Talk:Kepler's laws of planetary motion

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. — Preceding unsigned comment added by 82.173.223.232 (talk) 14:44, 1 February 2015 (UTC)

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. — Preceding unsigned comment added by Jwkeohane (talk • contribs) 16:02, 1 March 2021 (UTC)

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.  Wikiklaas  15:23, 4 February 2015 (UTC)

Restatement of Kepler's Third Law

Law number 3 is stated incorrectly in two places on the page. It makes a statement about a single planet. The correct version should make a statement about multiple planets.

Two places on the page state "The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit." One other place makes a correct statement by quoting directly from Kepler: "the ratio which exists between the period times of any two planets is precisely the ratio of the 3/2th power of the mean distance".

I suggest substituting a slightly more general statement than Kepler's for the two incorrect statements: "The ratio of the square of an object's ["orbital period"] with the cube of the ["semi-major axis"] of its orbit is the same for all objects orbiting the same primary."

SpencerRugaber (talk) 19:15, 5 July 2020 (UTC)

Proposed Modification of the Third Law

A new book, "Air of Doubt" (ISBN: 979-8697917329) by Dr. Frank A Tinker, offers an argument for modifying Kepler's Third Law in the same spirit as Newton's modification adding planet masses. The proposal is to add a factor involving the orbital energy to improve the comparison of two planet's orbits. In doing so, he resolves the Mercury perihelion precession anomaly without resorting to General Relativity.

For completeness, it appears that reference and proposal should be included in this topic. Link: www.airofdoubt.com.

Yes, that is me. But I'm not about to edit this without discussion. AoDFT (talk) 01:04, 20 October 2020 (UTC)

The source is WP:self-published and therefore not acceptable for Wikipedia. Femke Nijsse (talk) 18:04, 28 October 2020 (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". — Preceding unsigned comment added by 2A00:23C4:4E9F:D101:5CBE:469F:427D:3656 (talk) 14:20, 1 June 2021 (UTC)

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

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