Question on gravitation law derivation

Click For Summary
SUMMARY

The forum discussion centers on the derivation of Newton's Universal Law of Gravitation, specifically the mathematical ratios involved in understanding the relationship between angular velocity (ω), linear velocity (ν), distance (s), and orbital period (T). The user seeks clarification on the initial steps of the derivation, particularly the limits and ratios presented. Key ratios discussed include ω/ν = s/r and t/T = s/(2πr), which illustrate how changes in time and distance relate to each other in the context of orbital mechanics.

PREREQUISITES
  • Understanding of limits in calculus
  • Familiarity with angular and linear velocity concepts
  • Knowledge of orbital mechanics and period calculations
  • Basic grasp of trigonometric functions, particularly the use of π in circular motion
NEXT STEPS
  • Study the derivation of Newton's Universal Law of Gravitation in detail
  • Learn about the relationship between angular velocity and linear velocity in circular motion
  • Explore the concept of orbital periods and their calculations in celestial mechanics
  • Investigate the application of limits in physics, particularly in motion and gravitation
USEFUL FOR

Students of physics, particularly those studying classical mechanics, educators teaching gravitational concepts, and anyone interested in the mathematical foundations of orbital dynamics.

Thiafon
Messages
2
Reaction score
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; <br /> \lim_{t\rightarrow 0} {s} \rightarrow 0<br />
we have the following ratios
\frac{\omega}{\nu}=\frac{s}{r}, and \frac{t}{T}=\frac{s}{2πr}
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.
 
Last edited:
Physics news on Phys.org
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?
 
Yes, thank you a lot! I had kind of intuitive feeling about it, but I wasn't sure if it is correct.
 

Similar threads

Graduate Question about the Derivation of the Gravitational Law
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Find period of circular-orbiting source based on max observed freq
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Why must partialS/partialα_n = -β_n where S is the complete integral?
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Derivation of Hamilton's Principle: Questions
  • · Replies 19 ·
Replies
19
Views
2K
Undergrad Extending Newton's laws -- Is the concept of force still defined?
  • · Replies 35 ·
2
Replies
35
Views
5K
Undergrad Rolling Without Slipping
  • · Replies 59 ·
2
Replies
59
Views
5K
Graduate Deriving the lever law using infinitesimals
  • · Replies 10 ·
Replies
10
Views
2K
Undergrad Using reference frames for derivation of Lagrangian
  • · Replies 25 ·
Replies
25
Views
3K
Undergrad Deriving formula for kinetic energy
  • · Replies 3 ·
Replies
3
Views
1K
Deriving Newtonian law of gravitation
  • · Replies 6 ·
Replies
6
Views
2K