THE DECEMBER 1874 TRANSIT OF VENUS

Transits from Summer to Winter & Winter to Summer

The following abstract is an attempt to explain the physical and mathematical relationship that exists between the time interval of the tropical year and the orbits of Venus and Earth, and which made the observation of the 1874 Venus Transit possible.

It was argued that neither the intervals between transits listed in the catalog nor the mean values of the synodic periods, which vary due to the elliptical orbits of Venus and Earth primarily, can be employed for rigorous calculations.

A further analysis of past but most recent transit dates does reveal, however, that the intervals between the transits of June 1761 & 1769 to December 1874 & 1882 reflect mean tropical synodic time, while mean sidereal synodic time seems to be employed after the 1882 transit.

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

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

Dec. 9, 1874 at 04:07 to Dec. 6, 1882 at 17:06 = 2919.6 days

June 6, 1761 at 05:19 to Dec. 9, 1874 at 04:07 = 41457.9 days

June 6, 1761 at 05:19 to Dec. 6, 1882 at 17:06 = 44377.5 days

Dec. 6, 1882 at 17:06 to June 8, 2004 at 08:20 = 44378.6 days

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

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

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

As the data shows, there were 44377.5 days between the 1761 transit and the 1882 transit, but between the 1882 transit and the 2004 transit there will be 44378.6 days. It should be noted that 121.5 tropical years consist of 44376.93 days, whereas 121.5 so-called sidereal years would consist of 44378.65 days. Also, 197.5 Venus tropical orbits of 224.695 days each consist of 44377.26 days, whereas 197.5 Venus sidereal orbits of 224.701 days each consist of 44378.45 days.

SYNODIC TIME vs. NODE MOVEMENT

Mean synodic period of 583.9184 days (based on 360° tropical orbits of Earth and Venus) & mean synodic period of 583.9227 days (based on 360°sidereal orbits):

5 synodic periods = 2919.59 days.................. 2919.61 days

71 synodic periods = 41458.2 days.................. 41458.5 days

76 synodic periods = 44377.79 days................ 44378.1 days

152 synodic periods = 88755.59 days................ 88756.25 days

Venus orbital periods (node to node):

NOTE: Since it still remains unclear whether the rate of the node movement is about 20" per tropical year (red) or more than 30" (blue), both periods are listed for comparison.

13 Venus orbits = 2921.06 days.................. 2921.08 days

184.5 Venus orbits = 41456.67 days................ 41456.97 days

197.5 Venus orbits = 44377.74 days................ 44378.05 days

395 Venus orbits = 88755.47 days................ 88756.1 days

The one fact that becomes immediately apparent is that the time difference between 71 synodic periods and 184.5 Venus orbits is approximately 1.5 days, regardless of the rate of orbital node movement. According to the catalog, the time interval between the transits of 1761 and 1874 is 41457.9 calendar days, which closely matches the mean synodic cycle of the 360° tropical orbit period of both Venus and Earth.

The question is how was it possible to observe the transit of December 9th 1874?

The first thing that would come to mind is that our Earth moves in an elliptical orbit around the Sun, implying that Earth speeds up as it approaches perihelion in December, while slowing down again towards June. Yet this would not affect transits occurring from June to June or transits from December to December. Winter- and Summer transits do not happen in the same year; they are more than a hundred years apart. And in the linear progression of time, these transits cannot be regarded as separate cycles or series (descending node transit series vs. ascending node transit series). So how would an elliptical orbit of Earth affect the long-cycle relationship between those transits, if Earth speeds up towards winter and slows down towards summer?

As a matter of fact, it takes Earth about 183.5 days to travel from Summer Solstice to Winter Solstice, while it takes only 181.75 days to travel from Winter Solstice to Summer Solstice. According to the work of science author Peter Bros, the Earth does not speed up or slow down in its elliptical orbit around the Sun. He argues that the actual distance the Earth has to travel around the Sun is shorter from Winter to Summer than from Summer to Winter, due to the motion of the Sun itself.

Could this answer our concern regarding the actual position of the orbital node of Venus on December 9, 1874 with respect to the position of the Earth?

Based on historical information, the transit was observed on December 8th at certain locations on Earth. It is important to realize that transit dates are given for a hypothetical observer, located at the "center of the Earth". But if an observer on the surface of the Earth changes position with respect to the Greenwich Meridian, the window of observation increases to ± 12 hours. Hence, a different location or positioning in "time" could make the observation possible.

Perhaps an analogy might help:

Imagine a passenger train moving at a constant speed on a looped track, where the distance from points D to J is a little shorter than from J to D. On a smaller, more circular but tunneled track, moves a locomotive at a different but also constant speed around the same center as the passenger train does. There are only two openings in the tunnel, exactly 180-degrees apart and in alignment with points J & D. Every so often an observer in the train has the chance to see more or less directly the locomotive going through one of these openings. Sometimes it can happen that the observer just barely misses the locomotive. It seems the observer's only chance to catch a glimpse of the locomotive would be to change in advance his location by either moving to the front or rear of the train.

But remember we said that our train moves at a constant speed and that it must travel a greater distance from J to D. Compared to another train running alongside at the same speed on a circular track that has the same circumference from D to D (or J to J) as our passenger train's track, our train would require extra travel time from J to D. Of course, it would make up that difference on the stretch from D to J, thus arriving always at the same time as the other train on its circular track. That means, while an observer in the train on the circular track could miss to see the locomotive going through the opening in the tunnel at point D, our observer on the passenger train has the possibility to see it due to his "late" arrival. The same principle would apply to the other stretch of the track from D to J; i.e. our observer might arrive "early" at point J, not seeing the locomotive. If our passenger train wants to keep running parallel to the other train on its circular track, it has to speed up on the longer stretch of its track and slow down on the shorter stretch. But if the train on the circular track misses the locomotive, so will our passenger train. Obviously, a "speeding-up" from J to D or "slowing-down" from D to J will NOT accomplish the same result as going the "extra distance" at a constant speed.

NOTE: In the diagrams, the orbital patterns are not drawn to scale and the proportions of the angles, circles and the ellipses are exaggerated for clarification only.

In the case of Venus, the observer on Earth needs to know the EXACT orbital times and orbital distances (or apparent changes in orbital speed) of both planets, in order to make an accurate calculation or prediction based on the calendar, as to when and where the next transits of Venus will be visible.

Uwe Homann

May 10, 2004

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In Memory of Pathani Samanta of Orissa (1835-1904), the remarkable and self-educated Siddhantic Astronomer who predicted and observed the 1874 transit of Venus without the aid of clocks and telescope.

http://rathnasree.htmlplanet.com/Pathani.htm

http://orissagov.nic.in/eminent/astrologer.htm

The Royal Astronomical Society Library has recently published a rare image of the 1874 transit that was taken by French solar astrophysicist Jules Janssen.

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DISCUSSION:

Considering the findings of Peter Bros and other researchers regarding the Sun's motion in space, we must ask ourselves whether or not a shift in perihelion, lunisolar precession and a roughly twenty minutes longer 360° orbital period of the Earth around the Sun can accurately explain the observations of Venus transits.

Evidently, Earth's orbital path around the Sun is longer from the position of Venus' descending node in June to its ascending node in December than from the December node to the June node.

The notion that our Earth speeds-up in its orbit towards December and slows down towards June does not explain the recorded observation of the transit of Venus on December 9, 1874. A greater orbital distance for the Earth (from descending node to ascending node) requires more rotations or days, whereas an increase in Earth's orbital speed over the same distance implies less time and therefore, fewer days. But the counting of days in our calendar does not run faster in Winter or slower in Summer.

So according to Kepler's laws and based on our reckoning of time, the moment when Venus and Earth came in direct conjunction with the Sun in December of 1874, Venus should have already crossed the ecliptic in front of the Sun's disk almost two days earlier.

NOTE: The tropical year is shown as a 360-degree orbit period, contrary to the theory of lunisolar precession. Tropical synodic time is not the same as correcting 'sidereal' synodic time for 'precession'; i.e. the wobbling of Earth's equator relative to the Sun. This fact is proven by the celestial mechanical phenomenon of solar eclipses.

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© 2004 Uwe Homann, Sirius Research Group

updated May 27, 2004