I'm confused on how you get the formula v=root(2GM/R²). I know you can use work=forcexdisplacement (W=Fd) so F=W/d. W=½mv² and R=d. Hence, F=½mv²/R Equate that to F=GmM/R² and rearrange to get v=root(2GM/R²). That makes sense as it involves the kinetic energy needed/work done in reaching orbit (or is it for escaping orbit?). However, why can't you use the formula F=mv²/R and equate that to F=GMm/R² ? It gives you v=root(GM/R²). That's slightly different to the formula that involves kinetic energy.