Re: Venus?

[Bob LaMontagne <rlamont@POSTOFFICE.PROVIDENCE.EDU>]

Gary Karshner wrote:

> John,
>          I am asking myself if I really want to keep this going. Maybe I
> can get you to help with a very old problem. My source of this is in annual
> Review of Astronomy and Astrophysics Vol.6, page 307, in an article by
> Goldreich and Peale. They state:
>           "We have seen that the rotational period of Venus is with in a
> few tenth of a day 243 day retrograde. If the period is 243.16 days the
> same face of Venus will be oriented toward the Earth at each conjunction of
> the Earth and Venus."
>
> I have a margin note that says how? with a calculation of the synodic
> period. I could not see where they got this, which is "why memory served"
> at all.  They go on to calculate the tidal forces involved. From the work
> they did they must have been very sure of this fact.
>          Any ideas?

If you triple the 243.16 period you get 729.5 days, which is almost exactly 2
earth years (730 days). This is obviously a spurious resonance, but fascinating
nonetheless.

If Earth and Venus are along the same line from the sun, they will form that
configuration again in 584 days (synodic period). (The orbital period of Venus
is 224.7 days and the orbital period of the Earth is 365, therefore, 1/224.7 -
1/365 = 1/584) The time for one Venutian day (local noon to local noon) is
116.7 earth days (1/224.7 + 1/243 = 1/116.9).
Therefore, whenever we are in a line with Earth, Venus, Sun (584 days), Venus
has gone through 5 (584/116.7) of it's days and presents basically the same
face to us! It's only when we are close to Venus that a telescope can make out
any semblance of markings - so we are only aware of Venus' rotation visually
when it is closest to us every 584 days.

It's going to be embarrassing if I've screwed up these calculations :-)

Bob at PC

Bob at PC