We are supposed to graph velocity squared against period. My instructor specifically said:
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The gradient of this graph is acceleration and
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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.
Best Answer
I don't know how this is supposed to simulate planetary motion, but we can still look at what data you would expect. The force on the stopper is $\frac {mv^2}r$, which if there is no friction (good luck!) equals the gravitational force on the masses at the bottom. We would therefore expect that for given mass on the bottom, $r \propto v^2$, which doesn't look like your data at all. Were you changing the mass on the bottom as you changed $r$? That would make a better simulation, as the force of gravity is stronger when the satellite is close to the planet.
As the gravitational force is an inverse square law, for your simulation $M$, the mass at the bottom should be proportional to $\frac 1{r^2}$. In that case we would have $\frac {v^2}r \propto \frac1{r^2}$, or $rv^2$ is a constant. Your data is not too far from this.