Proof to Kepler's first and second laws

Click For Summary

Discussion Overview

The discussion revolves around finding proofs for Kepler's first and second laws of planetary motion. Participants explore the complexity of these proofs and their suitability for a 10th-grade understanding, touching on various mathematical approaches and historical context.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant seeks a simple proof for Kepler's laws, indicating they are a 10th-grade student.
  • Another participant suggests that the definition of "simple" varies and mentions that Lagrange mechanics could provide a straightforward proof, though it may be too advanced for a typical 10th-grade class.
  • It is noted that the second law can be derived from the conservation of angular momentum, which may be more accessible.
  • A historical perspective is provided, mentioning that Kepler's laws were derived from Tycho Brahe's observations and that Newton later explained them using geometric principles.
  • Other derivations involving vector calculus are mentioned as alternatives, but their complexity is not specified.
  • A participant expresses understanding of basic calculus, which may influence their ability to grasp the proofs discussed.

Areas of Agreement / Disagreement

Participants generally agree that the simplicity of the proofs is subjective and that different mathematical approaches exist. However, there is no consensus on a specific proof that is deemed simple enough for a 10th-grade student.

Contextual Notes

The discussion highlights the varying definitions of simplicity in mathematical proofs and the potential limitations of participants' mathematical backgrounds in understanding advanced concepts.

Shahar
Messages
43
Reaction score
2
I am a 10th grade student, and I tried for a few weeks now to find a proof to Kepler first and second laws.
Is there a simple proof to Kepler' s laws?
 
Astronomy news on Phys.org
As with most things, this depends on your definition of "simple". You can do it pretty simple in Lagrange mechanics, but this is quite far from the scope of your typical 10th grade class. The easiest one is probably the second law, which essentially is just the conservation of angular momentum.
 
  • Like
Likes   Reactions: Shahar
Shahar said:
I am a 10th grade student, and I tried for a few weeks now to find a proof to Kepler first and second laws.
Is there a simple proof to Kepler' s laws?
It depends on what you consider to be "simple".

Kepler derived his three laws from examining astronomical observations made by Tycho Brahe. It took many years of work for Kepler to deduce his laws, but an explanation of why these laws were true had to wait until Isaac Newton came along. He gave an explanation in his Principia which was based on geometric principles. Other derivations involving vector calculus have been offered.
 
  • Like
Likes   Reactions: Shahar
Orodruin said:
As with most things, this depends on your definition of "simple". You can do it pretty simple in Lagrange mechanics, but this is quite far from the scope of your typical 10th grade class. The easiest one is probably the second law, which essentially is just the conservation of angular momentum.

Oh yeah, I found a solution using conversation of angular momentum.

Well I understand basic calculus(derivatives, basic integrations).
 

Similar threads

Undergrad Data Model of Kepler's Second Law of Planetary Motion
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Estimating Mass of Central Object Using S2's Orbit Motion and Kepler's 3rd Law
  • · Replies 3 ·
Replies
3
Views
2K
High School Re-evaluating Dark Matter and Kepler's Law in Spiral Galaxies
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Kepler 3rd law for circular orbits
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Separating Masses in Kepler's Third Law
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad How did Kepler derive his laws WITHOUT law of gravitation?
  • · Replies 11 ·
Replies
11
Views
3K
Using Kepler's laws to calculate elliptical planetary motion
  • · Replies 7 ·
Replies
7
Views
1K
Undergrad Mathematical Proof of Kepler's First Law of Orbits
  • · Replies 5 ·
Replies
5
Views
4K
Tusi discovering laws of planetary motion before Kepler?
  • · Replies 1 ·
Replies
1
Views
2K
Quantum Books recommendation covering the Hydrogen atom and Kepler's laws (separately)
  • · Replies 4 ·
Replies
4
Views
2K