CORRESPONDENCE WITH DR. FRED ESPENAK

REGARDING HIS "TRANSITS OF VENUS CATALOG"

April 27, 2004 via email

Dr. Fred Espenak

Planetary Systems Branch - Code 693

NASA/Goddard Space Flight Center

Greenbelt, Maryland 20771 - USA

Re: "Transits of Venus - Six Millennium Catalog 2000 BCE to 4000 CE"

Dear Sir:

I am working on a research project that examines the relationship between a number of properties of Earth's rotation and orbital periods. The work involves among other things a mathematical analysis of the predicted transit dates of Venus. As a reference for my calculations, I have used the astronomical information and data published on your website at:

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

While studying the material, I have noticed some inconsistencies in the data. Therefore, with all due respect, I would appreciate if you can please clarify a few points for me:

1. In March 2003 your calculations of the transit dates of Venus have shown that, for example, the 2012 transit would occur on June 5th ("First Contact" at 22:10 UT). In your revised version of February 11, 2004 that data has been corrected to June 6th ("First Contact" at 22:09 UT).

I note that the "First Contact" of the transit in 1769 occurred on June 3rd, while the "Third Contact" occurred on June 4th. Although you did not specify, it appears that before February 11, 2004 you gave the calendar date for the instant of the "First Contact"; i.e. when transit begins. At least this seems to be the common practice. However, in your Footnotes you have added now that, "the calendar date is given for the instant of greatest transit".

Question: Is there a reason for all of the subsequent corrections you have made to your tables? Or is the definition of a transit date arbitrary; i.e. subject to changes?

2. According to your transit predictions, the time difference between the transits of June 6, 1761 to June 3, 1769 and of June 8, 2004 to June 6, 2012 is 2919.7 days for each 8-year period. Based on the information you have provided on the orbit periods of Earth and Venus, the time difference between 5 synodic cycles and 13 Venus orbits would be about 1.5 days. Since 5 synodic cycles consist of 2919.6135 days, there appears to be a time discrepancy of 0.0865 days for each of the 8-year periods.

However, your transit data shows that the combined discrepancy of 0.173 days directly affects the predicted calendar time between the transits of June 3, 1769 to June 8, 2004. There is a difference of 0.2369 days between the calendar time and the 147 synodic cycles that occur from 1769 to 2004. The difference between 0.2369 days and 0.173 days is 0.0639 days. This result re-appears after the transit of June 6, 2012 as the time difference between 157 synodic cycles and the calendar time between the transit dates of June 6, 1761 and June 6, 2012.

Question: Do these "expansions & compressions" in calendar time represent a correction or compensation to the synodic cycle in the linear progression of time and/or to the orbital period of Venus to move from same node to same node?

3. Evidently, the exact synodic period of Venus and Earth is based on the 360-degree orbit periods of Venus and Earth around the Sun while the calendar is based on the tropical year. In order to accurately calculate and predict the actual transit dates according to the calendar (365.2425 days), it is essential to know whether the orbital nodes of Venus shift forward through the seasons at a rate of about 20" or more than 30" per tropical year. For instance, a yearly 10" difference in node movement would cause a time discrepancy of 0.7 days after a period of about 250 years. Again, this would affect the prediction of the transit dates and/or the path of Venus in front of the Sun's disk.

In the introduction of your catalog you assert that, "The position of the orbital nodes of Venus with respect to Earth are slowly changing with time. [...] At present, the transits occur within a day of June 7 and December 9. In about 1500 years, the transits will occur during Earth's solstices (June 21 and December 22). This trend in the shift of transit dates is readily apparent in the catalog below. Over a period of approximately eighty thousand years, the transit dates will migrate forward one complete cycle through the seasons."

According to the catalog, the rate of the forward movement of the orbital nodes of Venus is more than 33" per tropical year. This would imply that the transit dates migrate forward one complete cycle through the seasons in less than 40000 years.

Question: How do you reconcile this figure with the approximately 80000 years, which would imply a forward movement of the orbital nodes of less than 20" per year?

4. Based on the theory of lunisolar precession, the Earth comes up 22,000 miles or roughly 20 minutes short of completing a 360-degree motion around the Sun each tropical year; i.e. about 50" short of its same position on the ecliptic (orbit path) the prior year. This would translate into roughly 3.4 days after 243 years, implying either a smaller 360° tropical orbit period or an orbit of less than 360°.

Since the occurrence of transits is a celestial mechanical phenomenon that is not affected by Earth's precession, it appears that precession (i.e. the apparent progression of the sphere of the fixed stars) is added to the observable, only to be removed again in order to make the calculation fit with the observation.

Question: How can the transits of Venus occur accurately as predicted, if calculations are based on a 360° sidereal orbit period of Earth and Venus, while lunisolar precession causes Earth to "slip back" in its orbit relative to the Sun and Venus?

Thank you very much for your time. I appreciate your assistance in this matter and look forward to your reply.

Sincerely,

Uwe Homann

cc Dr. Drake Deming

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April 27, 2004 via email

Dear Mr. Homann -

The calendar dates listed in the Venus transit catalogs posted at

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

are for the instant of maximum transit. There is no agreed definition on how to date a transit. However, the above convention is consistent with the dating of solar eclipses in predictions appearing on the NASA Eclipse Home Page (http://sunearth.gsfc.nasa.gov/eclipse/eclipse.html).

The catalog narrative describing the basic orbital mechanics of transits is intended as a simple aid in understanding the periodicity and recurrence of transits. As such, it is not suitable as a basis for accurate calculations or predictions. The synodic periods given are only mean values which vary due to the elliptical orbits of Earth and Venus, thus they can not be employed for rigorous calculations.

The transits in the catalog were actually predicted using a detailed planetary theory VSOP87, constructed by Bretagnon and Francou at the Bureau des Longitudes of Paris. The orbital elements for the transits come from the work of Jean Meeus ("Transits", Willmann-Bell, 1989). I refer you to Meeus' book for a thorough description of the transit predictions.

For a detailed discussion on secular changes to the orbits of Venus and Earth, I refer you to "More Mathematical Morsels" by Jean Meeus (Willmann-Bell, 2002). I think that this is much more pertinent to your research than using the intervals between transits listed in the catalog.

Sincerely,

Fred Espenak

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Name: Fred Espenak Planetary Systems Branch, Code 693

e-mail: Fred.Espenak@gsfc.nasa.gov NASA/Goddard Space Flight Center

Voice: 301-286-5333 Greenbelt, MD 20771

FAX: 301-286-0212 USA

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April 28, 2004

Dear Mr. Espenak,

Thank you for your prompt reply and for the additional book references. I appreciate the clarification regarding the dating of transits, albeit I had hoped for an explanation on how precession affects transit predictions and to find some substantial data on the orbital node movement of Venus. I understand the "short-comings" of the catalog in terms of accuracy, but assume that for all practical purposes the predicted transit dates are accurate within a few minutes of the contact times given in UT. No doubt, many amateur astronomers worldwide rely on this data.

The up-coming transits of Venus are not only an exceptional cosmic event, but they offer us an exciting opportunity to learn more about the dynamics of our solar system. I think we are very lucky to be able to witness this phase of a "new" Venus.

Once again, thank you for your time and for your help.

Best regards,

Uwe