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Chris Peterson wrote: ↑Sat Jan 11, 2020 12:05 am
MarkBour wrote: ↑Fri Jan 10, 2020 11:48 pm
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It may be that Jupiter is the most influential
planet for this, but I note that in the text accompanying the table (see the last link in the APOD caption) one finds the statement:
Due of the gravitational perturbation of the Moon (and to a much lesser extent the planets), Earth's actual distance at perihelion can vary from 0.9831914 AU (147,083,346 km) to 0.9833860 AU (147,112,452 km).
That leads me to believe that the timing of the lunar orbit versus Earth's orbit is the most influential factor causing the variations.
Yes, that could be right. It makes some sense if you look at the slightly scalloped shape of Earth's orbit because of the Moon. It would be interesting to look at the path of the Earth-Moon barycenter rather than just the path of the Earth.
...
I wondered the same thing.
I used JPL Horizons to answer that and other questions. I analyzed distances from the Sun to Earth, Sun to Earth-Moon Barycenter, and took the difference of two data sets to get the Earth to EMB distances (projected onto the Sun-Earth radial axis). I also analyzed all component distances with respect to the Solar System Barycenter (SSB). These latter analyses were enlightening but, because of posting space and time, is not discussed here. The timeline for all calculations is 200 years (1900 to 2100) with 1-yr time intervals (200 pts), and I used perihelion times that are within 8 minutes of AstroPixels' times. The AstroPixels data is also plotted for reference.
Conclusions:
- The AstroPixels Perihelion blurb is confusing and wrong:
- AstroPixels average (mean) Perihelion estimate leads to confusion.
As shown in plots, perihelion distances increase at a linear rate of 17.6 km/day (~6,400 km/century). IMO, AstroPixels' average perihelion calculation confuses the interpretation of the variation about the "mean" perihelion as well as suggesting some fundamental importance to the 2.28x multiplier of the Earth's equatorial diameter. AstroPixels chose to define the "mean" as the midpoint perihelion value (essentially the perihelion at year 2000) and, as they stated, the 2.28x multiplier applies to the 29,200-km peak-to-valley (p-v) perihelion range over 200 years from 1900 to 2100. However, from my experience, it's unusual to define a peak-to-valley (p-v) variation about a "mean" when there is a non-random (linear) component buried in the p-v values (i.e when a varying "mean" is not accounted for). Given the linear upward trend of perihelion distance, it's clear the multiplier value will depend on how long the total analysis time interval is. When the perihelion data is corrected by removing the slope of the longer-term systematic drift, the perihelion p-v range is reduced 30% from AstroPixels' data. Therefore, the more useful (and more constant) multiplier is now 1.58x.
→ The take-away is that, as presented, there is nothing special about this parameter, it's only an empirical result for the specific circumstances considered.
- The contribution from the other planets is significant (>50%). After removing the slopes, component fraction estimates are straight forward over the full 200-year analysis interval. Considering the full 200-yr range:
- The p-v Perihelion range about the corrected mean ≈20,100 km, NOT 29,200 km
- With the Moon's orbital component removed, the corrected p-v range in Sun to Earth-Moon Barycenter (EMB) distance
≈11,500 km , and - The p-v range variation of the Earth-Sun distance due to only the Moon's orbital motion ≈9,800km (2 times Earth-EMB distance at lunar apogee)
→ The fraction of EMB distance variation due to other Solar System bodies (primarily the Sun and Jupiter) is
≈11,500 km ÷ [11,500 km + 9,800 km] = 54%.
- → From 1900 to 2100, the Earth reaches perihelion about 1 day later roughly every 57 years,
- →The perihelion is increasing by about 6,400 km per century, and the aphelion is decreasing by the same amount
Plots:
- All vertical axes are kilometers
- Unless otherwise stated, left and right plots respectively show uncorrected (raw) data and with slopes removed
- Horizons Sun-Earth distances here agree with AstroPixels' perihelia within 5 kilometers
JPL Horizons & AstroPixels Perihelia.JPG
- Horizons (200 years) and AstroPixels (100 years) data are shown.
- Left plot shows AstroPixels' 200-yr 29,204 km p-v variation and the increasing perihelion distance = 0.176 km per day
- Right plot (slope removed) shows the less confusing p-v variation = 20,132 km
→The more time-independent multiplier = 20,132 km ÷ 12,756 km = 1.58, NOT 2.28
JPL Horizons - Sun to EMB.JPG
- Shown are the Horizons Sun-to-EMB distances → As mentioned earlier, the contribution from the moon's orbit is subtracted out in these plots.
- Left plot shows the increase distance rate = 0.177 km/day
- Right plot shows the p-v variation over 200 years = 11,503 km The distance variation of the EMB component is significant.
→Without doubt, the other solar system bodies are driving the increasing perihelion distance over time, and the contribution to 200-yr p-v variation in perihelion distance is at least 50%
JPL Horizons - Earth to EMB_2 & Perihelion Date.JPG
- Left plot shows component of Earth's motion, wrt the EMB. Calculated by subtracting the Sun-Earth distance from the Sun-EMB distance at the same time, it is the distance projected onto the Earth-Sun radial axis.
- The 9,800-km p-v is consistent with 2 times the Earth-to-EMB distance at lunar apogee
- Because the asynchronous lunar orbital period wrt to Earth's year, the plot is dominated by aliasing. Interestingly, the upper ~74 peaks over 200 years define an average period ~2.7 years which also happens to be the rough period between Blue Moons (using the 7-Blue Moons every 19 years rule-of-thumb).
- Right plot shows the perihelion date increasing about 1 day every 57 years
Well, the answer is a definitive YES to the question about the impact significance of the other solar system bodies on Earth's Perihelion & Aphelion. The analyses using the SSB as the origin generate the same component results but with slightly larger distance errors (±100 km instead of ±5 km). As I said, this exercise was enlightening. By the end, I couldn't help but feel the Earth is on a roller coaster ride bobbling along with a 2.5 million kilometer p-v.
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