Headscratchers / Project Hail Mary

No elements heavier than lead?

• For Eridians to have such advanced materials science yet never have heard of radiation would almost certainly imply they do not have access to any material heavier than lead (While it took humanity comparatively long to discover that there are no stable isotopes of Bismuth, the other heavy elements are radioactive enough as to produce notable material science effects after a couple of decades at most — often far faster). Now granted, Eridians do not have as intuitive an access to electromagnetic radiation as humans do (iirc radioactivity was first discovered when a sample of Ore Mountain minerals left weird splotches of color on photographic paper despite that photographic paper having been kept in the dark) so they might have a different pathway of discovering it, but if you try to work with radioactive substances all sorts of wonky stuff happens that has no explanation in chemistry and can only be gotten to the bottom of if you discover radioactivity. As for a planet simply not containing even the tiniest trace amounts of stuff like Thorium or Uranium — how exactly would it fuel its plate tectonics?
  • I assumed that the Eridani system was significantly older than our solar system, to the point that most radioactive elements had almost completely decayed. Whatever remnants were left didn't have a significant impact on Eridian studies of chemistry, so it's possible that Eridians simply weren't aware of radiation. On the other hand, they may be aware of alpha and/or beta radiation, just not cosmic gamma rays (as most elements decay releasing alpha or beta particles). Neither particle would have any impact on an organism that's mostly made of metal, so it's possible that they just assumed radiation was rare and harmless.
  • They are well aware of heavier elements than lead—Ryland mentions that Eridian life is full of heavy metals (their blood alone is mercury, just barely lighter than lead). There is no sign that there is any strange lack of Thorium or Uranium. They're mostly at 1950s science, ahead in a few areas (materials sciences) and behind in others (radioactivity). Between their thick atmosphere and strong magnetic fields, even radioactive sources on the planet itself would be easy to miss since they're not looking for them.
    • But that is exactly the thing. If you have — for example — natural Uranium in a material (so — on Earth — 99.2% U-238 and the rest U-235) the slight but notable radiation will do things to the entire material over time that are notable with 1920s human material science — which is way below Eridian material sciences. True, the radiation itself was the first thing humans noted, because humans by then had developed several pretty sophisticated radiation detection processes (including photography, which is how pitchblende was identified as "this stuff does something odd"), but Eridians being advanced in material science, they should've at least detected radiation damage if not developed radiation material science...
• Also, Eridians know atomic number (i.e. the number of protons/electrons in the neutral atom) as evidenced by Rocky's referring to iron by its atomic number — there are, even before you get to lead/bismuth — two elements of which only radioactive isotopes exist. And those isotopes are indeed so radioactive that humans have only found out those elements exist (in the tiniest traces) outside human-made nuclear reactors by observing their characteristic decays in samples of other radioactive materials. Their very names are indicative of their history "the technology stuff" ("Technetium") and "born of fire" ("Promethium") — many of their chemical properties were quite accurately predicted by Mendeleev and others because of where they sit in the periodic system of elements. It stretches belief that Eridians never found it odd that the periodic system of elements has two "holes"...
  • Perhaps they are finding it odd that there's holes and unknowns in their periodic system, and their scientists are still experimenting and finding answers for the "Missing Electron Phenomenon" and thus the breakthrough for radioactivity and nuclear science. They're still taking their first steps in space science when Rocky's mission starts, after all. Also, remember that Rocky is an engineer in a crew of 23 (or is that 15 in base 6?); He's a briliant tinkerer, but do not neccesarily need to be up to date with the bleeding edge. And unlike Grace, he doesn't have a library of Literally Everything on his palm to read up on while stranded in Tau Ceti.

Why do Eridians have days?

• Eridian timekeeping includes days, just as ours does. Theirs are much shorter because of their planet's faster rotation. But the reason prehistoric humans were aware of what a "day" is, despite not understanding the astronomy behind them, is because, well, we can see the sun. The rotation of Earth plays a huge role in our ecology, with light and temperature fluctuations leading to all sorts of evolutionary strategies and adaptations. But Erid's atmosphere blocks all light, and its greenhouse effect, combined with the planet's even faster rotational period than our own, would make the temperatures on the sunward/antisunward sides more or less uniform (or at least that's what I suspect; I'm not a planetary scientist). It makes sense that they might recognize the concept of a year, provided their planet's orbit has enough eccentricity to cause seasonal changes that would affect the life that evolved there, but how would the ancient Eridians have known about the concept of a day? (They know about it now, of course, but they've only been exploring space for a few centuries. There would be no practical reason for them to upend their timekeeping system just based on the discovery that they live on a spinning ball, so that knowledge had to have come much earlier in their history.)
  • Tides? On Earth, the solar tide is about a third the magnitude of the lunar; enough to make a perceptible effect — spring tides vs. neap tides.
    • That could be it. It wouldn't even be necessary for Erid to have noticeable spring and neap tides; the sun alone is enough to cause daily high/low tides, as it presumably would be on Erid as well (Erid has higher gravity, but is also closer to their star than Earth). If the tides alone affected the lives of the Eridians enough that they made it part of their calendar, that could imply they have a close ecological relationship with their oceans' shores.

Why no mention of music?

• There's no mention of music, other than as the source for the beetles' names. Since hearing is the Eridians' primary sense, why doesn't Grace play at least some samples of Earth music, to get Rocky's opinion? Meta level: if Weir didn't want to go into that, he could have covered it in a paragraph, with Rocky dismissing it as nearly mono-tonal, repetitive, whatever.
  • For Eridians, every song is acappella! That said, I could totally see human musicians composing songs where the music 'says' something in Eridian meant to accompany the human lyrics. Sort of like a round?

Were the coma-inducing systems tested on the crews before the fateful trip?

• Stratt's diligence to keep as much of the Hail Mary using standardized, tested hardware and software had limits, and one of these was the medical-bed coma procedure process and computer. The mission would've ended in TOTAL failure if all three crew died on the trip. Thankfully, the one person with enough scientific capacity to run the ship and solve the astrophage survived. There's no information in the book that implies or suggests that the prime and backup crews were put into comas to verify they'd be no complications in either the crewmember or in rectifying issues by the medical computer.
  • The coma technology was perfected by a company that was going to use it on Earth, and they had human test subjects at one point. Grace walks through a whole room full of artificially-comatose monkeys during a flashback. Stratt is unhappy about using the coma technology precisely because it is experimental, but decides it is less risky than keeping the crew all awake in a confined space the whole four-year trip.

Eridians weak to radiation?

• Shouldn't a creature whose body is mostly metal and ceramics with minimal organic parts be very resilient to radiation?
  • Their physiology most likely does give them increased protection of a certain type, but that protection isn't perfect, and their inability to recover from cellular damage means cosmic radiation is still dangerous to them even at the reduced dosages they receive. An analogy: consider a medieval swordfighter who wears heavy mail, but also has hemophilia. The armor might make him less likely to be cut, but when he does get cut, the damage it causes is far greater than it would be for someone else.

Block the Astrophage from getting to Venus?

• If they have the tech to build Hail Mary and the beetles, then they should be able to build a giant blocker to block them from getting to Venus, or make multiple runs to scoop them up in a large net of solar-sail-type material before they get there. Not only would they slow the dimming of the sun, giving the Hail Mary more time to work ad giving Earth more time to work on backup plans if the mission fails, they'd be collecting astrophage without having to breed them. The ship could even potentially fuel itself!
  • Who's to say they didn't? The entire book, including flashbacks, is from Grace's POV, so there's no telling what Earth might have tried after the Hail Mary departed. For all we know, the beetles never made it back to Earth and they found some other crazy solution that worked. Maybe a collector/blocker like you mentioned. Maybe they genetically engineered their own pathogen. Maybe they put satellites around Venus that lure astrophage away from the Sun using Petrova light.