View source for Talk:Kepler's laws of planetary motion

{{talkheader}}
{{WikiProject banner shell|class=C|vital=yes|1=
{{WikiProject Mathematics|small= |importance=high }}
{{WikiProject Physics|importance=High}}
{{WikiProject Astronomy|importance=Top}}
}}
{{Archive box|auto=yes}}

{{User:MiszaBot/config
|maxarchivesize = 100K
|counter = 3
|minthreadsleft = 5
|minthreadstoarchive = 1
|algo = old(365d)
|archive = Talk:Kepler's laws of planetary motion/Archive %(counter)d
}}

__TOC__
{{Clear}}

== Supposed comparison ==

Under the heading "Comparison to Copernicus", the passage occurs, "...agrees with Copernicus: 1. The planetary orbit is a circle...". I was under the impression that Copernicus used many epicycles and was aware that the orbits of the planets are not exactly circular on a heliocentric basis. <small class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/82.173.223.232|82.173.223.232]] ([[User talk:82.173.223.232|talk]]) 14:44, 1 February 2015 (UTC)</small><!-- Template:Unsigned IP -->

I agree with the above comment.  I just read this and took the time to look here to see if anyone else noticed this mistake too.  It also belies many misconceptions about the history of astronomy that even professional astronomers often have. Nobody in the 1500s thought the planets orbited the sun in perfect circles.  This is clearly not the case, because the greatest elongation of mercury is not a constant.  In fact, Aristarchus of Samos proposed a heliocentric model, which was later rejected by Greek astronomers for many good reasons, including that it did not explain the non-constant nature of the greatest elongation of mercury.  (And other reasons too, most of which were resolved by Galileo.)

So, I would strongly advise getting rid of the comparison.   The important thing, if a comparison is to be made, is that Kepler put the sun in a special place.  Under Copernicus, the sun was kind-of-sort-of in the center of the planet's primary orbit.  But under Kepler, it was exactly at the location of on of the Ellipse's two foci.

In fact I was about to link this page to my students' astrophysics problem set, but I wanted to check if it was accurate and understandable first.   <!-- Template:Unsigned --><span class="autosigned" style="font-size:85%;">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Jwkeohane|Jwkeohane]] ([[User talk:Jwkeohane#top|talk]] • [[Special:Contributions/Jwkeohane|contribs]]) 16:02, 1 March 2021 (UTC)</span> <!--Autosigned by SineBot-->


:In historical perspective (somewhat simplified) [[Ptolemy]] made a model of the universe in which heavenly bodies encircled the earth in perfect circular orbits. There are of course many problems with this simple model, for example, because the earths rotational axis is tilted with respect to its path. Another problem is the irregular motion of the planets. Ptolemy had to account for these irregularities in order to improve the predictive value of his model. For the planets he therefore included epicycles. Another way of explaining the variations in the planets movements, is to assume that they do not encircle the earth but another object. So Copernicus made a model with the planets revolving around the sun in circular orbits. And of course, as the planets do not move in circular orbits, this simple model too had too many problems that prevented it from being accurate. So instead of being able to present a simple but accurate model, Copernicus too had to include many artificial tricks in order to improve the accuracy of his predictions. It is said that in the end, Copernicus' model was even more complicated than that of Ptolemy. But his general idea was that the planets moved in circular orbits. <small><span style="border:1px solid gray;padding:1px;background:#FFF"><span style="background:#79C">&nbsp;[[User:Wikiklaas|<span style="color:white;">'''Wiki'''</span>]][[User talk:Wikiklaas|<span style="color:white;">'''klaas'''</span>]]&nbsp;</span></span></small> 15:23, 4 February 2015 (UTC)

== Table ==

In Arthur Berry's History of Astronomy, published in 1898, a table appears in the chapter on Kepler. It seems to be a photo-copy from a book by Kepler. It seems to differ from the table in this article, under the heading "Third law". <!-- Template:Unsigned IP --><small class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/2A00:23C4:4E9F:D101:5CBE:469F:427D:3656|2A00:23C4:4E9F:D101:5CBE:469F:427D:3656]] ([[User talk:2A00:23C4:4E9F:D101:5CBE:469F:427D:3656#top|talk]]) 14:20, 1 June 2021 (UTC)</small>

==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.[[Special:Contributions/2600:1700:6759:B000:1C64:8308:33BC:E2D6|2600:1700:6759:B000:1C64:8308:33BC:E2D6]] ([[User talk:2600:1700:6759:B000:1C64:8308:33BC:E2D6|talk]]) 20:35, 26 August 2023 (UTC)Christopher L. Simpson

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

== Split Proposal ==

{{Discussion top|result=There is '''concensus against splitting the article for each of the three laws.''' [[User:Gramix13|Gramix13]] ([[User talk:Gramix13|talk]]) 00:36, 10 June 2025 (UTC)}}

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. [[User:Pygos|Pygos]] ([[User talk:Pygos|talk]]) 11:04, 28 January 2025 (UTC)

:This page, of course, shall remain, as it describes the underlying assumptions of the laws and their historical background. [[User:Pygos|Pygos]] ([[User talk:Pygos|talk]]) 11:07, 28 January 2025 (UTC)
:I support this change, provided a qualified Wikipedian can confirm that enough can be written on each individual law to fill out an article. [[User:JohnR1Roberts|JohnR1Roberts]] ([[User talk:JohnR1Roberts|talk]]) 13:08, 31 January 2025 (UTC)

:How would individual articles about each law be different from the existing sections in this article? - [[User:Parejkoj|Parejkoj]] ([[User talk:Parejkoj|talk]]) 18:02, 2 February 2025 (UTC)
: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. [[User:ZergTwo|ZergTwo]] ([[User talk:ZergTwo|talk]]) 23:59, 8 March 2025 (UTC)
: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. [[User:Panji pana|Panji pana]] ([[User talk:Panji pana|talk]]) 00:17, 18 March 2025 (UTC)
: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.  [[User:Lithopsian|Lithopsian]] ([[User talk:Lithopsian|talk]]) 14:24, 18 March 2025 (UTC)

{{Discussion bottom}}

== 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. [[User:MajorTom117|MajorTom117]] ([[User talk:MajorTom117|talk]]) 16:18, 1 May 2025 (UTC)

: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? --[[User:FyzixFighter|FyzixFighter]] ([[User talk:FyzixFighter|talk]]) 22:47, 1 May 2025 (UTC)
::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 [[User:MajorTom117|MajorTom117]] ([[User talk:MajorTom117|talk]]) 05:44, 2 May 2025 (UTC)
:::Perhaps I'm misunderstanding the formula. [[User:MajorTom117|MajorTom117]] ([[User talk:MajorTom117|talk]]) 05:47, 2 May 2025 (UTC)
::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. [[User:MajorTom117|MajorTom117]] ([[User talk:MajorTom117|talk]]) 12:21, 2 May 2025 (UTC)