Tropical timings – the orbit of Neptune

Neptune

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The idea here is to derive the period of Neptune’s orbit from available information and compare it to the ‘official’ figure.

An internet search brings up Neptune: Facts – NASA Science, which says:
One day on Neptune takes about 16 hours (the time it takes for Neptune to rotate or spin once). And Neptune makes a complete orbit around the Sun (a year in Neptunian time) in about 165 Earth years (60,190 Earth days).

That’s the sidereal orbit period, but there’s another one to consider as a further check. Turning to the NASA planetary factsheet for Neptune we find:
Sidereal orbit period (days) — 60,189.018 — 365.256 — 164.79
Tropical orbit period (days) — 59,799.900 — 365.242 — 163.73

The last figure in each row is the ratio of Neptune to Earth i.e. years, not days. The plan is to focus on the tropical year period and see if it lines up with the displays on Arnholm’s solar simulator.

To improve the accuracy we use the tropical year of Earth as published – 365.24219 days:
59799.9 / 365.24219 = 163.726704 tropical years

Comparing this to the 166 tropical year period we’ve investigated in earlier ‘tropical timings’ posts, and originally here:
166 / 163.726704 = 1.0138888
1 / 0.0138888 = 72.00046
72*166 = 11952
11952 / 163.726704 = 72.9997 (73)

Therefore 11952 tropical years (TY) looks like 73 Neptune (tropical) orbits. This can be modelled on the solar simulator, but only within a 3000 year window. A quarter of 11952 is 2988 TY (= 18*166 or 3*996), which we think should be 73/4 = 18.25 Neptune orbits. So Neptune should be 90°(360°*0.25) further forward in its orientation with the Sun than its original position (in year 0) after exactly 2988 TY of orbiting – in theory.

Let’s see how it looks on the solar simulator, which says in its frame of reference it is ‘Looking down on Sun’s north pole’. The first image shows a 2988 TY comparison (7 May of year 0 to 7 May 2988).

It can be seen that the the Earth-Neptune angle with the Sun (above, right) looks a lot like 90°. To be a bit more scientific we can move the date forward by 1/4 of a year (right), when Earth should meet Neptune whose orbit only moves about 0.55° in that time, so Earth only needs 0.56 days ‘extra’ to make up for that.

These results confirm that the simulator represents the planetary movement of Neptune using the tropical orbit data. This can be extended to Jupiter and Earth as follows:
73 Neptune = 1008 Jupiter (144*7) = 11952 Earth (144*83 or 72*166 TY).

So the Talkshop formula for Neptune’s orbit in tropical years is:
166 – (166/73) TY = 163.726074 TY = 59,799.67 days.
That number is only 0.23 days less than the NASA number (59,799.90 days) over the whole period.
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Image: Neptune