Question on gravitation law derivation

In summary, the conversation is about understanding the first step of the derivation of Newton's Gravity Law on a webpage. The ratios of the angular velocity to the frequency and time to the orbital period are explained, and it is clarified that if one of these values is doubled, the corresponding distance traveled is also doubled. It is mentioned that the concept of limits is necessary to understand this step. The person asking the question expresses their gratitude for the explanation.
  • #1
Thiafon
2
0
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.
 
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  • #2
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
Yes, thank you a lot! I had kind of intuitive feeling about it, but I wasn't sure if it is correct.
 

Related to Question on gravitation law derivation

What is the gravitation law derivation?

The gravitation law derivation is a mathematical process used to derive the law of universal gravitation, which explains the force of attraction between two objects due to their mass and distance.

Who first derived the law of gravitation?

The law of universal gravitation was first derived by Sir Isaac Newton in 1687 in his book "Philosophiae Naturalis Principia Mathematica".

What are the key equations used in the derivation of the gravitation law?

The key equations used in the derivation of the gravitation law include Newton's second law of motion, the law of conservation of momentum, and Kepler's laws of planetary motion.

How does the gravitation law derivation relate to other laws of physics?

The gravitation law derivation is related to other laws of physics, such as Newton's laws of motion and the law of conservation of energy. It also plays a crucial role in understanding the behavior of celestial bodies in the universe.

What are the practical applications of the gravitation law derivation?

The gravitation law derivation has many practical applications, including predicting the motion of planets, satellites, and other celestial bodies, as well as calculating the force of gravity between objects on Earth.

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