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Re: Venus?



Gary Karshner wrote:

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."

Hmmmm. I blew a minus sign when I did the calculation
this morning. Also note that one needs to think
carefully about the difference between "rotation
period" and "day".

For practice, so you can see how the calculation
goes, let's calculate the _earth_ solar day.

Earth rotation period = sidereal_day
rp := 23.93446965 hours = 0.99727 Day
where "Day" refers to the standard mean solar day.

Earth orbital period
op: = 365.256363 Days

The time between one sunrise and the next, as
viewed by earthlings, is:
1
----------- = 1.00000 Day
1/rp - 1/op

which is not a surprising result.


Now for Venus, the rotation period is
rp := -243.021

which again refers to the _sidereal_ notion of
period. Do not overlook the minus sign, which
indicates retrograde motion.

The orbital period is
op := 224.701 Days

Again we calculate
1
vday := ----------- = -116.751 Days
1/rp - 1/op

which is the length time between one sunrise and
the next as seen by the Venerians. It is _faster_
than the sidereal rotation period, because of the
rather unusual retrograde rotation.

Meanwhile the synodic period is
vsyn := 583.92 Days

and the ratio is
vsyn / vday = -5.00141

which is remarkably close to an integer. If it
were exactly an integer, it would mean that every
five vdays, the earth would be exactly overhead
a given spot on venus.

If you believe the numbers at e.g.
http://nssdc.gsfc.nasa.gov/planetary/factsheet/venusfact.html
are accurate, they are good enough to _disprove_
the hypothesis that the venus rotation is phaselocked
to the earth orbit. But it's close.

The numbers available to Goldreich and Peale way
back then would not have been good enough to rule
out the phaselock hypothesis.

It's a little bizarre to think anything would
phaselock to the _fifth harmonic_ of the earth's
orbit.