VENUS TRANSITS & PRECESSION

ABSTRACT:

A preliminary analysis of the Venus Transit Data has shown that the Earth must go around the Sun 360 degrees in a tropical year, contrary to current lunisolar precession theory. The fact remains and the evidence suggests that the observed transit cycles reflect a more accurate correlation between the periods of 251 tropical years and 408 orbits of Venus around the Sun, than 243 and 395 respectively.

This paper examines what appears to be a pattern of resonance between Venus transit cycles, the mean synodic period and the time interval of the 360-degree tropical year based on Earth's non-precessing axis of rotation relative to the position of the Sun.

As we know, Venus transits occur in a pair separated by 5 mean synodic cycles. Venus crosses the ecliptic almost symmetrically between the first and the second transit of each pair.

A complete 360-degree cycle occurs after 157 mean synodic periods, or exactly 251 tropical years and 408 orbits of Venus. The mean orbital period of Venus is calculated as follows,

365.24219878 mean solar days × 251 ÷ 408 = 224.695568367 mean solar days

Further calculations reveal that the mean synodic period consists of 583.922241369 mean solar days.

The relationship between these mean orbital periods is represented in the next diagram. The synodic cycle occurs retrograde (clockwise) in a series of five mean synodic periods. In a 360° circle each series constantly switches positions by 2.292994°.

5_________________357.707° _______________________________152______________2.292994°

71*_______________183.43949° _____________________________153____________217.834°

76*_______________181.146497° ____________________________154_____________73.376°

142_________________6.879° ______________________________ 155____________288.917°

147_________________4.586° ______________________________ 156____________144.459°

150________________291.210° _____________________________ 157____________ 360°

151________________146.752°

* There are also 2.292994° between 71 and 76 synodic cycles. In the diagram, the nodeline (as marked in the circle) is not situated between these two positions. This would imply a central transit at synodic position 76 and no transit at position 71. In practice, however, a transit pair does occur due to the elliptical orbit around the Sun in which the Earth has to travel a slightly longer distance from descending node (June) to ascending node (December) than from December to June. Hence, the node line is positioned between the 71 and 76 position. If one compares the transit pairs of December and June, the path of Venus in front of the Sun's disk is slightly "off-set" from the center of the Sun in December.

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The table below compares the time intervals of transit dates listed in the catalog with the calculated intervals based on the mean synodic period as noted above. It shows, for example, that in 2012 a time difference of 69.67 minutes occurs after exactly 157 mean synodic periods.

____________Transit Dates*________________Interval_________ Synodic Cycle___________ Interval__

June 6, 1761 at 05:19 to June 3, 1769 at 22:25 = 2919.7125 days ---------------- 5 ----------------- 2919.61120 days

Dec. 9, 1874 at 04:07 to Dec. 6, 1882 at 17:06 = 2919.54097 days --------------- 5 ----------------- 2919.61120 days

June 6, 1761 at 05:19 to Dec. 9, 1874 at 04:07 = 41457.95 days ----------------- 71 ---------------- 41458.47914 days

June 6, 1761 at 05:19 to Dec. 6, 1882 at 17:06 = 44377.49097 days ------------ 76 ---------------- 44378.09034 days

Dec. 6, 1882 at 17:06 to June 8, 2004 at 08:20 = 44378.63472 days ------------ 76 ---------------- 44378.09034 days

June 6, 1761 at 05:19 to June 8, 2004 at 08:20 = 88756.12569 days ----------- 152 ---------------- 88756.18069 days

June 6, 1761 at 05:19 to June 6, 2012 at 01:29 = 91675.84028 days ----------- 157 ---------------- 91675.79189 days

* (all times UT - "Greatest Contact", Source: Fred Espenak GSFC-NASA, "Transits of Venus Catalog")

As the dates show, transit pairs are separated by approximately 2919.6 days. Since there are 2921.93759 days in 8 tropical years a difference of about 2.33 days occurs.

In the following analysis the term 'day' refers to a mean solar day of 86400 seconds, and the term 'year' refers to a 360-degree orbit period of a non-precessing Earth around the Sun.

It was said that the mean synodic cycle consists of 583.922241369 days. This relationship is based on a tropical year of 365.24219878 days and a Venus orbit of 224.69556837 days. The same mean synodic period can also be derived from slightly larger 360° orbits; i.e. from sidereal year of 365.256361 days and a Venus orbit of 224.7009537 days.

If there are157 synodic periods in a tropical year, then 5 synodic periods are separated by 2.292994° (360° ÷ 157), which equal 2.326383 days in a tropical year (365.24219878 ÷ 360 × 2.292994). The difference between 8 tropical years and 5 synodic periods is also 2.326383 days.

If there are152 synodic periods in a sidereal year, then 5 synodic periods are separated by 2.368421° (360° ÷ 152), which equal 2.403002 days in a sidereal year (365.256361 ÷ 360 × 2.368421). However, the difference between 8 sidereal years and 5 synodic periods is 2.439681 days.

We must remember that both scenarios are based on a non-precessing Earth; i.e. the equator or the pole of the Earth does not wobble relative to the position of the Sun, and that there is no motion of the orbital plane or the nodeline of Venus.

Interesting is therefore, the following calculation of time differences*:

2.439681 minus 2.326383 = 0.1133 days_____equal to 9788.92 s in 8 years or 1223.6 s/year

2.439681 minus 2.403002 = 0.03668 days____equal to 3169.05 s in 8 years or 396.1 s/ year

2.403002 minus 2.326383 = 0.07662 days____equal to 6619.88 s in 8 years or 827.5 s/year

396.1 s + 827.5 s = 1223.6 s

Assuming 1223.6 s represent 50.25"/year, then 396.1 s and 827.5 s represent 16.27"/year and 33.98"/year respectively. However, an annual 50.25" 'precession of the equinox ' (i.e. the apparent movement of the sphere of the fixed stars) is NOT the same as a yearly orbital node movement of 16.27" combined with 33.98".

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* If there were 157 synodic periods in a sidereal year, then 5 synodic periods are separated by 2.292994° (360° ÷ 157), which equal 2.326474 days in a sidereal year (365.256361 ÷ 360 × 2.292994). And if there were 152 synodic periods in a tropical year, then 5 synodic periods are separated by 2.368421° (360° ÷ 152), which equal 2.4029092 days in a tropical year (365.24219878 ÷ 360 × 2.368421).

2.439681 minus 2.4029092 = 0.03677 days____________equal to 3177.2 s in 8 years or 397.1 s/year

2.4029092 minus 2.326474 = 0.07644 days____________equal to 6604.0 s in 8 years or 825.5 s/year

2.439681 minus 2.326474 = 0.113207 days____________equal to 9781.08 in 8 years or 1222.6 s/year

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CONCLUSION:

The calculations show that the equator or the pole of the Earth does not wobble relative to the position of the Sun. The Earth makes a complete 360-degree revolution around the Sun in a period of one tropical year, and over a period of exactly 251 tropical years 157 synodic cycles occur between Earth and Venus. A harmonic occurrence of transit pairs would imply no motion or deviation of the nodeline of Venus. However, owing to the Precession of the Equinox, on the one hand, and the movements of Venus and Earth on the other, the position of the Sun with respect to both planets is displaced in the same direction and to the same extent.

DISCUSSION:

It appears that similar mathematical results could be obtained by employing

a) an approximately 1223 s longer (larger) 360° Earth orbit period around a stationary Sun, consisting of 152 synodic cycles

b) a retrograde motion of the orbital nodes of Venus at a rate of approximately 16"/year relative to inertial space

c) a forward motion of the orbital nodes by approximately 33"/year relative to the equinox

d) lunisolar precession

While observations, measurements and calculations produce and provide facts to support concepts, concepts are not facts and may therefore, not describe reality.

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Hopefully, the following story will help the open-minded reader to better understand the true motions of our Earth.

Imagine two observers standing on a certain meridian, who have both witnessed the 1761 transit on June 6th around 5:00 UT. The one observer is located on a non-wobbling Earth that makes a 360° tropical year (365.2422 days) around the Sun, and the other observer is located on a non-wobbling Earth that makes a 360° sidereal year (365.2564 days) around the Sun.

Venus continues its orbits regardless of the Earth and whether or not our observers know anything about its orbital period or any node movement.

91675.8 mean solar days further in the progression of time, both observers look again towards the Sun from the same location (meridian) around the same time (OK, about 4 hours earlier than 5:00 UT). They will see another transit of Venus in front of the Sun's disk. The Earth, for both of our observers, is positioned directly in conjunction with Venus and the Sun (157 synodic periods).

Let's "freeze" the Earth's orbital position in space and time to properly analyze the situation:

In the year 2012, the tropical observer looks at the calendar to see that it's June 6th. The sidereal observer looks at his calendar only to see that it is not June 6th, because his Earth has not quite completed 251 orbits of 360° and is therefore, about three days away from his original June 6th orbital position.

Still somewhat confused, an astronomer comes along and says to the sidereal guy, "You forgot that the Earth wobbles relative to the Sun. Just calculate the amount of lunisolar wobble and you will see that your position also reflects June 6th. Since wobble does NOT affect the mean solar day, your location (meridian) and observation time of 1:00 UT will not change. Only your Earth's pole and equator have tilted a little bit with respect to the Sun; i.e. by about 50" per year."

The observer takes a calculator and comes up with 251 years × 1223.5 s/year of season shift, which equals 3.55 mean solar days. "See", he proclaims, "I also have June 6th, the same place and same local time as the tropical guy."

Then the tropical guy says, "If you wobble the Earth 3.55 days on its axis, what about those 0.55 days or roughly 13 hours? Doesn't that put your meridian on the other side of your Earth, making it impossible for you to witness the transit at 1:00 UT? Or does your Earth no longer rotate, and it got somehow shifted forward roughly 78000 miles (3.55 × 22000 miles per year) in its orbit around the Sun? In either case, you won't be able to see the transit. Look, it takes the same amount of mean solar days for both of us to see another transit of Venus on June 6th. Even if you were to shift your Earth back again to account for the amount of days, do you also want to move Venus and her orbital plane backward around the Sun in synch with your wobbling Earth?"

"Help", cried the sidereal observer, but the astronomer was already gone.

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© 2004 Uwe Homann, Sirius Research Group

May 31, 2004