dede2002 wrote:In fact the formula is very simple:
To calculate the takeoff speed it is v = root of r * g
I don't know what you call "take-off" speed (I think you've already seen a lot of planes take off with a much slower speed)
what you are calculating there is the speed of orbiting in fact (that of a circular orbit).
But I don't know how to explain the "2" ...
there is a theoretical explanation based on the virial theorem ...
in fact it comes from the fact that the potential energy is in r ^ (- 1} (i.e. in 1 / r and that 2 is 1 +1 . (ie if the gravitation was in "r ^ (- n)" or 1 / r ^ n we would have a factor n + 1 between the two).