Masterotter117

System Era: Lucky Numbers (Sidereal and Synodic Periods) Pre-T2/A1.0 Planet Orbits

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With the last official update to the pre-alpha slated to come out tomorrow, and a new moon being added with T2 before they crank out 1.0, I wanted to share this, not knowing if any of the info would change. I also have not seen anyone look at this yet, so if someone has, I'd love to double check my numbers against theirs. TL;DR, I found the orbital periods (Sidereal Periods) of each planet currently in the game, their resulting Synodic Periods with each other planet, and discovered System Era likes Lucky Numbers (using the Sieve of Josephus Flavius), within error.

This post does not go into great detail about what sidereal or synodic periods are, or lucky numbers. The methods used and results are given. Personality Type-D people looking for pragmatic information can use the table shown here. This table outlines when a given planet will align synodicly with any other planet in opposition, same side of the star. This excludes Barren, which was only calculated with Terran. Yes, the table below shows you'd have to wait longer than 25 minutes to launch from Terran to Tundra from the same point. Given the planets are slightly closer that the edge of Terran's launch-range, the actual time needed to wait before being able to reach Tundra is slightly less. This is why experienced players recommend planet-hopping if you have a Hydra-zine Thruster capable shuttle.

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Terran is represented as H, for Home-Planet. Tundra to Radiated is highlighted in Red, as it is impossible to travel directly between the two bodies given the distance.

Before divulging my methods, the answer to the WHY? question is that I have always been fascinated with how we can tell for certain how planets move, and wanted to try for it myself. I was also inspired by the loading screen, given the very nice round number they chose. It is clear the loading screen was designed very intentionally with this concept in mind.

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Loading Screen.

If you watch the loading screen long enough, you see that the each planet from the star completes five, three, and one orbital cycle from the first planet outward respectfully, before realigning. Those figures happen to have a very short total synodic period.

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Alignment 1, T=0 is six seconds into the recording.

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Alignment 2, Dropping frame-rate caused capture issues.

Also note, that satellites, like Barren, have a synodic period based on the planet they orbit. Additionally the next image illustrates that just because two bodies align synodically, it does not have to be from the point they were last aligned.

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Synodically aligned, not at origin.

So to find the in-game sidereal periods of each planet, I began with Radiated. It is obvious it has the fastest orbit around the star, thus I could record significantly less. One difficulty in using Radiated is that most of the error in time stepping comes from not having a camera-lock feature in launch mode (I don't want one either) and another is the increasing distance to other planets increases reliance on video resolution. To begin, I calculated the sidereal period of Radiated. Then I timed the synodic period with every other planet. Using the equation below, you can find the missing sidereal period of the other planet in question. Then I verified my calculations by observing the sidereal period for both Terran and Arid. I quit after that because I was disheartened about likely losing my saves with tomorrow's update. Screenshots with time stamps showing what was used in the image are given below.

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Equation Used. Note, absolute value in the denominator.

The results shown in the table here have striking similarity, within rounding, to Lucky Numbers found using the sieve above, after the 7th-number filter. Coupled with the deliberate choice in the loading screen, I hypothesize this is very intentional. This also adds huge favor of System Era in my book!

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Results. Note Barren's Synodic Period is in relation to Terran (H).

Finding the Least Common Multiple for all sidereal periods of the planets, excluding Barren, the total synodic period ranges anywhere from 61 to over 1,000 years. These numbers vary largely when even one sidereal period is altered by a fraction of a percent. As such, it is currently inconclusive just how long one will have to wait to get the "perfect" screenshot with all planets in superior opposition to Radiated with respect to the star. It is also inconclusive what my current error is as the official sidereal periods are not posted anywhere. Seeing as I was able to use a game to teach myself basic concepts in astrophysics, I support leaving these numbers unpublished as well. If anyone has done this and would like to compare, let me know!

For more math fun, because the orbits are periodical, they can be represented by a sine wave. Therefore each planet has a frequency. Because there are multiple frequencies, the resulting sinusoidal wave will change shape, exactly like adding musical frequencies that can develop beats. By adding each planets wave, you can find the overall solar system's wave function in regards to the orbit.

Yes, I know I have way too much time on my hands. Sorry for the long post, thanks for the read!

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First Sidereal Stamp, T=0, Radiated.

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Second Sidereal Stamp.

 

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Verifying Terran Calculated Sidereal.

Posted on Reddit by me as TeemoWorship.

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Very nice work.  I still contend that the small craft should only go to the closest planets and the larger could go to any planet without waiting for movement to allow closeness.  That's why it has a larger tank right?

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