Hi, guys. I was wondering on Newton's Gravity Law derivation, and I found this page: http://www.relativitycalculator.com/Newton_Universal_Gravity_Law.shtml Everything seems clear, but the first step is just killing me, because I can't get it. Assuming small incremental changes in s; [tex] \lim_{t\rightarrow 0} {s} \rightarrow 0 [/tex] we have the following ratios [itex]\frac{\omega}{\nu}[/itex]=[itex]\frac{s}{r}[/itex], and [itex]\frac{t}{T}[/itex]=[itex]\frac{s}{2πr}[/itex] Could someone help me out? Explain, or just say, which part of math do I have to cover in order to understand that? (btw, I did pre-calculus, and calculus, so concept of limits is familiar to me) Thanks in advance.
It's just telling you the ratios of everything. The vector changes at the same rate that the distance traveled does since v and r are equal. If you double w you double s as well. In the 2nd ratio, T is the total time of one orbital period and 2*Pi*R is the total distance of the orbit. As t changes, which is the time it takes to transverse the incremental time period s, s changes as well. If you double t you double s. Does that make sense?