hi again!

Grace says he has enough food to get to Erid and then for a few months more on page 468, but he also gives us some hard numbers earlier in the book: he has 40 months of coma slurry (page 417), and 51 days of real food left the day of the taumoeba outbreak (page 434)(Grace has had like one serving of coma slurry at that point but his estimate of real food has decreased significantly which is why I'm using 51 days instead of his estimate from page 417 which is three months), meaning he's got 41.7 months of varying qualities of human chow left when he discovers the taumoeba outbreak. It also took him 35 (six weeks, page 455) to get to Rocky after the taumoeba leak, meaning he had a grand total of 40.5 months of food left on the ship by the time he found Rocky.

We can then head over to omnicalculator's space travel calculator and start plugging in numbers to get exactly how many months it'd take to get to 40 Eridani (look I did the math to calculate the distance from the edge of the Tau Ceti system to 40 Eridani, too, the difference is negligible). The Hail Mary weighs 100,000 kg without fuel (we don't need fuel for the calculation)(page 165), accelerates at 1.5 g (or about 15 m/s^2)(page 19), and it's 10 light years from Tau Ceti to 40 Eridani (9.99913031 light years from the edge of the system but it literally does not change the answer by any significant amount)(page 301). So it takes about 43.705-43.71 months to get from Tau Ceti to 40 Eridani (like I said, not much of a difference), and if you'll notice he has an absolute maximum of 43 months of food left if we're solely going from page 417's estimates, and a 40.5 months by the numbers estimate from when he finds Rocky and makes the estimate above on page 468, so that's it. Grace is on the taumoeba diet for 3 months before getting to Erid. Except it's not... quite that simple.

While we don't know the caloric value per kilogram of taumoeba or exactly what eating it does to the human body, the two named nutritional deficiencies, beriberi and scurvy (lack of vitamin b1 and c respectively), actually give us a good indicator of the timeline, whether Andy intended it as such or not.

According to this article on B1 deficiency, you have around four weeks after you stop intake of B1 before you contract beriberi, and while we don't know what type of beriberi he contracted, we know you have at most about a week before it's fatal. So, we can conclude that Grace switched to the all taumoeba diet at most a month before arriving on Erid, most likely later.

And this article on scurvy indicates you can develop it in 1-3 months, so assuming the coma slurry is formulated to store both vitamin c and b1 long term and it didn't break down (a feat on this own considering this article from NASA, and the irony is the article is about a mission testing the feasibility of producing b1 and c on demand in space) both the scurvy and beriberi were caused by a lack of vitamin b1 and c in the taumoeba, and would've developed after about a month of the taumoeba diet (possibly longer for the scurvy), which is an impressive turnaround on the Eridians' part for producing vitamin B1, even if you assume they have it somewhere in their ecology.

So, the absolute earliest he can go on the all taumoeba diet is 4 weeks before reaching Erid, and until then he has to subsist off of the coma slurry.

If you'll notice, purely by the numbers and eating only one type of food at a time, Grace runs out of human chow three months before reaching Erid.

So, we have a few narrative options here:

Grace was lying about how much food he had left so Rocky wouldn't worry

Andy Weir fudged the numbers, the quote from page 468 is accurate, and Grace didn't actually run out of human chow until after he'd docked on Erid's space elevator or possibly after he'd gotten down to the biodome

Grace miscalculated somewhere and either has way more food than he thought and was fine, or way less, and if he hadn't turned around and gotten the taumoeba idea from Rocky he wouldn't been In Trouble

Grace miscalculated on page 468 and ended up stretching the coma slurry by cutting it with taumoeba, this got him to or past the maximum time from Erid he could've possibly switched to the all taumoeba diet and survived but then he ran out of the slurry

And if someone goes for options one, three, or four (I'm an option four man myself) then we can infer that even though the taumoeba are giving him calories, he's getting 100% of those calories from microbes, and while I don't... think anyone's researched "can you shovel scoops of amoebas into your gullet and live" in a scientific capacity? I can't imagine that alien microbes are giving Grace enough macronutrients to avoid a calorie deficit, even alien microbes that eat the most energy filled thing in the book (or he gets like, protein poisoning or something depending on exactly how many proteins to carbs he's getting).