There’s another Science-in-SF blogger, Alex R. Howe, who reviews the tale’s issues here: The Science of Project Hail Mary
Key to Andy Weir’s tale is the existence of energy manipulating organisms that can turn energy into mass and then back into energy, on demand. Somehow. Probably via neutrino physics we don’t yet know (something very beyond the Standard Model, right?) As the blog post above mentions the neutrinos are thermal – at the same temperature as the Astrophage and Tauamoeba that interact with them. Alex Howe has done the checking – the escaping neutrino flux from Tauamoeba eating the Astrophage are unlikely to kill the main characters via neutrino radiation poisoning!
The Alien encountered by the main character came from 40 Eridani (Keid, if we use its Arabic name), which is also home star of Kal-El and Spock.
[PS… apparently I misremembered Kal-El’s home star. It’s LHS 2520… Care of the Guardian Neil deGrasse Tyson reveals location of Superman’s home planet]
From Keid to Tau Ceti is just over 10 light-years. The known planet of Keid, which is a K1 dwarf, is a Super-Earth that masses more than 8 Earth-masses. In the tale the Eridians don’t know relativity, thus they’ve flown to Keid assuming Newtonian mechanics. Interestingly that means they would have arrived with a lot more reserve propellant than they had computed. The subjective time for thrusting at 2.2 gee is less than the Newtonian travel time. As the required photonic reaction mass depends on the thrust duration, there would’ve been a lot of Astrophage propellant left in the tank.
Using Roger Wilcox’s venerable Inter-Stellar Data-Base the distance between the stars is 10.1548 light-years. After Gaia, that’s probably changed a bit, but for an estimate, it’s good enough.
Newtonian travel-time for a constant-gee brachistochrone trajectory is 4.23 years at 2.2 gee. A total delta-vee of 9.6 cee. The mass-ratio required is LARGE ~e^(9.6). However, as mentioned in Part 1, Andy miscalculated by only accounting for boost phase, not the braking. The figure would’ve been more like 121 rather than over 15,000.
Relativistic travel-time, on board ship, is 2.84 years – or 6.45 cee delta-vee. Thus e^(9.6)/e^(6.45) = 23.33 mass-ratio remains after flying to Keid. Plenty of Astrophage leftovers to gift to the human expedition.