We are supposed to graph velocity squared against period. My instructor specifically said:
The gradient of this graph is acceleration and
We should observe a trend of decreasing orbital velocities at an increasing rate.
My problem is that, from my knowledge, this graph should not be curved. How can an acceleration graph be curved?
I think it should be straight because acceleration is a rate of change, and you cannot have a rate increase at a rate. Further, the centripetal force formula does not suggest the graphical relationship we obtained.
My instructor said it has something to do with the inverse square law, and something being proportional to something and something obeys the inverse square law, hence this curve. I cannot confirm any of my knowledge because I don't have access to the sheet he gave to the class which, I think, showed a derivation of some sort.