Talk:Kepler's laws of planetary motion

Figure 1

The size of the lettering within Figure 1 could be increased, to make it readable.

Neither the figure nor its caption seems to indicate where the ends of the distances a1 & a2 are.

82.163.24.100 (talk) 13:44, 27 August 2009 (UTC)

Shouldn't this say "the star" not the sun, as this diagram does not show our own solar system, but one with exaggerated elliptical motion? Richard LaBorde (talk) 23:19, 24 May 2010 (UTC)

I see no reason to say "surface area" rather than just "area". No surface is involved. Jeff Root (talk) 13:55, 27 January 2011 (UTC)

Stable orbits

According to the third law, the period of a planetary motion is propotional to the 3/2 th power of radius ( or semi major axis. ) But this is an idealised case. In reality, there is a very diffuse gas in the Solar system and the motion of the planets around Sun may be retarded by this gas. To be sure, the retarding effect is negligable. But the cumulative effect over millions of years may be considerable, which means that the delicate balance between the gravitational and cetrifugal forces is in danger. But luckily, we haven't observed any spirally inward motion of any planet. I think that the article must have a section to explain how the planets maintain their orbits over billions of years. Nedim Ardoğa (talk) 06:33, 15 October 2009 (UTC)

I think that this subject belongs in another article, perhaps secular variations of the planetary orbits. This article is about Kepler's laws.

NPOV

Stating these laws in terms of the sun is heliocentric. The intro should either place the laws firmly into their historic context, or should avoid any biased language. -Craig Pemberton (talk) 21:15, 25 October 2009 (UTC)

this argument is absurd because the historical context is heliocentric. "Kepler's laws are concerned with the motion of the planets around the sun. Newton's laws of motion in general are concerned with the motion of objects subject to impressed forces." if you have evidence contradicting this, please offer it. -- 99.233.186.4 (talk) 02:32, 29 October 2009 (UTC)

I never claimed the laws were not heliocentric, only that the article is being heliocentric because the intro gives no such context. Even what you've said above would improve the article immensely in this regard. As it stands there is no such context. When I find the time I'll take a stab reworking the intro. -Craig Pemberton (talk) 03:53, 29 October 2009 (UTC)

As all wikipedia readers live in this solar system, being heliocentric does not violate WP:NPOV. Bo Jacoby (talk) 22:48, 5 November 2009 (UTC).

merge proposal opposed

This is to oppose the recent merge proposal in respect of the section 'Position as a function of time': Discussion is offered here. Terry0051 (talk) 00:08, 29 November 2009 (UTC)

Current text

The current text says, "... Kepler stated these laws as they apply to the Sun and the planets". The four brightest moons of Jupiter were coming to the notice of the public in Europe in 1610. I am not sure who was the first to note that the three laws applied to the four moons. —Preceding unsigned comment added by 86.157.177.188 (talk) 13:44, 29 December 2009 (UTC)

Kepler used the observations of Tycho Brahe who did not use a telescope and consequently did not see the moons of Jupiter. Bo Jacoby (talk) 13:16, 4 February 2010 (UTC).

The four brightest moons of Jupiter are visible without a telescope. I agree that Tycho

probably over-looked them in point of fact. Kepler himself had bad eye-sight

and probably could not see any moons of Jupiter. Some one other than Kepler was probably the first to say Kepler's laws applied to the four moons. —Preceding unsigned comment added by 86.177.254.83 (talk) 09:22, 19 May 2010 (UTC)

"The four brightest moons of Jupiter are visible without a telescope." I really doubt that. Truly astounding seeing and eyesight would be required. It is geometrically plausible, Callisto getting as far 10 minutes of arc away from Jupiter at opposition (the naked eye's angular resolution is about one minute of arc). The problem is glare: the apparent magnitudes are -2.94 vs. 5.65, a factor of 2700 ratio (note also how close Callisto's apparent magnitude is to the naked eye's limit of about magnitude 6). Urhixidur (talk) 15:14, 23 November 2011 (UTC)

See Godefroy Wendelin. Wendelin noted that Kepler's third law applied to the moons of Jupiter. He wrote in 1643. Glare can be eliminated by getting Jupiter behind an opaque object, such as some brick-work. — Preceding unsigned comment added by 86.171.253.163 (talk) 10:36, 28 January 2012 (UTC)

Relations now known as Kepler's laws: problems over accuracy

The text of recent edits says: "Almost a century later, Isaac Newton was able to derive Kepler's relationships from Newton's own laws of motion and law of universal gravitation, using classical Euclidean geometry."

The corresponding earlier text said: "Later, Newton's work showed mathematically how the three relationships resulted from a central gravitational attraction according to an inverse-square law, as an approximation that would become more exact as the relevant planetary masses could be assumed smaller in relation to the mass of the sun and as the planetary mutual perturbations could be thus ignored."

Maybe the older text was not of the best, but there is a problem about the new text. What Newton derived was different from Kepler's relationships (at least as Kepler stated them). He showed that relationships of that form would prevail only in certain idealized circumstances that don't occur naturally (e.g. 2 bodies only, and/or orbiting bodies of vanishingly small mass), and specifically, that in a multi-planet system they only approach exactness as the planetary masses tend towards zero. He stated correctly that the relationships are not exactly fulfilled in the real solar system. (As approximate observations, the "laws" are of course approximately true enough to the levels of accuracy achievable in Kepler's time.)

What is likely to happen, if the distinction between approximation and exactness is not carefully maintained here according to the sources, is that readers will come away with the (mis)understanding that Kepler found and stated the laws that apply to the planets' motions and Newton then proved what Kepler had stated. This is both untrue to the reliable sources, and likely to lead to all sorts of faulty conclusions if relied on by readers.

Part of the problem of faithfulness to the sources here is that while the sources do show that "Kepler's laws" have been called "laws" for about 270 years (though not in the time of Kepler or Newton), their status as "laws" is something very peculiar, seeing that the sources also show that they are not (exactly) true as Kepler stated them, and that what Newton proved was not (exactly) what Kepler stated.

The article text does therefore seem to need some more work including in the lead section. This looks like a case where the inevitable and necessary process of summarizing is specially sensitive, because it can easily change the sense of what is summarized (and inadvertently falsify it). Terry0051 (talk) 21:55, 29 December 2009 (UTC)

Copernicus was not exactly right because Kepler's laws are more precise. Kepler's laws are not exact because Newton's laws are better. Newton's laws are not exact because general relativity is better. General relativity is not exact because it doesn't take quantum mechanics into account. Probably no natural law is exactly true. Bo Jacoby (talk) 09:57, 4 February 2010 (UTC).

Thank you for your response.
(1) Before your edit, the intro section was, in an important respect, in accordance with the reliable sources here. The sources clearly identify Kepler's 'laws' as approximate (and also show that they were not called 'laws' in Kepler's time or for a century afterwards.) Because this is (to some people) a surprising idea (see the G E Smith source cited in the article for support and explanation of that point), it seems important that the intro also tries to offer the reader a 'handle' on the true position, with citations. Your edit took away from the intro section the essential qualification that the 'laws' are not exact, took away the inline references to the citations, and left incorrect and unsupported statements, untrue to the cited reliable sources, that Kepler's laws apply (without the qualification 'approximately') to the planetary system and other planetary systems etc.
(2) Your post seems to try to brush aside the approximate character of the Kepler relationships, and to suggest that this is the same as, say, the approximate character of Newton's laws when seen in the light of relativity. Where do you find support for that? I can only suggest that you look at the already-cited sources on this matter (especially the cited items by G E Smith and Curtis Wilson.) And where is there support in sources for the 'because' statements in your post? It seems unlikely that such sources are available; all of those 'because' statements appear to be false. As a specific example, sources show that the exactness/inexactness of the relationships or laws that you mention has to do with their comparison to physical reality, in other words it's about how well they 'model' physical reality -- it's not "because" of the existence of later or other theories.
(3) I have no problem with a history section -- as long as the result is supported by the reliable sources and clearly conveys the content to the reader. But the introductory section still needs to be left in a state that is consistent with the sources, and properly foreshadows the citation-supported content, not to contradict it. Terry0051 (talk) 11:44, 4 February 2010 (UTC)

1. I merely moved the historical information away from the introduction and into a special section.
2. The Perihelion_precession_of_Mercury is a physical reality accounted for by general relativity, but not by classical mechanics.
3. The introductory section should be a summary. References to sources are found later in the article.

Do you object against the use of the word law for a statement that is only approximately true? Well, a lot of approximate rules are called law in science, see Physical law#Laws_as_approximations. Bo Jacoby (talk) 12:33, 4 February 2010 (UTC).

About your point 1: Agreed your edit was a move, but it was not a 'mere' move; it took away from the introductory section the previous mention of characteristics essential to the correct meaning according to the sources.

About your point 2: Yes, I agree the facts about the perihelion precession of Mercury -- but that doesn't seem to say anything about the current topic. General relativity is still standing up well (last I heard) to tests of its accuracy. Newton's theory also stood up accurately to tests for a time, and it was only after about a century and a half (towards the end of the 19th century), that it became clear that the Mercury phenomenon was beyond its explanation. But in contrast to both of those, there never was any time when the Kepler 'laws' looked accurate without observations being known that were contradictory to their accuracy. Even Kepler himself noticed some of the discrepancies, as per the cited sources.

About your point 3: Agreed the introductory section should be a summary: but of course it also should not be a misleading summary. (I believe there is no rule against references to citations in an introductory section. They are also important in a subject like this.)

About "Laws as approximations", the article-section to which you refer lacks support from any citation. I think it will be found that the position shown by reliable sources is rather different from the oversimplified version that the unsupported article sets out. Answering your question "Do you object against the use of the word law for a statement that is only approximately true?", I have no problem with anything that clearly accords with the sources, and is not misleading. The present case is possibly unusual (see earlier posts in this section). If the characteristics discussed go without mention, then the resulting oversimplified statements are shown by the sources to be incorrect and misleading. (Just to try and avoid misunderstanding: it's worth reminding that the 'misleading' enters so far as the 'laws' are said to apply to the solar system bodies without qualification as to their approximate character -- and Kepler's statements were indeed about the planets in the solar system. By contrast, relationships with the same form as Kepler's laws were shown by Newton to apply exactly in idealized systems, e.g. the limit case of planetary masses tending to zero. But the limit cases of accuracy are not the real cases found in nature.) User:Terry0051|Terry0051]] (talk) 20:33, 4 February 2010 (UTC)

I suggest that you reestablish my edit and improve the article from there on, rather than just having it reverted, according to the rules of Wikipedia:Reverting.

It seems that we agree that a section on history is appropriate.

That physical laws are only approximately true is the rule rather than the exception, e.g. Boyles law. Newton was aware that his theory of gravitation was unlikely to be the final truth because instantaneous action at a distance is unexplicable. Einstein was aware that his general theory of relativity was unlikely to be the final truth because is does not take quantum mechanics into account. So that Kepler also noticed some discrepancies is not in contrast to Newton and Einstein.

Bo Jacoby (talk) 10:03, 5 February 2010 (UTC).

Thank you for your further comment. Yes, we are agreed that a history section is appropriate. I also agree that some shortening of the introductory paragraphs is appropriate too. Hopefully, consensus can be reached at least on the central points, and because of your suggestion I have just now made an edit that implements both the intro-shortening and the history section along a generally similar format to the one you chose, and I believe it is also consistent with the desiderata about accuracy.

It seems that you may be suggesting that my revert of your former edit was contrary to WP:Reverting, but if necessary, I would certainly point to details of the nature of the edit, and the history that went before it, and defend both the substance of the revert and the procedure adopted as in accord with the guideline. It seems desirable, and helpful to the reliability of the encyclopedia, that new edits respect any accuracy points that are already on the recent edit record of an article and its talk page. Perhaps there is no need for me to go further at present, it may be that there is sufficient agreement on a few main editing issues. Terry0051 (talk) 20:19, 5 February 2010 (UTC)

1. Why write "The relationships now known as Kepler's laws" instead of simply "Kepler's laws"? It adds nothing to the meaning or understanding.
2. Why highlight the approximate nature of Kepler's laws? They are not special in this respect.
3. The rule for reverting is: Don't revert a good faith edit.

Bo Jacoby (talk) 10:14, 6 February 2010 (UTC).

1 "The relationships now known as Kepler's laws": This originates in the sources, see for example page 73 in the article on Johannes Kepler by O Gingerich in Planetary Astronomy from the Renaissance to the Rise of Astrophysics, Part A : Tycho Brahe to Newton, Volume 2, Part 1; eds. René Taton, Curtis Wilson, Michael Hoskin (Cambridge, 1995, CUP), for a reference to "the three relationships now called Kepler's laws". (I also refer again to the other already-cited sources, especially the G E Smith and C Wilson references -- as well as to the posts here that preceded your edit -- for the reasons why this is significant, and why for the general reader it adds to the meaning and understanding.)

2 About the approximate nature of the laws: Again I refer you to the already-cited sources, esp. the G E Smith (2007) citation, for a better explanation than I have succeeded in giving, about why this is specially significant in connection with Kepler's laws.

3 Reverting: I refer to the article (wp:reverting) itself.

Terry0051 (talk) 11:12, 6 February 2010 (UTC)

1. Your link page 73 says: "the Epitome astronomiae Copernicanae gave a systematic tretment of all of heliocentric astronomy including the three relationships now called Kepler's laws." This means that the relationships were not called Kepler's laws in the Epitome astronomiae Copernicanae, but now they are called Kepler's laws, so we should call them that.
2. Surely Kepler's laws are approximate, but so are the other planetary theories of Ptolemaios, Copernicus, Newton and Einstein, so it is not specific for Kepler's laws.
3. wp: reverting says: "Revert vandalism on sight, but revert a good faith edit only as a last resort".

Bo Jacoby (talk) 14:03, 6 February 2010 (UTC).

1: Please do not forget the effects of all of the other references referred to in the discussion and cited in the article.

2: The cited sources explain how the degree of approximation was different and rougher here than in the later examples, and actually known to be so by reference to observations known and available in Kepler's & Newton's time.

3: I am sorry that I could not see any alternative to reverting your edit, but please would you also bear in mind: that the error reintroduced had recently been mentioned on the talk page and in the recent edit history; the text for which you altered the meaning was clearly supported by the cited reliable sources; you did not attempt to seek any consensus for your changes; and the nature of your edit seems to indicate that you did not make any attempt to take into account the matters that had previously been discussed in thh edit summaries and talk page. As against all of that, having the introduction stand with wrong information in spite of all of the above points is a substantial negative. I appeal to your sense of professionalism to respect the need for the encyclopedia articles to rely on support in reliable sources. I have taken the trouble to reintroduce at your suggestion the presentational changes that you wanted to bring to the opening sections. I note that all of the arguments about content that you have brought to the present discussion lack any reference to reliable sources.

Terry0051 (talk) 15:18, 6 February 2010 (UTC)

1. The reference you relied upon did not support your point of view. Of course Kepler's laws are called Kepler's laws.
2. A discussion on the accuracy of planetary theories would be nice, but not within the scope of this article.
3. Apology accepted. You are not precise in what you call "wrong information". I refer to C.D.Murray and S.F.Dermott, Solar System Dynamics. See [1].

Bo Jacoby (talk) 02:06, 7 February 2010 (UTC).

It might be worth mentioning that Kepler's second law was originally that the speed of a planet varies in inverse proportion to distance from the sun (i.e., not correct), and Kepler derived the correct form from that by means of an erroneous argument (as described in both Thomas Kuhn's The Copernican Revolution and Richard S. Westfall's The Construction of Modern Science). Lippard (talk) 22:14, 24 February 2010 (UTC)

And yet it does work out that the inverse of the square of the velocity of a planet is directly proportional to its radius. Uglysses —Preceding undated comment added 19:59, 14 March 2011 (UTC).

Oh no!! TASDELEN´s recent changes (May 5th) are in bad form, and seem inflammatory, overly opinionated, and likely to confuse and mislead the new reader. Will somebody please edit?

77.249.214.182 (talk) 15:08, 5 May 2010 (UTC)

As

Under the heading "Generality", the phrase "as to know" appears. I am not sure what it means. It is true that Kepler's laws apply approximately out-side the Solar System. —Preceding unsigned comment added by 81.154.6.133 (talk) 08:50, 25 May 2010 (UTC)

I rephrased it.--Patrick (talk) 09:05, 25 May 2010 (UTC)

Variables

Throughout the article there is heavy use of variables but some of these are never defined. A section in its own right which defined each of this would be very helpful. The biggest issue is with M. It is only ever defined as the mean anomaly but later it is used as the mass of the sun, though that it is being used as such is never stated. Que? (talk) 02:46, 2 June 2010 (UTC)

The M is used first as the mass of a star with an exoplanet around it. The formula on exoplanets is neither necessary nor sufficient in this context and I am going to remove it. Bo Jacoby (talk) 08:12, 2 June 2010 (UTC).

I also inserted explanations for the variables in Newton's laws. It is not good that the mean anomaly and the sun mass share the same symbol M. What change do you suggest? Bo Jacoby (talk) 08:40, 2 June 2010 (UTC).

Delete "Estimating the eccentricity of earth orbit"?

The section "Estimating the eccentricity of earth orbit" seems to be out of place in the article. It's not really relevant to the rest of the article, is inaccurate and is unreferenced. Its presence does not enhance the rest of the article in any way. I do not see any compelling reason why it should be retained. -- B.D.Mills  (T, C) 04:17, 13 July 2010 (UTC)

It is commonly complained that wikipedia math articles are too theoretical to be comprehensible to newcomers. A tiny bit of explanation bringing the theory down to earth may be helpful to the reader. Bo Jacoby (talk) 05:00, 13 July 2010 (UTC).

This really doesn't address any of the issues I raised.

• Relevance: It may be more because it is misplaced within the article that makes the relevance questionable. If we need an example on the computation of the eccentricity, why isn't it with the other discussions on eccentricity such as the First Law section, instead of several sections before the First Law is defined? This placement is very sloppy.
• Accuracy: The example is clearly inaccurate. This on its own would be sufficient grounds to remove it from the article even if the other issues did not exist. Firstly, it splits the Earth's orbit on the equinox to equinox line which as a way of splitting the Earth's orbit is incorrect because the perihelion point is not at a solstice but is about 14 days from the solstice; only a split along the semiminor axis would be correct. Secondly, it uses a 365-day year which introduces another inaccuracy.
• Unreferenced: The example lacks references. Again, this on its own would be sufficient grounds to remove it if references cannot be found.

This brings me to an additional issue that I did not raise earlier:

• Probable original research: If the method in the example was made up by a contributor rather than being derived from an independent source, it is in violation of the Wikipedia guidelines on the prohibition of original research. If it uses an independently-published method to derive the example, this is fine. However, the sloppy accuracy and lack of citations makes it likely that this section does contain original research. Again, original research on its own is sufficient grounds to delete material from an article.

To fix this section, the following must be done:

1. Move it to the section on the First Law. This improves the flow of the article and addresses the relevance issue (which is really more a matter of bad placement within the article than a matter of relevance per se).
2. Do not use the equinox to equinox split of the Earth's orbit. This is inaccurate. Instead, use referenced sources to derive the length of time that the Earth takes to travel from one semiminor point to the other.
3. Use the anomalistic year (perihelion to perihelion), not the tropical year (equinox to equinox: does not account for polar precession) or sidereal year (fixed star to fixed star: does not account for orbital precession).
4. Use accuracy better than 1 day. I recommend 0.001 day because this demonstrates the difference between the tropical year of 365.242 days, the sidereal year of 365.256 days and anomalistic year of 365.260 days.
5. Provide references.

In short, the section has issues but it can be salvaged if the above issues are remedied. This demonstration can be helpful but such demonstrations need to be accurate and referenced just like any other Wikipedia content. -- B.D.Mills  (T, C) 00:26, 22 July 2010 (UTC)

You are course welcome to improve the article. The message of the subsection "Estimating the eccentricity of earth orbit" is merely that the eccentricity is nonzero. This is important because it distinguishes Kepler's laws from simpler models of the solar system. Perhaps the title should be changed to reflect this, and perhaps the contents should be reduced to remark that nonzero eccentricity explains the unequal 'halfyears'. I don't think that this article should contain a detailed description on how to determine orbital elements observationally. The difference between the siderial year and the anomalistic year violate Kepler's law and should perhaps be explained in another article. Bo Jacoby (talk) 07:07, 22 July 2010 (UTC).

Relation Of The Period with Areal Velocity

You can relate the period with the areal velocity by,

$T=\frac{p^2 (\log (1-\epsilon )-\log (\epsilon -1))}{\text{K1} \left(\epsilon ^2-1\right)^{3/2}}$

were K1 is the areal velocity. This means that it will be inversely proportional to the angular velocity at a given point, were the proportionally constants will depend only on $\epsilon$. For $\epsilon=0$ (circular motion) this will simply be,

$\frac{p^2 \pi }{\text{K1}}$

as expected. This can be derived by solving the keepler's differential equation, resulting in,

$t=\frac{p^2 \left(\epsilon \sqrt{\epsilon ^2-1} \sin (\theta )-2 \tanh ^{-1}\left(\frac{(\epsilon -1) \tan \left(\frac{\theta }{2}\right)}{\sqrt{\epsilon ^2-1}}\right) (\epsilon \cos (\theta )+1)\right)}{2 \left(\epsilon ^2-1\right)^{3/2} (\epsilon \cos (\theta ) \text{K1}+\text{K1})}$

--Paclopes (talk) 23:22, 1 September 2010 (UTC)

--Could you please derive these equations? or provide a reference where I can better understand them? —Preceding unsigned comment added by 157.193.10.67 (talk) 13:16, 21 October 2010 (UTC)

I am sory, i don't have much time, but i think i made some error in the derivation, my current result is:

$T=\frac{\pi p^2}{\text{K1} \left(1-\epsilon ^2\right)^{3/2}}$

I calculated it using T equal to 2 times the value of t at $\theta=\pi/2$. Actually i took the limit. All the calculations were done using a symbolic calculation package. The equation for t was done by solving the equation, (1/2 r[t]^2 \[Theta]'[t] == K1) with (r[t] -> p/(1 + \[Epsilon] Cos[\[Theta][t]]). —Preceding unsigned comment added by Paclopes (talk • contribs) 21:37, 21 October 2010 (UTC)

Badly placed foci in Figure 2

In Figure 2 in the section "First law", the foci are drawn way too far apart from each other for the ellipse shown. This can easily be seen by looking at the point at the top of the minor axis: the sum of its distances to the two alleged foci is obviously much greater than twice the semi-major axis. Can someone with graphics skills fix this figure? Duoduoduo (talk) 17:57, 22 April 2011 (UTC)

misplaced new section

The recently introduced subsection on Scale Invariance does not belong here, in my opinion. Bo Jacoby (talk) 07:22, 18 November 2011 (UTC).

Maybe this section should be moved to the scale invariance page. But this property is an (may be the most) important aspect of Kepler's third law, and it is the key to deriving Newton's law of gravitation. So I think it deserves mention at least. Cstalg (talk) 14:37, 21 November 2011 (UTC)

No, the inverse square law for acceleration is already derived in the article. It is strictly kinematic, involving only geometry and time. Your new subsection uses dynamical concepts, (force, mass, angular momentum etc.), which are alien to Kepler's laws. So please move the subsection somewhere else. Bo Jacoby (talk) 15:13, 21 November 2011 (UTC).

Though Kepler's laws are kinetic, they leads to the law of gravitation, which is dynamical. In the section about Newton's gravitional law, we do make use of Newton's dynamics. Without dynamics, Kepler's laws will be of less interest. I have to emphasise that, as I've mentioned in the section about scale invariance, Kepler's third law dose have something to do with mass: the orbit of the planet is independent of its mass! This makes the essential difference between the motion of particles in a gravitational field and the motion of particles in an electric field. Cstalg (talk) 14:38, 23 November 2011 (UTC)

We have other articles on gravitation and dynamics (mechanics) and electricity, but this article is about Kepler's laws of planetary motion. The historical and logical relation between Kepler's laws and dynamics is of cause important, and it is treated in the article. But the full-grown arsenal of dynamical concepts belongs somewhere else. Bo Jacoby (talk) 21:28, 23 November 2011 (UTC).