Saturn and the Sun

[Starry Knight]

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*stars
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*Saturn
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*Sun /
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*Earth

Consider the golden-yellow planet Saturn, the Scythe, who
has the longest sidereal period of the five double-ensign
planets, at an average of about 29.45 mean tropical years.

With each passing year, Saturn is seen to rise heliacally
on average about every 378.1 solar days, or about 13 days
longer than Earth's tropical year; hence Saturn's synodic
period is about 378 days. The slow precession of Earth on
her rotational axis causes distant stars to appear rising
heliacally progressively later in the year to the tune of
one ecliptic degree longitude per ~71.1856 tropical years,
which is about 26,000 solar days per degree of precession,
i.e. about 25,626.8304 mean tropical years per great year.

Thus Earth's precession is relatively quite slow compared
to Saturn's progress who "zooms" around the Sun at a rate
of about 12.22 degrees longitude per tropical year. We'll
add the approximately -0.014 degrees per tropical year of
precession to Saturn's progress, and you have about 12.21
degrees per year that Saturn progresses against the stars
as viewed from Earth. By watching Saturn at times when he
is approaching inferior conjunction/opposition to the Sun,
you'll see Saturn enter retrograde motion ~138 solar days
on average approximately centered on inferior conjunction.
At these times Saturn appears to "stand still" in the sky
as he turns retrograde, then 4 1/2 months later returning
to normal motion. Each of these points in time repeat for
the long-term average synodic period of ~378.1 solar days.

Year after year, these synodic intervals progress against
the stellar backdrop, which when compensating for Earth's
precession, proves to the observer that Saturn's sidereal
year is about 29.45 mean tropical years as already stated.

Daniel Joseph Min

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