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Proper Orbital Elements

I feel there is a problem with giving orbital characteristics at a given (arbitrarily chosen) epoch for bodies such as minor planets which have significantly perturbed orbits. Their characteristics change so greatly and so quickly with time that these values are soon out of date and thus cannot be used as the basis for accurate calculations. Would it not be better to give the Proper orbital elements, as listed on such sites as AstDyS? (Possibly as well as characteristics at a given epoch?). AstDyS is run by the Space Mechanics group, Dept of Mathematics, University of Pisa, Italy (with whom I have no connection!). Further information can be found on their website: http://hamilton.dm.unipi.it/astdys/
— AstroSteve (talk) 23:05, 12 July 2011 (UTC)

Do you have an example article in mind where such orbital characteristics are in use? Also, would a better solution be to remove the characteristics completely (and if so, or if not, why)?
— V = IR (Talk • Contribs) 16:54, 13 July 2011 (UTC)

All articles on solar system bodies give orbital characteristics, as they are a standard part of the "Planet" infobox template. Removing them completely would be totally wrong, as such data is a fundamental part of the specification of a planet/dwarf planet/asteroid/comet/(etc!). My point is that for major planetary bodies such as the earth, the characteristics vary only very slowly with time and within quite small limits and so giving them at a specific [standard] epoch is entirely reasonable. For a smaller body such as an asteroid, however, because it is subject to large perturbations (primarily from Jupiter) the characteristics vary significantly in extent and very rapidly in time. For example, work I have done on minor planet Ceres showed that its orbital period can vary from 1680.3 to 1682.7 days in just three orbits. This is not just a "one-off", either: such variations are entirely typical. Quoting the value for a particular orbit (which is essentially what the value at a given epoch is) can thus give an entirely misleading impression. Indeed, the value currently present for Ceres (1680.5 days) is clearly rather to the low end of its range and thus appears to be "wrong" when compared to the Proper Element value of 1681.567 days. This is important because values given on Wikipedia are generally believed and widely copied, often without the all-important context. The value of 1680.5 will thus tend to become the accepted value, independent of epoch: this is clearly undesirable. (It is probably not a coincidence that of those hits in a Google search which mention a period in days, almost all of them quote 1680.5!). Also, if this value is used in calculations (of synodic period, for example) an incorrect answer will result. The Proper Element values remove the effect of the large variations (which are present in all the characteristics) by producing a "very-long-term average" independent of epoch: this can thus be taken as the true mean value. [Note that I am not suggesting that Proper Elements be used for all minor bodies. Whereas for asteroids the perturbations are periodic in nature and so can be "averaged out", in the case of comets (for example) the perturbations are essentially non-periodic and so the orbit is somewhat chaotic. In this case the epoch format is the accepted way of giving the orbital characteristics.]
— AstroSteve (talk) 23:41, 13 July 2011 (UTC)

I'm quite surprised there has been only one comment on my suggestion, and that even this was not followed up when I answered it. This is the reason I have used the "edit protected" template even though I do not have a fully worked-up suggestion - it would clearly be pointless deriving one if it wasn't going to be supported. I am thus firstly seeking agreement in principle before moving forward.

The reason I am suggesting the change is fully explained in my earlier comments, so will someone please reply to say they agree, or that it is not a good idea (giving reasons, of course!). My view is that if the change is not made then (as explained above) Wikipedia will be guilty of (albeit unwittingly) disseminating incorrect information into the Internet more widely.
—AstroSteve (talk) 23:16, 17 September 2011 (UTC)

As long as an epoch is specified, I do not see it as a horrible thing. Anyone doing serious research will not be using Wikipedia for orbital elements. Does AstDyS give Proper Orbital Elements for lesser known bodies? Perturbations are a given for any astronomical body. How do I get the proper orbital period from AstDyS for Ceres? I do not see the orbital period under proper elements at AstDys-2 for Ceres. I can get epoch 2010-Jul-23 elements for Ceres very easily. Shouldn't we use a source that can be verified by an average editor, unless there is a need for added precision? -- Kheider (talk) 01:05, 18 September 2011 (UTC)

The DES shows 90377 Sedna with an orbital period of 12144 years (Epoch 1990), JPL shows it as 12402 years (epoch 2011), and a more in-depth barycentric solution shows a period of 11,400 years. -- Kheider (talk) 01:12, 18 September 2011 (UTC)

As I see it, the major problem with the use of the "epoch/value" format is that I'm not sure the average reader will be quite sure what it means and what it implies. Even if they notice the "Epoch" line and follow the link, this rapidly gets quite complex so is unlikely to help much. More likely, they will just say "oh, that's just the date it was calculated, is it?" without realising that the same calculation on a different date has the potential to give a considerably different result. This isn't all that important for the major planets, whose orbital parameters are reasonably constant over a moderate timescale, but it is very important for asteroids, whose parameters change quite a lot as they tend to have highly perturbed orbits. If there is no realisation that the value for a parameter calculated in this way is only correct at the particular epoch, the two easily get separated and so the "epoch-specific" value becomes the value of the parameter rather than just the value at a given instant. I noted above that this has already happened for Ceres, where multiple websites give its orbital period as 1680.5 days without any further qualification.

You are of course right to say that anyone doing serious research will not be taking their values from Wikipedia but surely even a "casual calculator" deserves to have access to basically correct information? Given the tendency alluded to above for people to believe Wikipedia and copy its data without too much further thought, is there not a responsibility to ensure that this data is as accurate as possible? By this I mean "accurate for all general purposes", not just "accurate at a given moment", of course. This requires the quotation of the Proper Orbital Element values, not the values at a given (and apparently arbitrary) epoch.

You ask whether AstDyS gives POEs for lesser known bodies. Its "Objects" page currently says that it holds data 428392 objects, so I don't think there will be any concerns on that score. You then say you don't see the orbital period in the data - in fact it is there, but under its alter ego of mean orbital motion (as used more commonly by astronomers), indicated by the letter "n". The value given (78.1933 deg/yr) must be divided into 360 to give an orbital period (4.604 years or 1681.567 days). While you can, as you say, easily get epoch 2010-Jul-23 elements, it is worth noting that they (in particular the orbital period) are significantly different from those quoted on the Ceres page at present, which I think neatly proves my point.

If it is considered important to give a source which can be easily verified, it might be necessary to give the mean motion parameter in the Infobox, with a conversion to the two orbital periods also provided. I don't see this as a big problem. As for the "added precision" issue, this is not really the point I am making. Given that the (epoch-style) value for the orbital period of Ceres varies from about 1679 to 1683 days, if it were simply a question of precision one should quote a (fixed) value of 1680 days, independent of epoch. What I am asking for is a value that not only has greater precision (i.e. more significant figures) but also greater absolute [long-term] accuracy.

The uncertainty in Sedna's orbital period is not just due to different ways of showing the same thing (as in epoch versus POE) but also to there not having been insufficient observations of its position to calculate a fully accurate orbit. However, to the extent that it is a presentational issue, the values you give yet again make my point for me, as the final footnote of Sedna's Wikipedia page say that different epochs give different answers (albeit for different reasons than for Ceres). I rest my case!

So, in summary, the epoch style is OK for major planetary bodies, whose parameters are reasonably constant, and for such things as comets, whose parameters tend to change quickly and do not have the same significance as for bodies with "regular" orbits in any case, but for bodies with basically stable but highly perturbed orbits such as asteroids we must use Proper Orbital Elements else the values quoted will tend to be deceptive and open to mis-use.
—AstroSteve (talk) 00:45, 19 September 2011 (UTC)

You listed Ceres as having an orbital period of "1680.3 to 1682.7" days over 3 years. So I checked with JPL Horizons using a heliocentric solution. I see that on 2010-Nov-01 Ceres had an orbital period of 1679.58 days and that on 2012-Aug-01 Ceres has a period of 1684 days. I also see that on 2035-Feb-01 Ceres has a period of 1684.8 days.

• What interval is used by AstDyS to calculate POEs? It looks like they use a 2 Myr integration (1Myr forward + 1Myr backward with stepsize 100,000yr)? I would like to know the accuracy of these numbers if we are going to use them in the major asteroid articles such as 1 Ceres and 4 Vesta.
• For Ceres you tell me to divide 360/78.1933 which gets me 4.6039. My calculator shows 360/78.1933*365.25=1681.60, how did you get 1681.567? Or did you round-off somewhere? -- Kheider (talk) 05:34, 19 September 2011 (UTC)

What I actually said was that the orbital period can vary from 1680.3 to 1682.7 days over 3 orbits, not 3 years (which would not be enough time to complete even 1 orbit). I included this information just to show how variable the orbital period is over even a small number of consecutive orbits. Also, the numbers I was quoting are "actual" periods i.e. the time difference between successive passages through zero longitude, not "calculated" values (hence my use of a number of orbits rather than a time-period). We are thus talking about slightly different things. However, your JPL numbers show that the period can vary by even greater amounts when considered over a longer time-period, which is of course the point I have been making all along.

As I understand it, POEs are not calculated simply by numerical integration but by taking the output from such an integration and applying a smoothing process using Fourier-type transforms to find and remove the periodic elements. More information can be found in this document:- http://hamilton.dm.unipi.it/~astdys2/papers/astIII.pdf. From reading the document, I would say that there should be no concerns as to the accuracy of the elements listed.

You have used the number of days in a Julian year to convert from the period in years rather than the number in a Gregorian year (365.2425). What one means by "a year" is often an issue in calculations of this sort, but I always use Gregorian years (or tropical years - 365.2422 days) as this is what is most commonly meant by a year. It also ensures that the results align with actual calendar years.
—AstroSteve (talk) 11:58, 19 September 2011 (UTC)

So you and I are both saying the elements of Ceres will vary over time (mostly by Jupiter). How would you deal with perihelion and aphelion values of a major main-belt asteroid (MBA)? I would think most readers would want to know the current perihelion value of a MBA, not a potentially incorrect (long-term) average. For Ceres, on 2006-Feb-01 perihelion was 2.54411018AU (QR value) where-as on 2019-Jun-01 perihelion is 2.5587253AU. The epoch 2010-Jul-23 perihelion value is 2.5465AU. -- Kheider (talk) 16:53, 19 September 2011 (UTC)

It is important the Wikipedia use reliable sources that can be understood by an average reader. So far it looks like explaining how to convert AstDyS-2 Synthetic "mean motion (n)" to Gregorian years will be doable, but will require a paragraph to explain. We may also need a reliable source explaining why we prefer a Gregorian calendar which uses 365.2425 days to define a year. -- Kheider (talk) 16:53, 19 September 2011 (UTC)

I suggest that both be provided, with a reference to an explanation of the differences. Too often I've seen clarity sacrificed for the sake of inappropriate brevity. The 3D display program that I use (Celestia) normally uses osculating elements, although more sophisticated ephemerides like SPICE kernels can be used. Seldenball (talk) 20:20, 19 September 2011 (UTC)

I agree both should be provided. Proper elements are also different because they include the perihelion and nodal rates as opposed to the argument of perihelion and node longitude. So, both are actually needed since in order to specify proper elements one needs to specify the argument of perihelion and node longitude at a particular epoch. Ruslik_Zero 18:44, 20 September 2011 (UTC)

Infobox

In the Planet Infobox template do we want to add a section below "Orbital characteristics" called "proper elements" that includes:

• proper semimajor axis (a_p),
• proper eccentricity (e_p),
• proper inclination (i_p),
• proper mean motion (in deg/yr) which is converted by an additional template to an orbital period (in days)
• any others? -- Kheider (talk) 19:40, 20 September 2011 (UTC)

Aha! Do I detect support for this idea beginning to grow? I would also agree that both formats be provided (as I suggested in my first post) because, as has recently been stated, they give you different but complimentary information. Do I take it from Kheider's suggested elements that the necessity for "reader verification" of the quoted values has been lessened? While I assume the conversion between sin(inclination) and inclination is fairly obvious, how about that between mean motion and orbital period previously discussed? I was going to suggest that the template should display mean motion as its primary value (so the reader can relate it back to AstDyS, or whichever source is used) but the template should also display the orbital period in both years and days by automatic conversion from the mean motion value: I think this is possible within a template. This should avoid the need for any explanation.

Including the proper period in years would be desirable for consistency with the epoch-style values but of course this brings us back to the Julian or Gregorian year issue if AstDyS is used as the source. In my example above I simply assumed that, as the AstDyS output was not qualified in any way, it would be using Gregorian years as this is the normal "man in the street" definition of a year and would normally be presumed unless there was a statement to the contrary. However, because we are working in an astronomical context, I freely admit I may have got this one wrong. With no obvious way of resolving the issue (the site does not say which it uses, as opposed to, for example, JPL HORIZONS which explicitly says that Julian years are used) I sent a message to the AstDyS team asking which year it was they used to convert from the days in which (presumably) they calculated the values into the "deg/yr" actually used in the datafiles. I have yet to receive an answer, but I'll post it if/when I do.

I don't think we need to complete the set by adding the precession periods as they are somewhat specialised and can be found directly from AstDyS by the interested reader anyway. I think adopting a common epoch for the epoch-style section across the major asteroids would be helpful though - they're a bit of a mixture at present.

Might I further suggest that the existing template is not itself changed, but rather that a "child" template be created ("Infobox_asteroid"?) which includes both epoch-style and POE information? As mentioned above, epoch-style is fine for bodies whose parameters are not greatly perturbed (and for comets) so POE data is only really needed for asteroids.
—AstroSteve (talk) 22:09, 20 September 2011 (UTC)

Most comet articles use the Template:Infobox comet (the featured article Halley's comet being an exception). But Osculating orbital elements are more important because they give initial conditions that can be used to compute the actual location, while proper elements only give "typical" values that are rather useless for this purpose. Given that most asteriod articles will continue to only use the more common osculating elements (at whatever epoch the article was created at), I am not sure creating another Infobox that has to be modified concurrently is a good idea. I think we should modifiy the existing Infobox planet. It took years to get rid of the old "Template:Minor Planet" that was much less current/useful than the Infobox planet one. -- Kheider (talk) 16:16, 21 September 2011 (UTC)

Question is though - what will most readers be using the information presented in the Infobox for? I would suggest it won't be for calculating present position: this is most easily found by other means entirely (one could even add a link). What the casual reader will want to know is exactly what the POE tell you: typical values of the parameters. The reader looking for accurate values with which to perform simple calculations (such as synodic period and Kepler's Laws) will also be much better served by POE rather than osculating elements which, as has been repeatedly shown in this discussion, can be highly variable in nature from instant to instant. The consensus seems to be that we should retain the epoch-style/osculating elements though, so surely no problem.

You say that "most asteroid articles will continue to only use the more common osculating elements". I had intended that if an Infobox:Asteroid (or whatever) could be agreed then it would be used for all asteroids: I have only been using Ceres as an example. As to whether a new template should be produced, I was assuming (maybe somewhat naively!) that templates could be nested in some way so that a change to a parent template e.g. Infobox:Planet, would trickle down automatically to a child e.g. Infobox:Asteroid, thus avoiding the maintenance overhead. If this is not technically possible, how about a "switch" of some sort to turn off the POE section in those cases where it is not needed?
—AstroSteve (talk) 17:11, 21 September 2011 (UTC)

I assume that if none of the proper elements are assigned a value then the proper elements section would not be displayed. I believe this is how it works for the "Physical characteristics" and Atmosphere subsections. But I know very little about how templates are built/nested on Wikipedia. -- Kheider (talk) 19:52, 21 September 2011 (UTC)

If it did work like this then that would be perfect, thus avoiding all maintenance problems and any thought of switches etc. 'Fraid I don't know anything about the mechanics of templates either (as I've already demonstrated!).

Do we then think that a consensus could be reached on adding add a new section Proper Orbital Elements to Infobox:Planet, listing the proper values of semi-major axis; eccentricity; inclination and mean orbital motion, with automatic conversion of the latter element into an orbital period in both days and [Julian] years? If no elements were listed, the new section would not be displayed. Data to be taken from (and referenced to) AstDyS.

If so, presumably we should at least mention this to the AstDyS people (and encourage them to give an answer to the question I posed about the Julian/Gregorian year issue!).

If the above forms the basis of an outline agreement, how should it now be moved forward in order to actually get the new section added? [given that the template is protected].
—AstroSteve (talk) 22:41, 21 September 2011 (UTC)

I believe that we have already created a good consensus. We just need someone smart enough to edit the Infobox planet template (or make a test template for adding the finished product to the Infobox planet template). Based on existing variables, I suggest variable name such as proper_semimajor, proper_eccentricity, proper_inclination, proper_motion. -- Kheider (talk) 22:56, 21 September 2011 (UTC)

Sounds good to me. The actual template can't be edited by a mere mortal of course, as it's protected. Playing around with a test version in the sandbox could help to find out what will work, but I'm not sure I would be able to deduce the right syntax in all cases (particularly the conversions to orbital period from mean motion). Could be interesting to have a go though. Might also be time to flag-up the situation to the administrators by using the "edit protected" template. No idea how we would attract the attention of a "template guru" otherwise.
—AstroSteve (talk) 23:49, 21 September 2011 (UTC)

I added proper elements to Template:Infobox_planet/sandbox. Ruslik_Zero 08:01, 22 September 2011 (UTC)

Well, that answers that question - just wait around and a "guru" will pass by! Thanks, Ruslik, for your timely contribution.

Exercising my massive talents with "cut-and-paste" editing (!) I've changed around and added to Ruslik's addition in the following ways:-

• ensured that the elements are in the same order as they appear in AstDyS
• added an orbital period in days
• changed some units for "more obvious" versions
• added internal links to Wikipedia articles (are these called "wikilinks"??)
• changed the description of the precession elements
• changed "periastron" to "perihelion"

I note from the way the existing template is used for Ceres that all the complexity (such as units, internal links, mathematics etc.) is contained within the values assigned to the template parameters when it is used on a particular page. I opted to put this stuff directly in the template for the POE section in order to avoid the need for a page editor to guess what units the values should be in: all they have to do is set the parameters to the values given by AstDyS and the template does the rest. If this contravenes some template construction standard I'm sure someone will tell me! I changed periastron to perihelion because, for the bodies needing to use POE i.e. asteroids, this is an accurate description. The same syntax as used in the Orbital Characteristics section could be used to change the terminology according to the apsis parameter but I felt this is perhaps an un-necessary complication at the moment. If a case where perihelion is not appropriate for a body for which POE are appropriate ever occurs, the change could be made then.

If the version of the template in Template:Infobox_planet/sandbox is getting close to what we had in mind, the only remaining question is the Julian/Gregorian issue. I've still had no response from AstDyS to my enquiry: maybe they'll be more forthcoming if I tell them that a major reference to their work from Wikipedia is hanging on their reply!
—AstroSteve (talk) 23:21, 22 September 2011 (UTC)

So, for Ceres the infobox would look like:

Ceres

Ceres as seen by Hubble Space Telescope (ACS). The contrast has been enhanced to reveal surface details.
Discovery
Discovered by	Giuseppe Piazzi
Discovery date	1 January 1801
Designations
Designation	1 Ceres
Pronunciation	/ˈsɪəriːz/ or as Latin: Cerēs
Named after	Ceres
Alternative names	A899 OF; 1943 XB
Minor planet category	dwarf planet main belt
Adjectives	Cererian /sɨˈrɪəri.ən/
Symbol
Orbital characteristics
Epoch June 18, 2009 (JD 2455000.5)
Aphelion	2.9858 AU (446,669,320 km)
Perihelion	2.5468 AU (380,995,855 km)
Semi-major axis	2.7663 AU (413,832,587 km)
Eccentricity	0.07934
Orbital period (sidereal)	4.60 yr 1680.5 d
Average orbital speed	17.882 km/s
Mean anomaly	27.448°
Inclination	10.585° to Ecliptic 9.20° to Invariable plane
Longitude of ascending node	80.399°
Argument of perihelion	72.825°
Proper orbital elements
Proper semi-major axis	2.7671 AU
Proper eccentricity	0.11620
Proper inclination	9.647°
Proper mean motion	78.1933 deg / yr
Proper orbital period	4.60398 yr (1681.602 d)
Precession of perihelion	54.0703 arcsec / yr
Precession of the ascending node	−59.1700 arcsec / yr
Physical characteristics
Equatorial radius	487.3 ± 1.8 km
Polar radius	454.7 ± 1.6 km
Surface area	2,850,000 sq km (1,100,000 sq mi)
Mass	9.43 ± 0.07×1020 kg 0.00015 Earths 0.0128 Moons
Mean density	2.077 ± 0.036 g/cm3
Surface gravity	0.27 m/s2 0.028 g
Escape velocity	0.51 km/s
Sidereal rotation period	0.3781 d 9.074170 h
Axial tilt	about 3°
North pole right ascension	19 h 24 min 291°
North pole declination	59°
Albedo	0.090 ± 0.0033 (V-band geometric)
Surface temp. min mean max Kelvin ? ~167 K 239 K
Spectral type	C
Apparent magnitude	6.7 to 9.32
Absolute magnitude (H)	3.36 ± 0.02
Angular diameter	0.84" to 0.33"

Thank you Ruslik. I see that p_mean_motion handles the conversion to years and days (Julian) automatically!

I think "Orbital characteristics" should link to Osculating orbit instead of orbit. -- Kheider (talk) 20:01, 23 September 2011 (UTC)

The automatic conversion was a joint effort, actually. Ruslik led the way with his initial contribution and then I modified it as already described. However, Wikipedia is a collaborative venture, so that's fine. I note that a "round" function has been added by Ruslik (good idea) but I think quoting to a precision of 0.864 of a second (.00001 of a day) does seem slightly excessive! I've changed it to just 3 dec. places for "days" but left it at 5 for "years". I've also made the number of dec. places for the other parameter values consistent.

Great to see the new version of the template actually in use! However, this has shown that (for consistency) the "degree" sign in proper inclination should not be present in the template itself but be part of the parameter setting: I have changed that now.

I agree with Kheider's suggestion that "Orbital characteristics" should link to "Osculating orbit" (as it now does) as it helps to make the distinction between this section and the new POE section.

So the only outstanding issue seems to be to confirm which sort of year AstDyS were using when quoting the mean motion in deg/yr. I shall send a further message, stressing that we need to know in order to include a POE section in the Wikipedia template: hope that sounds a good enough reason to reply!
—AstroSteve (talk) 23:07, 23 September 2011 (UTC)

I got no reply from AstDyS unfortunately so I contacted Jean Meeus, the eminent Belgian "mathematical astronomer" to see if he knew the answer. He passed the query on to his colleague Rene Bourtembourg, who said that proper elements are expressed in Julian Years. So, there we have it: the final piece of the jigsaw.


In the meantime, I did a few bits of "tidying" to the template and added a p_orbit_ref citation to the example use of the template (above). This was taken from Kheider's addition to the "Orbit" section of the Ceres page. Not sure it should be there, but that's another discussion entirely!


The final step seems to be to contact an administrator to get the change made. MSGJ is the editor who has most recently been involved, so I shall contact him via his Talk page.
—AstroSteve (talk) 16:54, 1 October 2011 (UTC)

I synchronized template with sandbox. Ruslik_Zero 18:41, 1 October 2011 (UTC)

Wow! Thanks Ruslik - I hadn't realised you were an administrator editor (perhaps I should have checked!). I've updated the Ceres page to use the new section and it looks just great! Now all I have to do is update the documentation for the Infobox_planet template - "the job's never done until you've completed the documentation" was always drummed into me when I was a programmer. Still, maybe not tonight!
—AstroSteve (talk) 19:39, 1 October 2011 (UTC)

A hard day's editing has now updated the documentation for the template and added POEs for the first 10 asteroids: probably enough to be going on with!

I think we can therefore say that the end of this particular road has now been successfully reached. Many thanks to everyone who got involved with the discussion, the editing and the transfer to the template. A good job done, I reckon.
—AstroSteve (talk) 18:57, 2 October 2011 (UTC)