Centripetal acceleration of objects in orbit around the Earth

Hi all. The answer to this might be trivial. If it is, sorry for posting. If you calculate the acceleration due to gravity of an orbiting satellite, it could be around 8.5-9.5m.s-2, depending. So, it's tangential velocity is such that as it falls towards earth, earth curves away and the satellite never comes closer to earth - here's my problem. If it's is accelerating towards earth at say 9m.s-2, then every second it's downward velocity increases by 9m.s-1. If it continually accelerates in this way, eventually you have massive downward velocity, yet tangential velocity remains constant...the satellite should come crashing down. So, perhaps it's reached terminal downward velocity? But there's scant air resistance.. what gives?

jbriggs444
Homework Helper
"downwards" is not a fixed direction. As the satellite moves along its orbital path, "downwards" now is different from "downwards" a moment ago and from "downwards" a moment from now. After 1/4 of a complete orbit, the new "downwards" acceleration is no longer adding velocity along the original direction at all.

sophiecentaur