Are transits and the rotation of Venus linked? 

Posted: September 28, 2017 by oldbrew in Maths, solar system dynamics
Tags: , ,

Credit: NASA


This is from a Q&A on a website linked with Sydney Observatory. We add brief notes at the end.

Lionel asks: Congratulations on your Venus book.

Excellent. I notice that there is a 243 year cycle for Transits of Venus
243 x 365.242 = 224.7 x 395
So far so good. The axial rotation period for Venus is 243.1 days.
Is this a coincidence or is there some underlying geometrical fact that I cannot see?
well-done,

Answer: An interesting and complex question that I address below.

Patterns in the transits of Venus
Let us first look at the patterns in the transits of Venus. We need to note that Venus and the Earth line up with the Sun every 583.92 days or 1.59872 years. This is called the synodic period.

If there was a transit, say the one in June 2004, for another transit to occur, the two planets must not only line up with each other and the Sun, but do so after an integer number of years so that they are back in the right places on each of their orbits.

Venus and Earth fulfil these requirements after five synodic periods = 7.9936 years as this is almost, though not quite, equal to the integer eight. Thus transits of Venus generally occur in pairs eight years apart. However, because of the slight inequality there is no third transit after another eight years.

A more accurate relationship occurs after 152 synodic periods = 243.00544 years or ~395 Venus years. The pattern of Venus transits thus repeats at 243 year intervals (This is the cycle quoted by Lionel in his question above). For example, the first pair of June transits after 8 June 2004 begins on 11 June 2247. Of course, in the meantime there is also a pair of December transits beginning in 2117.

The rotation of Venus
Scientists using radar observations from the 1960s onwards discovered that Venus spins backwards, that is in the opposite direction to its motion around the Sun, at the slow rate of 243.02 days.

They soon realised that means that Venus, almost but not quite, shows the same face towards the Earth each time the planets are lined up with each other and the Sun. Somehow there is a resonance between the motion of the Earth around the Sun and Venus’ spin around its axis. Scientists are unsure why this is the case, but one suggestion is that Venus is more massive on the face turned towards the Earth at those times and consequently it was gravitationally captured by the Earth.

How is it worked out that Venus shows the same face towards the Earth each time they line up? The quoted value of 243.02 days is with respect to distant stars. With a little arithmetic (taking inverses) we can easily convert that value to the rotation period with respect to the Sun or, in other words, to the day on Venus. It is 116.75 (Earth) days. Five of those periods equal 583.75 days, which is almost the same as the 583.92 day synodic period. So each time the planets line up Venus shows almost the same face to the Sun and hence the same face to the Earth, which is always on those occasions on the opposite side of Venus.

Coincidence or not
As Lionel points out it is interesting that transits of Venus repeat in a cycle of 243 years while the rotation period of Venus with respect to the stars is 243 days, The above detailed discussion indicates that there is no obvious connection that gives rise to the same number in each case. However, the calculations all depend on many of the same factors such as the orbital periods of Venus and the Earth so maybe there was a chance that the same number should recur.

Note the values quoted above are from the NASA Venus Fact Sheet.

Source: Are transits and the rotation of Venus linked? – Observations
– – –
Talkshop notes

Re: ‘Five of those periods equal 583.75 days, which is almost the same as the 583.92 day synodic period.’ [‘Venus and the Earth line up with the Sun every 583.92 days or 1.59872 years’]

Note 1: 23 solar rotations @ 25.38 days = 583.74 days
This also looks like a resonance, this time between the Sun and the Venus day.
. . .
Re: Venus and Earth fulfil these requirements after five synodic periods = 7.9936 years
A more accurate relationship occurs after 152 synodic periods = 243.00544 years or ~395 Venus years.

Note 2: using their own data, 157 synodic periods is more accurate, i.e. closer to a whole number of Earth orbits.
1.59872 * 152 = 243.00534 years (as stated in their notes)
1.59872 * 157 = 250.99904 years (~408 Venus years)
Of course that would be an ‘extra’ five synodic periods = 7.9936 years.

That may contradict the official ‘wisdom’ but there it is. It was discussed in some detail in this 2015 Talkshop post (some readers may find the comments to be of interest):
Why Phi? – a Venus transit cycle model

Comments
  1. The Badger says:

    We had ALL this knowledge once and made a super little mechanical computer which showed how it all worked, unfortunately its a bit rusty and some bits are missing now. Restoration / back engineering is a work in (slow) progress.

    Antikythera.

    The very fact that you could make a mechanical computer which showed the planetary relationships is evidence that it is all “linked” or synchronised in some way. I suggest that for solar systems that do survive (as opposed to those that end up smashing themselves to pieces) there is some kind of mechanism (gravity related) which ensures a degree of stability and non collision.

    Of course the other non collision explanation possibility may be that there is a repulsive force as well as attractive force. This could be electrical charge.

  2. oldbrew says:

    Resonance is an important factor. It’s observed so it’s real.

  3. BoyfromTottenham says:

    Badger, but how the heck did the ancient folk who made the Antikythera device know so much about the workings of the solar system over cycles of hundreds, if not thousands of years? Let alone figure out how to engineer the mechanism to demonstrate this level of knowledge? As a clockie, I was seriously impressed when I heard about the mechanism, which as I understand it predated the equivalent modern era clockwork complexity by a milennium or more. So much knowledge has been lost…and we think that we know so much.

  4. dai davies says:

    It’s resonance all the way down.

    dai

  5. oldbrew says:

    The ratio of a Venus day to a Mercury day is 3:2

    The ratio of a Mercury rotation to a Mercury orbit is 3:2

    The ratio of a Venus rotation to an Earth orbit is 3:2

    The ratio of a Venus orbit to an Earth orbit is 13:8
    – – –
    For very slow-rotating Mercury and Venus the length of day (LOD) is a big number, whereas for all other major solar system planets it’s far less. Pluto is tidally locked with Charon in a binary system (1:1 rotation and LOD).

  6. ferdberple says:

    “linked” or synchronised in some way
    ==============
    why does a boat turn sideways to the waves? because it takes less energy to roll than to pitch. this “relationship” is found throughout nature. somehow nature knows how to take the lowest energy path for all interactions.

    in the case of 2 bodies orbiting in a plane around a third, even though the forces between the bodies may be small, they are not zero. and in a friction-less environment even the smallest force will result in motion.

    Perhaps there is a small difference in the total forces depending upon whether you are at a resonance point or slightly ahead or behind, and this small difference is sufficient to “lock” the orbits into near resonance.

    for example: if expect the earth speeds up or slows down slightly in its orbit depending on where Venus is in its orbit, which will change the time that Venus acts upon the earth, as well as changing the Earth’s orbit around the sun. it would not be surprising to find that there are “stable” points almost like lagrange points. call these berple points.

    for example, there may be a minimum (berple point) each side of the resonance point, with maximums at the resonance point and 180 degrees out of phase. it wouldn’t take much difference in the absence of friction.

  7. oldbrew says:

    ferd – re. ‘Perhaps there is a small difference in the total forces depending upon whether you are at a resonance point or slightly ahead or behind, and this small difference is sufficient to “lock” the orbits into near resonance.’

    See: The Orbital Dance of Epimetheus and Janus
    http://www.planetary.org/blogs/emily-lakdawalla/2006/janus-epimetheus-swap.html
    [graphic below]

    Harmonics of Saturn’s moons….’rhythmic gravitational tugs by the masses of the moons accumulate’…

    All of Saturn’s moons create complex wavelike structures within Saturn’s rings, which make them appear finely corrugated. The waves are excited because of orbital resonances between ring particles and moons — at certain distances from Saturn, ring particles and the moons have orbital periods that are integer ratios of each other, so they meet and part and meet again over time, and repeated, rhythmic gravitational tugs by the masses of the moons accumulate to change the orbits of the ring particles. The wavelength of the structures, how quickly they damp out, and other parameters are very subtly responsive to the orbits and masses of the moons.

    [see link above]
    – – –
    It seems unlikely that planets would be unaffected by such types of forces. There’s the obvious example of ‘orbital periods that are integer ratios of each other’ with 13 Venus orbits = just under 8 Earth orbits.
    – – –
    This is an illustration of the horseshoe orbits of Janus and Epimetheus around Saturn. The dates in this image were taken from “The Rotation of Janus and Epimetheus” by Tiscareno et al. published in Icarus, July 6 2009. The size of Saturn is proportional to the average orbital radius, but the distance from the average radius to the inner/outer radii has been exaggerated 500-fold. The sizes of the moons are exaggerated 50-fold.

    http://en.wikipedia.org/wiki/Janus_(moon)

  8. The Badger says:

    @BoyfromTottenham.

    You ask the right question. How did the guys who made the Antikythera computer know both the workings of the planets and have the mechanical/engineering knowledge to create the device.

    There are only 3 possibilities:

    1. They worked it all out for themselves (like we think we do/did). So you would be correct in that we seem to have lost a lot of knowledge.

    2. Somebody else did it for them.

    3. Part 1 above and part 2.

    So for 2 and 3 you need to look for the evidence of “somebody else”. Clearly here we are thinking of an extra terrestrial “interference”. Is there evidence of this? Possibly. We see some ancient pictorial records which seem to show space ship like craft but I have similar pictures in childrens’ books written in the last 50 years which we know are “imagination”. So for me the evidence of ET is there but is relatively weak. To eliminate possibility 1 above we need much stronger evidence of ET.

    We should really be looking for it but it’s not currently a recognised and respected scientific profession. This means few people do it and those that do are usually poorly qualified. There is a good opportunity here for qualified and knowledgeable experts to change career mid way and become ET hunters.

    Any volunteers?