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Question on gravitation law derivation 
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#1
Feb213, 07:01 PM

P: 2

Hi, guys.
I was wondering on Newton's Gravity Law derivation, and I found this page: http://www.relativitycalculator.com/...vity_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 precalculus, and calculus, so concept of limits is familiar to me) Thanks in advance. 


#2
Feb313, 10:52 AM

Mentor
P: 11,485

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? 


#3
Feb313, 11:03 AM

P: 2

Yes, thank you a lot! I had kind of intuitive feeling about it, but I wasn't sure if it is correct.



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