alright this took me NO JOKE almost 3.5 hours to figure out. i recalculated the PHM timeline and therefore the timeline for my Eridian Shifter AU (and also the Pebble Shifter AU).
WARNING: while I did plan on studying astrophysics, i havent actually done math beyond like "how much will these supplies cost" and "whats the most efficient use of this paper" and math for my framing job at michaels in YEARS. like i understand complex math but like. thats sooo much work. so i bs'd the whole thing.
the numbers i got for the relativity stuff is literally this: grace experienced 4.7 years on his way to tau ceti, traveling at 92% of the speed of light. earth experienced 12.852 years while he did that. i took that ratio of time and then made a calculator figure out the equivalents between tau ceti and erid and erid and earth. its probably wrong but like. andy weir fucked up the astrophage calculations for the hail mary in the book. if he can keep his 2mil kg number, i can keep my probably incorrect relativity math. (yes i did attempt to actually calculate the time dilation. i will reiterate: i am not an astophysics major. i switched from that to fucking book arts. i do printing presses and bookbinding, and study physics and astronomy and astrophysics for fun. so i decided it was too much work and gave up on actually calculating it all by hand)
i also calculated out how old Grace is in my AU(s), so expect that below!
Grace's Age
I have decided that he graduated high school 2 years early! I actually was going to do this but ended up not doing it because that's so much work and I hadn't decided what I wanted to study yet (I was in between comp sci and physics/astronomy at the time). So Grace graduates American high school at 15 years old (just go with it).
It takes him 4 years to get through undergrad (double major in microbiology and molecular biology. pretend whatever college/uni he went to will let him do that even though the courses would be way too similar and they wouldn't let him double dip everything for the requirements). 2 for grad school. I do not have a PHD, and based on my research, it on average takes someone 5 years to complete two PHDs at the same time. I headcanon that Grace has two PHDs - one in microbiology and one in molecular biology. this is to cover for the fact that the movie changed his doctorate for some reason. he's smart but PHDs fuckin suck and even a smart cookie like him couldn't do it faster. So by the time he gets both PHDs, Grace is 26 years old.
I imagine the UNESCO incident happened pretty soon after, during his postdoc. Like within the year. (I did zero research on postdocs for either of his fields, sorry). So he's just about 27 when this happens!
It takes somewhere between 6 months to a year for him to get his teaching certification in the state of California (yes I know it typically takes at least a year, if not more. but pretend he took teaching classes for some of his electives throughout his college/uni days and that helped speed things along). So he's 27 1/2 when he starts teaching.
I think he honestly wasn't teaching for very long when he gets kidnapped by Stratt. My guess is 2.5 years. This is entirely guesswork and kind of based on his energy cause as someone who's not only taught kids that age (and is currently doing so, just not in a traditional classroom) and has multiple friends who are teaching that age range (in a traditional classroom), Grace has not yet hit the exhaustion state of teaching that hits after a few years of being in the classroom lmfao. this is again entirely based on both personal and my friends' experiences. just go with it. he's 30 when Stratt nabs him!
I honestly do not remember if the book lists how long the taskforce takes to build and launch the Hail Mary. The movie implies its stupid fast, like a few months. I have decided that's stupid and would result in even more explosions and that I want to go with 4 years. Maybe a little less. but roughly that much from the moment Grace is grabbed from his classroom to when the Hail Mary Launches. I went with 4 years because that's with the best minds on the planet, no one keeping track of a budget, and them speedrunning designing and building the ship from scratch. normally that takes like 10 years for a manned ship. but they cut it down to 4 years. Grace is 34 when he is launched into space.
Grace experiences 4 years, 8 months (4.7 years) on his way to Tau Ceti due to time dilation. He's roughly 39 when he wakes up.
Timeline of PHM itself:
This is based on my own math and again, as stated previously, is not perfect. I 100% made up the timeframe that Grace spends at Tau Ceti, and how long he's heading back to Earth before the Leak. I don't remember what the book says and I'm too lazy to go digging for it. Everything else I tried to keep semi accurate lmao. I did not pick a year for PHM to take place in. honestly, I don't really care. I know the movie has his arrival at Tau Ceti set in 2032 but like. I don't wanna do that lol. So imagine the Hail Mary was set roughly in the mid 2020s. Like right now. idk.
This will be split into several timelines since yknow. time dilation, relativity, all that fun stuff! Earth experiences WAY more time than Grace does.
Most of the numbers are gonna be in decimals. because i didnt feel like calculating exactly how many days. its mostly years with some months. ill have the proper numbers on the pretty timeline im gonna make this week. like im drawing it out and color coding it on a huge piece of paper rather than in my sketchbook cause it did NOT fit in there.
Time units are also in Earth units for now. I'll do another version where it's Eridian units in the future!
Grace's Timeline
Earth -> Tau Ceti = 4.7 years (he's 39 years old physically)
Tau Ceti = 0.34 years
Tau Ceti -> Taumoeba Leak = 0.0834 years
Taumoeba Leak -> Blip-A = 0.167 years
Blip-A -> Erid = 4.01 years
From Earth to Erid, Grace experiences 9.3004 years
Beatles arrive on Earth 1.723 years after Grace and Rocky get to Erid
Sol's light returns to normal 16.3 years after that point.
Now for the AU parts!
The Songbird construction = 1.85 years
Erid -> Earth = 6.44 years
In the Eridian Shifter AU, Grace spends 19.873 years on Erid. From the launch of the Hail Mary, they experience 35.6134 years. He develops his shifting ability a couple of weeks after the Adrian incident, before he and Rocky split ways. From that point to when the Songbird makes it to Earth, Grace spends 31.1 years as an Eridian. That's 87.33% of their life since developing the ability. They are technically 69.6134 years old when the Songbird reaches Earth, but due to spending 31.1 of those years as an Eridian, their human body appears to be about 40, maybe 41. Ish. They physically appear younger, since while their human body did age (just slower), they weren't putting stress on it, so it didn't experience as much pain and wear and tear as literally every other human, so they still look younger than their physical body appears to be.
Rocky's Timeline
Erid -> Tau Ceti = 4.01 years
Solo @ Tau Ceti = 46 Years
Meeting Grace + at Tau Ceti = 0.34 years (Rocky is physically 291 years old)
Tau Ceti -> Leak = 0.0834 years
Leak -> Grace's arrival = 0.167 years
Grace's arrival -> Erid = 4.01 years
Beatles arrive on Earth 1.723 years after Rocky and Grace get to Erid
Sol's light returns to normal 16.3 years after that point
AU time!
Songbird construction = 1.85 years
Erid -> Earth = 6.44 years
Rocky's mission, from departure of Erid to return to Erid, takes 54.6104 years (experienced). He is 315.4734 years old when he leaves on the Songbird, and 321.9134 when they get to Earth.
Earth's Timeline
This is the time experienced by humans on Earth. So while I say "Earth -> Tau Ceti", that is how long Earth experienced from when the Hail Mary launched to when Grace reaches Tau Ceti, etc etc.
Earth -> Tau Ceti = 12.852 years
Tau Ceti = 0.34 years
Tau Ceti -> Leak = 0.0834 years
Leak + Beatles Launched!
Beatles Launched -> Earth = 12.852 years
From the Hail Mary's launch to the Beatles' arrival back on Earth, Earth experiences 26.1274 years.
Alternatively:
Leak + Beatles Launched -> Blip-A = 0.167 years.
Blip-A -> Erid = 10.962 years
From the Hail Mary's launch to when Grace and Rocky arrive on Erid, Earth experienced 24.4044 years. (Yes, that does mean that Grace and Rocky beat the Beatles by 1.723 years, but that's space travel for you)
Grace and Rocky on Erid = 19.873 years
Songbird Launch -> Earth = 17.604 years
From the Hail Mary's launch to when the Songbird arrives, Earth has experienced 61.8814 years.
Erid's Timeline
...I just realized I forgot to update my math for the time experienced by the Eridians.
I will update this post with the timeline/numbers tomorrow. I've been doing this for 4 hours now (yes it took me 30 minutes to type this post out). So don't reblog this if you care about the math for the Eridians being included lol
Pebble Specific Math
Again. I didn't finish updating this math lol. It's mostly just me comparing Grace's human age to the average Eridian lifespan and showing his age in pebble form. He's about 39, but for a pebble, that's still small and young. I'd have to redo the math but that's still about equivalent to a human 4 year old. ish.
Your brain is so wrinkly and massive. I'm so hooked on your shifter au that I forgot I was supposed to eat around now lol. I was wondering if you can explain eridian time? I have no idea what base 6 means. Just that, love your work and idead and concepts, really excited to read the rest of the series! Oh also, huge fan as a fellow aroace nonbinary, lots of love from Argentina!
omg please make sure you're taking care of yourself!!! my fics (and all fics) will always be there for you to read after you eat or hydrate or sleep. im really glad you like it!!!
also HELLO!!! im so happy that my silly au(s) have reached beyond my little bubble of [redacted], USA. love love love!
im so excited that you asked me to explain base 6! im putting it below because its probably gonna devolve into me explaining more than just base 6 lol (im writing this before the explanation). if im confusing or it doesnt help, yell at me again and ill try and explain it a different way! i love helping to explain topics.
im gonna do my best to explain Eridian time, what base-6 is and means, and maybe some other stuff lol. ill list all my sources at the end since im gonna definitely be quoting andy weir and the 40-eridani website! sorry if said citations suck ass, im way too used to chicago citation format since i like to write research papers for fun (no im not joking but thats another topic) [edit from post making of this post serif, yeah i just hyperlinked the sites. im not doing real citations. sorry lmfao]
What is Base-6?
This explanation will be split into a couple paragraphs and hopefully organized. I may modify it in the future if I decide I did a bad job. I am also not a mathematician so I may get things wrong but I'm pulling from both experience and sources to try and do my best. I'm sorry if I sound like I'm infodumping or overexplaining things; I'm not sure what everyone's foundations of knowledge are so I'm going from what I consider the beginning. Feel free to correct me or ask me questions!
Base-# systems have existed since humans began doing math. As far as I know and have been able to find, humans have been counting in base-10 for thousands of years, with a few examples of base-5 and base-20. Base-10 is the number system that is by far the most common; in languages and cultures that use arabic numerals (0,1,2, etc), that basically means we count from zero/0 until nine/9, and then we do something cool. We take that digit (9) and start it over at zero, adding a new digit before it and starting at one. Once we hit 19, we increase the tens place to 2, and loop back around the ones place to 0. Yes, I just realized I nonbinary-explained counting. This is base-10! Most common because the average human has 10 fingers (counting thumbs) and yknow. finger counting. it's very old.
Base-2 is another very commonly used number system, even if you don't actually know it. You might also know it as "binary code" or "binary system". It's 1's and 0's, the very stuff computers and electronics run on. On and off, open and shut. You may be running Linux or Windows but computer languages are just ways for us to better understand and use computers because otherwise you'd have to know how binary works. Binary code is very cool. The number of numbers in a string gets very long very fast. 0 is 0. 1 is 1. But 2 is 10. 3 is 11. 4 is 100. 5 is 101, etc. There's converters online that are fun to play with if you want to hide messages in stuff - I've done it before for projects where I turned a word into binary and then copied the numbers as spaces being 0 and lines being 1s, if that makes sense. But yeah. Base-2!
Base-3 through Base-5 all exist. You basically just start at 0 and add on numbers until the number of numbers matches the numerical system (i have no idea if that makes any sense whatsoever). So base-3 means you'd use 0, 1, and 2. Base-4 is 0, 1, 2, and 3. Etc. Base-4 and Base-5 have been used by some cultures, but I am not educated enough to speak on their history or reasons why.
Base-6! Base-6 is what Eridians use! Essentialy, they count 0, 1, 2, 3, 4, and 5. Once you hit 5, you roll over just like you would for other numerical systems. From my understanding, this is because Eridians tend to walk on 3 limbs and use 2 to hold items, for a total of 6 fingers to count on. As a result, if you converted 46 (the number of Earth years Rocky was solo in the Tau Ceti system) into base-6, it would be 114. Now, Rocky did not actually spend 114 Earth years at Tau Ceti; Eridians simply do not have words/characters/numbers past 5. Instead of saying six/6 like humans would, they would rollover from 5 to 10. It's really weird for us to understand because we're so used to base-10 (or sometimes base-2, for those who know binary. I can convert numbers, but I can't do letters). So it's the same amount of time, just represented differently. It gets more and more crazy - in Earth years, the average Eridian life is 689. Convert that to base-6, the average is 3105. That's a pretty big difference, and if you didn't know that I was using base-6 for that longer number, you might get confused and think that Eridians live longer than most human civilizations last.
How does Eridan time work?
Eridian time!!! This is going to pull heavily from the Eridian document by Andy Weir and the 40-Eridani website. I know how to convert it, but I can't do it in my head.
Because Eridians use base-6, all of their seconds, days, and years are already going to be different from Earth seconds, days, and years. Currently, as far as I'm aware, we know that Eridians have units of time equivalent to seconds, days, and years. Unless I missed it during my research, we do not know if Eridians have an equivalent of minutes, hours, weeks, or months. I could probably make some up, by divvying up days and years and stuff, but that's a lot of work and I'd probably be wrong. They're not canon. So. I'll list the equivalents and then give some examples of each in both base-10 and base-6. Eridians also have different symbols (albeit familiar ones) to humans for numbers, so I will copy those in as well as reference. The way I did the conversions is by using the calculators available on the 40-Eridani website! I could do it myself, but I am very lazy.
1 Eridian second is equal to 2.37 Earth seconds.
1 Eridian day (1 complete rotation of Erid around its axis) is equal to 18,397 Earth seconds (306.616667 minutes, or 5.11027778 hours).
1 Eridian year (1 complete revolution of Erid around its star (which is a whole other post - the 40-Eridani system is actually a trinary star system and Weir has only said that Erid is the closest planet to 40-Eridani-A; it might be around all three stars, around 40-Eridani-A, or around 40-Eridani-B and -C (both of which are in a binary pair and that pair orbits the A star)) is equivalent to 42.245 Earth days. (Note: this is directly from Weir's Eridian document and is based on what we thought was actual measurements of the planet Weir picked to be Erid, known as 40-Eridani A B. This planet unfortunately does not actually exist; we thought it did, but in 2024 reanalysis of the observations that we thought proved its existence determined that said planet doesn't exist. So the planet and orbital period is entirely fictional, but the 42.245 Earth day orbital period number was based on what we thought was actual data.)
What are the Eridian number symbols?
These are taken directly from the book/movie/40-Eridani website.
Zero/0 = ℓ
One/1 = I (it looks like a capital I with what are called crossbars, the additional lines on the top and bottom. If you want more in-depth rambling about typography, I will elaborate elsewhere!)
Two/2 = V
Three/3 = λ
Four/4 = +
Five/5 = ∀
Alright. Now for some examples.
I'm copy pasting my math directly from the converters and my calculator, I'm not rounding because it just shows how time on Earth is entirely dependent on our perspective and how Earth currently behaves and time is relative to your place and time in the universe.
How long was Rocky at Tau Ceti before Grace arrived?
46 Earth years (base-10). Converting this to Earth days gives us a total of 16,801.1412 Earth days (46*365.2422) [base-10]. Throwing this number into the time converter on the 40-Eridani website gives us a couple of answers. In base-10, Rocky was at Tau Ceti for 78,903 Eridian days and 2,278 Eridian seconds. That's equivalent to a very long 397.7072126878921 Eridian years [base-10], or 1,501 [base-6] Eridian years. In base-6 notation, that's 1,405,143 Eridian days and 14,314 Eridian seconds. In Eridian numerical symbols, Rocky has been at Tau Ceti for I+ℓ∀I+λ Eridian days and I+λI+ Eridian seconds.
How old is Rocky?
Rocky is 291 [base-10] Earth years old during the events of PHM at Tau Ceti. Let's convert that. That's 106,285.4802 [base-10] Earth days. Converted to Eridian time, that's 499,149 Eridian days and 723 Eridian seconds [base-10]. In base-6, Rocky is 14,410,513 Eridian days and 3,203 Eridian seconds old. That's 2,515.930410699491 [base-10] Eridian years, or 15,351 [base-6] Eridian years. In Eridan, that's I∀λ∀I Eridian years.
How about the average lifespan of an Eridian?
In Earth years that would be 689 [base-10], or 251,651.8758 [base-10] Earth days. That would be 5,956.962381346905 [base-10] Eridian years, or 1,181,834 Eridian days and 830 Eridian seconds [base-10]. Converting those to base-6 gives us an average Eridian lifespan of 43,324 Eridian years, or +λλV+ Eridian years. For Eridian days/seconds in base-6, that's 41,155,242 days and 3,502 seconds, or +II∀∀V+V days and λ∀ℓV seconds.
Basically, because of how base-6 works, numbers in base-6 notation often look much much larger compared to base-10 numbers, and they get exponentially larger. It starts small, with numbers only being a bit off, but as you can tell, when we get to larger numbers, the base-6 equivalent gets much longer compared to the base-10 number (5,956 years in base-10 is 43,324 years in base-6).
In conclusion:
I really hope this was a good explanation. I kind of went overboard. I got excited. Sorry.
Sources (I actually didn't use that many):
The fan-made 40-Eridani website
40-Eridani converter page
NASA page about no exoplanets orbiting 40-Eridani
Wikipedia page for the 40-Eridani system
Reddit post by Andy Weir with link to his Eridian biology document in post
