Sol Orrery Time-Shift Analysis

A technical note on estimating an implied epoch offset from Elite System Map orbital longitudes, with an emphasis on modulo ambiguity and robust fitting.

Author: CMDR HD41117 (3312) System: Sol Method: multi-planet modulo fit

Abstract

This note records an empirical method for estimating an implied time offset between two observed planetary configurations in the Elite: Dangerous System Map (orrery view). Approaching any Radicoida Unica site in HIP 87621 appears to induce an abrupt change in planetary longitudes and sometimes day/night presentation. We treat the two configurations as “snapshots” and solve for the elapsed time \(\Delta t \) that best reconciles their relative longitudes under the orbital periods displayed by the Elite System Map (ESM).

Key result (outer planets only): an implied offset of \(\Delta t \approx \pm \)72.6 years, i.e. about one Uranian orbit fraction, with inner planets suggesting that the altered configuration is staged or frozen rather than dynamically evolved.

1. Observational setup

Measurements are taken in a top-down system map view (directly above the ecliptic plane), using a fixed angular reference:


2. Data model

Let \( \theta_{i,A} \) and \( \theta_{i,B} \) be the measured longitudes (in degrees) for planet \(i\) at snapshots A and B. The displayed ESM orbital period \(P_i\) (in days) defines an angular speed \( \omega_i \) under a uniform circular approximation:

\[ \omega_i = \frac{360^\circ}{P_i} \]

Under a continuous evolution model, the “true” displacement between snapshots is:

\[ \Delta\theta_i^{\ast} = \omega_i\,\Delta t \]

However, map longitudes are only observed modulo 360°, yielding:

\[ \Delta\theta_i \equiv (\theta_{i,B} - \theta_{i,A}) \pmod{360^\circ} \]

Therefore, each planet admits an unknown integer wrap count \(k_i \in \mathbb{Z}\):

\[ \omega_i\,\Delta t \approx \Delta\theta_i + 360^\circ k_i \]

3. Measurement and handling the CW-positive convention

Two images were captured of the Sol system in Orrery Mode, pre and post timeshift. Most orbital mechanics conventions take counterclockwise-positive (CCW+) when viewed from ecliptic north. A measurement for each planetary position was recorded in degrees using Inkscape's angular measurement tool which takes clockwise-positive (CW+), so conversion was necessary using:

\[ \theta^{(\text{CCW})} = -\,\theta^{(\text{CW})} \pmod{360^\circ} \]

4. Estimation algorithm (robust modulo fit)

We solve for \( \Delta t \) by searching wrap counts consistent with a bounded time window and selecting the solution minimizing a weighted residual.


4.1 Candidate generation

For a slow-moving “anchor” planet \(a\) (typically Saturn or Uranus), the candidate time for each integer wrap \(k_a\) is:

\[ \Delta t_{(k_a)} = \frac{\Delta\theta_a + 360^\circ k_a}{\omega_a} \]

Candidate times outside a chosen window (e.g. \([0, 200\text{ years}]\)) are discarded.


4.2 Wrap snapping for each candidate

For each candidate \( \Delta t \), infer the best wrap for every planet by rounding:

\[ k_i = \mathrm{round}\!\left(\frac{\omega_i\,\Delta t - \Delta\theta_i}{360^\circ}\right) \]

Then define residuals:

\[ r_i(\Delta t) = \omega_i\,\Delta t - (\Delta\theta_i + 360^\circ k_i) \]

4.3 Objective function

With per-planet uncertainties \(\sigma_i\) (here, \(\sigma_i \approx 1^\circ\)), define weights \(w_i = 1/\sigma_i^2\). A simple least-squares objective is:

\[ J(\Delta t) = \sum_i w_i\,r_i(\Delta t)^2 \]

If we expect occasional outliers (misread angles, UI drift, or staged values), a robust alternative is the Huber loss \(L_\delta\):

\[ L_\delta(r)= \begin{cases} \frac{1}{2}r^2, & |r|\le\delta,\\ \delta\left(|r|-\frac{1}{2}\delta\right), & |r|>\delta, \end{cases} \]

yielding \( J(\Delta t)=\sum_i w_i\,L_\delta(r_i(\Delta t))\), typically with \(\delta \approx 2\sigma_i\) to \(3\sigma_i\)


5. The solution is naturally \( \pm \Delta t \)

Without an external arrow-of-time, the equations are time-reversible: if \(\Delta t\) is a solution, then \(-\Delta t\) also satisfies the congruences after consistent wrap adjustment. Thus the method returns a magnitude \(|\Delta t|\) and reports both signs unless contextual information selects one.


6. Results summary

Outer-planet-only fit

Restricting to Jupiter, Saturn, and Uranus provides a stable estimate (slow bodies strongly constrain wraps). Using ESM orbital periods, the implied shift was:

\( \Delta t \approx \pm 26{,}510 \text{ days} \approx \pm 72.6 \text{ years}. \)

This is consistent with “about one Uranus-scale timespan” while allowing integer orbit wraps for Jupiter and Saturn.


7. Data table

Planet ESM Orbital Period (days) Snapshot A angle (CW+) Snapshot B angle (CW+)
Mercury88.0-162-28
Venus224.71828
Earth365.3-13928
Mars687.0-36168
Jupiter4332.68595
Saturn10759.2154-63
Uranus30687.1294-141

8. Notes and limitations


9. Conclusion and a bit of tin foil

Solving the least-squares for seven planets has shown there is a single dominant magnitude at 26,518 days (≈72.6 years). There is no indication of a time arrow, so 26,518 holds true for epochs in the future and the past. While Uranus and Saturn hold stable for this duration, the inner planets are not shown in their respective corresponding positions; there is no precise time/position match, meaning Keplerian propagation was not used to generate the configuration of the inner planets shown after the time jump. This points to the Earth-Venus-Sun transit alignment being something curated, a flag of sorts, and something worthy of note. The angles of Venus and Earth at this epoch are shown at 28° and 28°, respectively, yet if we actually jumped back to that time, the planets would be at different positions and we would not witness a transit taking place. It should also be noted that the actual orbits of Venus and Earth are in a resonance period of 8 years (the number 8 is known to be significant, peppered throughout Elite lore).

At first I thought 72.6 years ago was insignificant in Elite lore, but after some digging, 72.6 years ago (3239) is exactly 88 years after the end of the first Thargoid War. At that time, The Alliance were making major advances in reverse engineering Thargoid technology; engineering which led to the development of the FSD. Is it possible the Thargoids are planning to halt the development of the FSD at source? (Probably not...)