Viewpoint character is a junior flight officer / medic? on a routine passenger liner from Earth to somewhere (Mars?). Something goes horribly wrong with the engine (which is powered by an atomic pile of the 1950s one-glitch-turns-it-into-a-bomb variety, IIRC) and they have to evacuate. The ship carries life pods which can get them a safe distance away, but then they have to wait for Earth to send out an unmanned "high acceleration rescue vehicle" and rendezvous with it. The viewpoint character is tasked with maintaining communications with all the life pods (from his own life pod) and preventing the passengers from freaking out too much. One gets the impression that all of the orbital mechanics involved were carefully worked out, with the possible exception of a bit of a handwave on how much reaction mass the life pods could reasonably carry.
I read this novel in the mid-90s, but I'm pretty sure it is much older, probably 1950s-70s pulp SF.