is about 0.7 days. This fact made the observation of the transit of June 3, 1769 possible, because the same difference has to be added to the 2919.6 days of the 13 synodic periods. That means without changing the actual synodic period, the entire synodic cycle (tropical or sidereal) will be shifted forward by roughly 0.7 days, like a vernier, or sliding gauge, in time.

How does that affect the observable transits of Venus, 243 & 251 Earth orbits later?

Please, view this diagram for a better understanding of the following calculations.

Let us compare again the 224.6974-day node cycle of Venus, as well as the predicted calendar dates, with both the tropical and the sidereal synodic period by adding about 0.7 days:

Orbital Periods...........................................Days........................... Difference Synodic vs. Node

395 Venus orbits: .....................................88755.473

152 syn. (tropical) 88755.597 plus 0.7: ......88756.297 .....................................+ 0.824 days

152 syn. (sidereal) 88756.254 plus 0.7: ......88756.954.......................................+1.481 days

calendar time: .........................................88756.1

_____________________________________________________________________________

408 Venus orbits: .....................................91676.539

157 syn. (tropical) 91675.189 plus 0.7: ......91675.889 .......................................- 0.65 days

157 syn. (sidereal) 91675.868 plus 0.7: ......91676.568 ......................................+0.029 days

calendar time: .........................................91675.8

By looking at the diagram, it becomes clear that the same result can be achieved by moving the sine-function of the node cycle backward (i.e. to the left) by about 0.7 days.

CONCLUSION:

The data and the calculations clearly show that the observable transits of Venus on June 8, 2004 and on June 6, 2012 can only occur according to tropical time; i.e. based on Earth's 360° tropical year of 365.2421988 mean solar days (31,556,925.97474 s) and Venus' 360° orbit of 224.695 days.

If Earth's 360°-orbit period around the Sun were to consist of 365.256361 mean solar days (31,558,149.5 s) and the 360°-orbit period of Venus has 224.701 days, it would not be possible for a transit of Venus to be visible from Earth on or around the 8th of June 2004. There is a timing difference of about 1.4 days between the node of Venus and the synodic cycle based on Earth's and Venus' sidereal orbit periods.

These calculations could have a tremendous scientific implication. In order to accept the accuracy of NASA's data on the transits of Venus in relation to the actual 360° orbit period of Earth and Venus around the Sun, it can only be concluded that the phenomenon of "lunisolar precession" (wobbling of the Earth's axis) does NOT exist in reality.

Not only does the backward movement of Venus' node line through the constellations of the zodiac require a valid scientific explanation, but also the observed annual progression of the stars with respect to the position of the equinox. Unless astronomers want to suggest that Venus has an undiscovered moon that causes problems just like our Moon, the astronomical data and practical observations do not seem to allow for any other conclusion to be drawn.

Uwe Homann

April 21, 2004