Talk:Kepler's laws of planetary motion

Is epicycles really wrong?

As of the date and time I'm typing this, this article contains the text "The planetary orbit is not a circle with epicycles, but an ellipse." But didn't Fourier show that ANY PATH, any path whatsoever, can be decomposed in some way so that it's the path of a point moving at constant angular speed about a circle's center that itself (the circle's center) is also moving with uniform angular speed about another circle's center, etc. for as many circles as is needed to result in the desired path? I swear that I have seen animations of a point carried on a circle carried on another circle for perhaps a few hundred circles-carried-on-circles, such that by programming (1) the radius of each circle (all radii different if need be), and (2) the uniform speed at which each circle-center travels around the circle on which it is anchored (all different speeds if need be), and (3) the starting-angles for each circle-center with respect to the center of the circle on which it travels (all different if need be), the resulting path of the last point is the same as a portrait of Fourier himself that you can draw using a pencil in one continuous tracing without lifting up the pencil. It may have taken dozens or hundreds of circles to achieve that, but an ellipse is nowhere near as complicated as a portrait of Fourier and surely Fourier's method can be used to decompose the non-random motion of a point (even if it's not at a constant linear speed, nor even a constant angular speed around the ellipse's center or a focus, but, rather, a speed that varies such that it traces out sectors of equal area (connecting to a focus) in equal time. Surely even adding THAT wrinkle to a path taken on an ellipse doesn't make it impossible for Fourier's method to decompose that path into circles whose centers ride along other circles, if a portrait of Fourier himself can be so decomposed. It may be true that the planets travel around the Sun in ellipses, but that doesn't make it false that they travel around on circles that are traveling around on other circles. The latter idea is NOT refuted by, nor incompatible with, the former idea. The ellipses ARE the results of motions of circles upon circles that are moving on circles, etc.

Bear in mind that Kepler didn't have computers, and that given a choice between (a) expressing the orbits of planets using the SHORTER equations that result from saying "they travel in ellipses at varying speeds such that equal areas of sectors to the Sun will be swept in equal times" versus (b) the far-longer (but mathematically, logically, intuitively, and visually equivalent) equations that would result from adding all the motions of circles-on-circles-on-still further circles, he chose (a) NOT because (a) is true and (b) is false, but, rather, chose (a) because they're both true but (a) reduces writer's-cramp and spends less money on parchment and ink.2600:1700:6759:B000:1C64:8308:33BC:E2D6 (talk) 20:35, 26 August 2023 (UTC)Christopher L. Simpson[reply]

Yes, it's wrong. Did you really expect a different answer? 98.248.84.55 (talk) 04:42, 27 August 2023 (UTC)[reply]

Split Proposal

The following discussion is closed. Please do not modify it. Subsequent comments should be made in a new section. A summary of the conclusions reached follows.
There is concensus against splitting the article for each of the three laws. Gramix13 (talk) 00:36, 10 June 2025 (UTC)[reply]

Greetings! When I came across this page, I'm rather surprised that there are no individual articles for all three laws. This notion is simply due to the fact that they are so important, and should deserve individual articles for more detailed description. However, I'm not very sure, so I'm asking for opinions here. Pygos (talk) 11:04, 28 January 2025 (UTC)[reply]

This page, of course, shall remain, as it describes the underlying assumptions of the laws and their historical background. Pygos (talk) 11:07, 28 January 2025 (UTC)[reply]
I support this change, provided a qualified Wikipedian can confirm that enough can be written on each individual law to fill out an article. JohnR1Roberts (talk) 13:08, 31 January 2025 (UTC)[reply]
How would individual articles about each law be different from the existing sections in this article? - Parejkoj (talk) 18:02, 2 February 2025 (UTC)[reply]
I can't see how each law is notable enough for a separate article. Additionally, I am unsure if there is sufficient information available for each law to create a comprehensive and well-written article. ZergTwo (talk) 23:59, 8 March 2025 (UTC)[reply]
I think that three seperate article are unnecessary. Newton's laws of motion is a single page despite having more fundamental (and well known and documented) laws than Kepler's. Each of Kepler's laws are fairly simple and can be covered succinctly within a single section rather than their own articles as is done here. Panji pana (talk) 00:17, 18 March 2025 (UTC)[reply]
Can't see how this would be an improvement. Individual discussions/formulations of the three laws forms a relatively small part of the article, so we'd either end up with most of the current article and some content hidden elsewhere, or three highly-repetitive articles, none of which provide full coverage of the subject. See WP:SPLIT fo reasons why to split an article; this doesn't seem to qualify on either the size or content criteria. Lithopsian (talk) 14:24, 18 March 2025 (UTC)[reply]
The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

First Law Formulary issue

The mathematical equation for the semi-latus rectum (the harmonic mean portion) seems to be incorrect if I understand the Harmonic mean#Harmonic mean of two or three numbers correctly. MajorTom117 (talk) 16:18, 1 May 2025 (UTC)[reply]

It looks correct to me. Can you clarify what about the equation here doesn't match up with the harmonic mean definition at the other article? --FyzixFighter (talk) 22:47, 1 May 2025 (UTC)[reply]
The current formula uses the (number)^-1 equation as seen near the top of the Harmonic Mean article. I'm saying it should be using the special cases formula for having only two numbers. That equation being found in the "Harmonic mean of two or three numbers" tab MajorTom117 (talk) 05:44, 2 May 2025 (UTC)[reply]
Perhaps I'm misunderstanding the formula. MajorTom117 (talk) 05:47, 2 May 2025 (UTC)[reply]
After further review it seems I missed the keyword "can" be written as. The original formula is not incorrect as they are interchangeable(?) as long as the parameters are met. New suggestion would be to keep the current formula but also acknowledging that I can be written in the format I explained. MajorTom117 (talk) 12:21, 2 May 2025 (UTC)[reply]

Change tables in the third law from AU^3/days^2 to AU^3/year^2

Currently, the value is approximately 7.5 * 10^{-6}, which equals 1/365^2. Therefore, the switch from days to years will change the value from a scary, misunderstood number to 1. The figure next to it already uses AU/year, so the change would streamline the article. Orkolus (talk) 08:33, 31 August 2025 (UTC)[reply]

Modern Data Nessesity

Is the modern data for comparison table in the third law really necessary for the article? It has no citation backing it up and it does not seem to convey any extra meaning to the article. Script7921 (talk) 18:55, 16 December 2025 (UTC)[reply]

I guess the values maybe normally available via http://nssdc.gsfc.nasa.gov/planetary/factsheet/planet_table_ratio.html Johnjbarton (talk) 19:51, 16 December 2025 (UTC)[reply]
allikas: https://en.wikipedia.org/wiki/Talk:Kepler%27s_laws_of_planetary_motion