# A question about conditions for Weightlessness

Tags: conditions, weightlessness
 P: 9 I read that if you are in a spaceship orbiting earth in a circular motion, the astronout feels weightless (meaning the normal force to the astronout is equal to zero). But according to newton laws equations you get: $N = \frac{GMm}{r^2} - \frac{mv^2}{r}$ and then if we assume N=0 (which is really what's happening according to my understanding), we get: $\frac{GMm}{r^2} = \frac{mv^2}{r}$ And I don't understand why is that true, if you can explain, or if there is any mistake in what i've said above, Thanks
force is $\frac {GmM}{r^2}$ and the acceleration is $\frac {v^2}{r}$