In Project Hail Mary, Grace and Rocky only have enough fuel to reach either Earth or Rocky's homeworld Erid, and they choose to go to Erid.
Why do they make this choice when it is stated that the Eridians have many decades before The Phage causes serious problems on their planet, meaning that there would be plenty of time to reach Earth, refuel and then return to Erid? The journey to Erid could be made at higher acceleration if only Rocky went, or a robot like if the Beatles were sent instead.
Given that the two of them know that the situation on Earth is more urgent, doesn't it make more sense for them to go there first?