Lawrence Wilson: Expert Opinion on the Earth’s orbit in Relation to Solar inertial Motion

My thanks to Lawrence Wilson, who has taken the time and trouble to continue investigating the controversy around the question of the focus of Earth’s orbit. This has an important bearing on the climate debate, as quite large swings in TSI will occur if the Earth orbits the solar system barycentre (SSB) rather than the Sun-Earth barycentre. Surprisingly, expert opinion seems to be that the Earth doesn’t orbit the Sun, but the SSB. I’m awaiting a reference to Newton’s calculations. All I’ve ever seen is a small illustration showing an ellipse around the sun, not an epitrochoid. This leaves me uncertain that Newton ever did detailed calculations resolving this issue.

Solar Inertial Motion – Earth/Sun Displacement
Lawrence Wilson – 19 Feb 2013

The phenomenon of SIM was defined mathematically by Isaac Newton, his conclusion being that all planets followed a primary orbit around the SSB (their primary orbital foci) rather than the CofM of the Sun, indeed the Sun itself also proceeding on a seemingly ‘haphazard’ orbital dance around the SSB. In more technical terms its path is described as an epitrochoid, a path which is near repetitive each 178 years. Scientists subsequent to Newton who have studied the phenomenon and its potential implications, such as Jose, Landscheit, Fairbridge, Charvatova and numbers of others too, have independently validated Newton’s analysis.

Richard Mackey in his essay on the related work of Rhodes Fairbridge describes it in this way:-

The general form of the sun’s barycentric orbit is an epitrochoid, a big circle continuous with a little ring nestling asymmetrically inside it. At one phase, the orbit is nearly circular, almost two solar diameters in diameter. At another phase, the Sun is impelled on a backward, or retrograde, journey in which it undergoes a tight loop-the-loop, crossing over its own path in a loop that is less than one solar radius. The epitrochoid’s asymmetric ring arises from the sun undergoing the retrograde loop-the-loop.

 

No alignment of the planets in relation to the Sun repeats itself exactly, because the solar system is

chaotic, containing intrinsic randomness. As a result, no two epitrochoid-shaped solar orbits are the same. Nevertheless, they can be classified into eight distinctive patterns, each of about 179  years duration, which is also the time taken for the planets to occupy approximately the same positions again relative to each other and the sun. In this time the sun completes about nine orbits, or one planetary cycle.

[Rhodes Fairbridge and the idea that the solar system regulates the Earth’s climate

Richard Mackey, Canberra, ACT 2600 Australia, [email protected] ]

The question of the relationship between Earth and Sun (E/S) via the SIM phenomenon has been a subject of debate on the Tallbloke blog on several occasions, with some debaters saying, a) – Earth is locked in orbit of the Sun (meaning its major orbital foci is the Sun’s CofM, or more precisely the E/S barycentre), whilst, b) – others say that Earth primarily orbits the SSB (meaning its major orbital foci is the SSB), and yet others or at least one other on one occasion having a dollar each way saying it’s a bit of each – whatever that means.

Others again say that the difference between a) and b) is so very small that it is insignificant from the point of view of Astronomy/Astrophysics, and quite possibly this is correct. But is it correct for all purposes. There is a body of science and mathematical computation which strongly suggests it is not correct for all purposes, indeed significantly in the context of the climate change debate.

The most recent thread of debate is that in the preceeding material of this thread. At the time I did have some more material almost ready to post, but a series of most interesting posts by Ninderthana with numbers of references, all to do with measurement of the Sun’s diameter, which he provided delayed my posting further. (see these above)

Having got the Christmas/New Year distractions out of the way, I focussed on studying each of those references, and reviewing other material I had on the subject, and following up on the very interesting December 2nd post by Clive Best, in which Clive quoted a response he had received from Dr Greg Kopp, lead scientist on the NASA/JPL Sorce-TIM project (see Dec. 2^nd above).

As I reread Greg’s response one of his paragraphs in particular captured my mental processes, and I requote it here:-

“…….In our orbital corrections, we use the JPL ephemeris VSOP87, which accounts for the positions of all the planets in the solar system as well as the Moon to make our Sun-Earth distance corrections to a fixed 1-AU; so you shouldn’t see any lunar signal in the ‘tsi_1au’, but you should (as you do) in the ‘tsi_true_earth’. This ephemeris also includes effects such as that the Sun itself rotates around the center of mass of the solar system, which, thanks to Jupiter, is close to the Sun’s surface and has a ~12-year period……”

And in particular, the last sentence of this para. As I interpreted that sentence, Greg was telling us that in adjusting their raw recordings to 1AU, the ephemeris they used (JPL ephemeris VSOP87), in addition to Earth/Moon variance, planet to planet variance, and Earth/Sun elliptical variance, also recognised and included Earth/Sun distance variations caused by the Solar Inertial Motion phenomenon.

In other words he was saying Earth (and all planets) orbited the SSB and not the Sun’s CofM (or the E/S B). Indeed, were this not the case, why would he even need to mention it?

To be sure of my interpretation I decided to seek direct contact with Greg to gain explicit confirmation: which I did, and which I got. I lay out the communication between Greg and I further below. I also comment further below on  the Sun diameter measurement reports by Ninderthana.

But prior to that I would like to advise this forum about other investigative exploration I have initiated on this matter over the past six or eight months with astrophysicists at three universities, in Australia, England and USA where the question was put to them. I did allude to having started that process of enquiry earlier last year in an earlier thread on this subject, and Howard Bailey made reference to it also in his post of Dec.30^th above. I supplied all of this information to the Bailey’s as it is fundamental to the Bailey Solarchord hypothesis; the universities’ responses are now reported on the Solarchord website, but I now set it out here:-

The essential question was put to several eminent astronomers/astrophysicists at distinguished universities around the western world; one at Cambridge, two (independently) at Swinburne, and two (independently as far as we know) at Cornell. I quote and paraphrase their responses here:-

Swinburne A (an ‘in person’ discussion): “It’s just not a matter of debate around the world of astrophysicists – it’s quite accepted and long accepted as solidly founded Newtonian science that all planets orbit the Barycentre whilst the Sun does its own related dance around the Barycentre.” Further this AP stated that many other astro-scientists, post Newton, including such as the Australian Rhodes Fairbridge have tested the proposition and come down totally convinced that it is the case. Amongst Astronomers at large it is simply not debated at all.

Swinburne B (via email): “The Earth and all the planets in the Solar System orbit the barycentre and not the Sun. The Sun is gravitationally perturbed by the planets (Jupiter in particular) and we can measure the motion of the Sun (see for example ‘Solar wobble caused by Jupiter’ -
http://sim.jpl.nasa.gov/images/solarwobble_high.tif and http://sim.jpl.nasa.gov/multimedia/videosAnimations/).
The International Astronomical Union defines the origin of the International Celestial Reference System to be the Solar System’s barycentre, so they’re very keen to get that right! A lot of effort (and money) goes into high precision astrometry using VLBI (very long baseline interferometry). For more details, see -”
http://aa.usno.navy.mil/faq/docs/ICRS_doc.php
http://www.iers.org/
http://www.ga.gov.au/earth-monitoring/geodesy/geodetic-techniques/very-long-baseline-interferometry-vlbi.html

Cambridge: (via email)“………it is quite correct, when discussing the internal dynamics of the solar system, to regard all the bodies — Sun, planets, asteroids, etc — to be orbiting about the common centre of mass.”

“I looked briefly at what Bailey has to say, and so far as what is in the brief outline in the first link you gave me, his statements about the true TSI (Total Solar Irradiance) are basically correct. I have not checked the details of what he claims to have happened between 2002 and 2007; it is not the most pertinent calculation to perform. What I did do was to estimate the irradiance variation on a decadal timescale arising from variations in the Earth-Sun distance brought about by Jupiter and Saturn.

On a timescale of 30 years or so, that variation is about 1.5 per cent, which induces a variation in irradiance on Earth of 3 per cent, namely about 40 Watts per square metre. So Bailey’s calculated 28 Watts per square metre over a particular interval of very roughly comparable yet rather shorter duration is quite plausible. I shall stay away from any debate about whether or not such a natural variation is ‘acceptable’ — it cannot be otherwise.”

Cornell A1 (via email):“Technically, what is going on is that the Sun, Earth and all the planets are orbiting around the centre of mass of the Solar System.

This is actually how planets orbiting other stars are often detected, by searching for the motion of the stars they orbit that is caused by the fact that the star is orbiting the center of mass of the system, causing it to wobble on the sky.

The center of mass of our solar system is very close to the Sun itself, but not exactly at the Sun’s center (it is actually a little bit outside the radius of the Sun). However, since almost all of the mass within the solar system is contained in the Sun, its motion is only a slight wobble in comparison to the motion of the planets. Therefore, assuming that the Sun is stationary and the planets revolve around its center is a good enough approximation for most purposes.”

Cornell A2 (via email): “Actually, both the Sun and the planets move around each other with their center of mass lying at the focus of the elliptical orbits. However, since the Sun contains 99.9% of the mass of the solar system, the center of mass is located almost at the Sun and so it looks like the planets are going around the Sun”

Cornell B (via email): “Sorry for the very slow reply. This kind of thing is best explained with pictures but I have limited time so I’ll do my best with words. The short answer is that your suggested answer to your own question is right.” [The inquirer’s suggested answer was that the Earth and all planets orbit the solar system barycentre)

“As I’m sure you know, there are many complications to orbits besides eccentricity – planets do all kinds of crazy things besides go in ellipses – that’s why celestial mechanics is so complicated. For the purposes of this discussion though, let’s just assume all planets go in perfect ellipses. It’s a pretty good approximation, that’s why we call it Kepler’s first law even if it’s not strictly correct. Secondly, the motion of the sun is chaotic because it’s got lots of planets pulling it around but for here let’s just consider Jupiter as the only planet that tugs on the sun significantly even though Saturn also has a large effect.

All of these ellipses have a particular focus on which they orbit. (Ellipses have two foci but one is useful for astronomy and the other not so much). The focus is the center of mass of the whole solar system. Jupiter therefore will always orbit such that it’s focus is always the solar system’s barycenter. The Earth will also orbit such that it’s focus stays put at the solar system’s barycenter and so on and so on.

The sun is included too – it travels in an ellipse around the solar system’s barycenter. Therefore, the sun will appear to have a wobble with respect to the Earth’s focus – it will seem to get closer and farther with a rate close to 1 Earth year (with a small correction due to Jupiter’s slow orbit). If we take our assumptions of perfect ellipses away and put in the gravitational effect of Saturn and the rest of the planets with respect to the sun, all planet’s will see a tiny chaotic “wobble” of the sun as it gets slightly closer and farther.”

Cornell also referred to this animated site for interest

http://astro.unl.edu/classaction/animations/extrasolarplanets/ca_extrasolarplanets_starwobble.html

Notes on the university responses

Only Cambridge was alerted that the context of the question was the Climate Change debate; accordingly the response arrived with some related commentary, and the respondent actually went to the trouble of doing wattage computations, confirming Frederick Bailey’s analysis. Others were not so alerted, the question being put in a purely astronomical processes context.

As will be seen all parties responded in the positive without equivocation, some adding their certain knowledge that astronomers and APs at large agreed with their position.

Respondents are not here named; their approval has not been sought but may be sought if relevant for ensuing serious enquiry after website posting; it is noteworthy that two of the respondents are at the most senior levels in their respective institutions. LAPW, Dec.30, 2012

Dr Greg Kopp Exchanges

I now lay out here the email exchanges with Greg Kopp:-

My first email of Jan. 28, and Greg’s response

Dear Greg

May I put a query to you which follows on from a posting by Clive Best on the Tallbloke blog December 2 last where Clive refers to your response to a question he had put to you earlier last year. http://tallbloke.wordpress.com/2012/12/02/tsi-sorce-and-a-signature/”>http://tallbloke.wordpress.com/2012/12/02/tsi-sorce-and-a-signature/

Here’s what Clive posted, with your response in italics – the part I am interested in is the para I’ve highlighted in yellow – my query follows below -

‘I emailed Greg Kopp (lead scientist on SORCE-TIM) last January about the lunar signal that pops out once the Earth’s elliptic orbital effects have been subtracted. He was kind enough to reply, explaining their analysis, thus both earning my deep respect for his scientific integrity and the professionalism of the TIM group’s data analysis. His reply helps explain the TSI data processing.

“The residual you show does not appear in our ‘tsi_1au’ value because we correct for the lunar effect on the Earth’s orbit (and many others). We produce the 1-AU corrected TSI for people studying the Sun’s output; and we produce the ‘tsi_true_earth’ value for those, such as climate modelers, wanting direct radiative inputs to the Earth’s system. Thus the ‘tsi_true_earth’ appropriately does not remove the effect of the lunar tug on the Earth, since that does affect the at-Earth radiative inputs.

In our orbital corrections, we use the JPL ephemeris VSOP87, which accounts for the positions of all the planets in the solar system as well as the Moon to make our Sun-Earth distance corrections to a fixed 1-AU; so you shouldn’t see any lunar signal in the ‘tsi_1au’, but you should (as you do) in the ‘tsi_true_earth’.

This ephemeris also includes effects such as that the Sun itself rotates around the center of mass of the solar system, which, thanks to Jupiter, is close to the Sun’s surface and has a ~12-year period.

We also correct for spacecraft effects, which include Sun-instrument distance changes due to the spacecraft’s low Earth orbit. These are comparable to the lunar effects (+/- 14000 km) and occur on 95-minute orbital time scales. And we apply Doppler corrections, as the instrument collects blue-shifted photons depending on its radial velocity toward the Sun, whether due to the spacecraft’s or the Earth’s orbital motions. These are ~50 ppm corrections over the spacecraft’s 95-minute orbital period.

If I’m understanding your lunar calculation correctly, you’re starting to apply some of the neat physics subtleties in these data — and now hopefully also starting to appreciate some of the many other corrections that we apply to make the accurate 1 AU data.”

He also pointed out that their latest value of TSI is 1360.8 W/m^2 at solar minimum (ref. Kopp & Lean 2011), which is considerably lower than the older 1367 W/m^2 value adopted by most IPCC models’

My Query – As I interpret the yellow highlighted para, it is referring to the Jovians driven Solar Inertial Motion phenomenon and the additional separation distance it causes between Earth and Sun. Firstly would you confirm that my understanding with this is correct.

Secondly, could you advise me how (and where) I may identify within JPL Ephemeris VSOP87 what is the magnitude of the additional E/S separation distance due to SIM only for each year over the period this data has been compiled or perhaps for a sample of years which would illustrate the typical magnitude. My understanding has been that E/S separation distances of up to over two solar radii may occur due to SIM, although infrequently at this level, but distances of up to one solar radius are not uncommon, perhaps regularly within a solar cycle period of 11 to 12 years.

I am an amateur ‘citizen scientist’, retiree aged 77 with lifelong interest in astronomy and astrophysics sciences. Chemical Engineer and Business management background. Location Melbourne, Australia

Appreciate any guidance you are able to offer.

Many thanks

Laurie Wilson

PS: Not sure how JPL creates names for its Ephemerides, but VSOP87 sure sounds like a good French cognac

Greg’s reply of Feb.2 was imbedded in my emailed message – to minimise repetition I have deleted much of the text here:-

“Hi Laurie,

Sorry for the delay responding. I’ve had to let e-mail pile up this week while I’ve tried to finish a long analysis report I just submitted this morning.

 

It was great to see the nice things Clive had to say about my reply from last year. Thanks for sending along that link!

 

I’ll embed my replies in your message below. Enjoy!

Greg”

 

My Query – As I interpret the yellow highlighted para, it is referring to the Jovians driven Solar Inertial Motion phenomenon and the additional separation distance it causes between Earth and Sun. Firstly would you confirm that my understanding with this is correct.

“Yes, that’s correct. The Sun really isn’t the center of mass of the solar system. Jupiter is the primary cause of displacing that center of mass to a point that’s near the solar surface. The other planets generally don’t cause so large an effect, being much less massive; although Saturn is close, with half the mass being out at twice the distance.”
Secondly, could you advise me how (and where) I may identify within JPL Ephemeris VSOP87 what is the magnitude of the additional E/S separation distance due to SIM only for each year over the period this data has been compiled or perhaps for a sample of years which would illustrate the typical magnitude. My understanding has been that E/S separation distances of up to over two solar radii may occur due to SIM, although infrequently at this level, but distances of up to one solar radius are not uncommon, perhaps regularly within a solar cycle period of 11 to 12 years.

“I couldn’t tell you how to get those values out of VSOP87 directly; but you can figure out the effect directly on the back of a napkin, and here’s how:

Jupiter’s mass is about 2e27 kg at 5 AU (1 AU = 1.5e8 km)

The Sun’s mass is 2e30 kg with radius 7e5 km

The center of mass of those two is thus separated from the center of the Sun by distance

R = distance of Jupiter * mass of Jupiter / mass of Sun = 5 AU * 2e27 kg / 2e30 kg = 5e-3 AU = 7.5e5 km, which is just larger than the radius of the Sun. Neat, huh?

 

You can apply the same techniques for Saturn, which is nearly comparable, and Neptune, which has the next biggest effect. You’ll see that if they do all add up together (i.e. if they are all in a line on the same side of the Sun), they can move the CM to about what you say, 2 radii from the Sun.

 

After doing those quick calculations, you’ll especially enjoy that cognac!”

 

 

My second email of Feb. 2^nd to Greg and his response:-

Many thanks Greg

That’s most helpful for me in getting clarity in my thinking about these things.

As I now understand it, extending the maths model you laid out in the second part – if I were to calculate in like manner the Moment for each of the planets, Earth included, at any point in their multiple orbital circuits, applying appropriate vector adjustments for each and then total these forces, that would give me an ‘aggregate’ planetary centre of mass and the consequent balancing Moment and position of the Sun.

One final thing – I trust you will be happy for me to quote you if the occasion arises in blog debate such as Clive Best did on Tallbloke.

All the best with your fascinating research with Univ. Colorado, and NASA.

Cheers

Laurie

Greg’s Response of Feb.2^nd:-

 

“Hi Laurie,

 

Yes, that’s right, on both accounts – the vector addition of forces and quoting me.

 

The ephemerides take these calculations another step by including all the interactions between multiple bodies, such as how Saturn affects Jupiter and other planets simultaneously. But that’s what computers are for – too much to fit on the back of our napkin!

 

Happy weekend,

Greg”

 

Finally on Ninderthana’s contributions re Sun diameter measurement:-

The six or seven references to learned papers which Ninderthana quoted in his posts above were extremely interesting and informative for me. However in a couple of them reference was made to the process of adjusting their raw measurements to a standard 1AU; just as we now find the SORCE/TIM data is adjusted, and as now confirmed by Greg Kopp inclusive within the ephemeride data is the Earth/Sun SIM displacement distance.

I could not find in these papers reference to precisely how they did that adjustment, and that is something I intend to follow up on if I can with the authors. But I’ll bet pounds to peanuts they too use the NASA/JPL ephemerides for this purpose, so that the SIM component is also factored out. In doing so they finish up with precisely what it is they are setting out to measure – the Sun’s real diameter and not an ‘apparent diameter’ which they would record if these 1AU adjustments were not made.

One last note probably previously known to all but me, JPL Ephemeris VSOP87 is apparently the creation of a French institution (can’t remember which) and is widely used including by JPL/NASA. The JPL/NASA ephemerides set found on their Horizons resource produces almost the same results – I ran out a dozen or so and they varied only after the 5^th decimal place by minor amounts.

Lawrence Wilson

February 19, 2013

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