Claim: ISON as the Winged Planet

Boodles

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There are various memes developing around comet ISON. It has been visible through small telescopes for a short while and will soon be visible to the naked eye, reaching it's closest point to us on the seasonally appropriate day after Christmas.

ISON tracked and presented in real time and proximity:

http://theskylive.com/ison-tracker

A graphic demonstrates it's near earth trajectory and some key dates.

http://www.solarsystemscope.com/ison/

NASA published this Hubble image of ISON, taken in April.
comet-ison-galaxies-hubble-1.jpg
This image has caused some controversy. A gentleman, presumably an amateur astronomer, has used the interface here -

http://hla.stsci.edu/cgi-bin/display?image=hlsp_ison_hst_wfc3_130430_f606w_v1&autoscale=&title=Ison 130430 WFC3 F606W

- to investigate the various properties of colour and light in NASA's published image and has come to the conclusion that the image was effectively masking (through pixellation, colour, contrast and saturation levels) an altogether different image. He found three separate entities within the image. In fact, as an aside, his finding immediately reminded me of a colossal triangular mothership not unlike that postulated by Edgar Rothschild Fouche when he speaks of the presumed primitive quality of a back-engineered TR3-B (nothing I've read online has drawn on this visual similarity as of yet but I guess people pick up on different things when they see what appears to be a fupping triangle in space). In any case, here is the gentleman's upload, there's no particular place to point to, he is short and demonstrates his train of thought and his process well; quite fascinating, and - at least at first glance - plausible sounding, see what you think:


I am on a rickety old phone and have to upload this before my battery dies. I will outline some counter arguments in a moment as there is various debunking (and supposedly debunking of debunking) going on with respect to this comet right now.
 
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Boodles

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I think he reveals his ignorance of astronomy more than anything else.

See: What's going on with the Comet C/2012 S1 (ISON) images? (STScI)
You have beaten me to it, in his subsequent uploads (I think there are two but haven't seen the third - bandwidth issues) he seeks to address this. It would be more ignorance of photography and certain mechanical or engineering processes than ignorance of astronomy itself.
 

cosmic

Senior Member
I stand by my statement based on the content of his videos.

It might help if you'd describe what exactly seems "plausible" to you in any of this, and why.
 

Boodles

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Plausible in the sense that he has pulled together an analysis of the published NASA image that usefully demonstrates how the image has been treated before publication.

Yes the NASA image is a composite but he seems to be focussing on the individual images within the composite, the ones with green and red filters, and in particular, the black and white, where the three entities are most visibly apparent. So on the face of it to a lay person that seems plausible, depends on one's threshold of plausibility, that's all.
 
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cosmic

Senior Member
Plausible in the sense that he has pulled together an analysis of the published NASA image that usefully demonstrates how the image has been treated before publication.
The Hubble blog featured that process several weeks earlier though. The video's author doesn't bring anything new or trustworthy to the table, he's just chasing anomalies and making wild accusations using publicly available imagery.
 

Boodles

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... he's just chasing anomalies
True.

...and making wild accusations...
I can't see where he is actually doing that, unless to just perhaps, by corollary, imply "the Hubble, it's a bit shit." ;)

What I mean by that is okay, the title suggests ISON may not be a comet, which is pretty wild, but he does not make any accusation other than taking a view that NASA have treated the image in such a way so as to downplay the appearance of three distinct entities, and in so doing he would seem correct.

I'm imagining the debate which may've gone on at the NASA photo lab. "Umm, this one looks like three comets in one", says one technician. "Ah, that's just drag, focus and relative positioning, de-contrast it and throw the brightness level up way high to create glare, no one will ever notice", says another, allegedly - in a make your own imagined conversation up type way.
 
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Pete Tar

Senior Member
This 'anomaly' was a thread on ATS last month, someone mapped out the movements of hubble in orbit to coincide with the exposures so it seemed pretty straightforward as an explanation.
Interested what the possible debunking of the debunking could even be.
 

cosmic

Senior Member
I can't see where he is actually doing that, unless to just perhaps imply "the Hubble, it's a bit shit." ;)
He's suggesting that NASA is hiding something from the public, and that ISON may not actually be a comet (!). That's also tame compared to his other videos on the subject. I can think of other, better descriptions for that sort of behavior but they'd certainly violate the politeness policy.

Honestly, I'm trying my best to be charitable here. He lacks expertise, and that's obvious from listening to him speak -- he doesn't have a handle on correct terminology or even pronunciation. He can't distinguish between a diffraction spike and a coronal mass ejection. His attempt at analysis is embarrassing to watch.

If I appear terribly unforgiving here, it's the result of years of these same sorts of videos. Even before YouTube existed, some people have had persistent, unnecessary freakouts over any object that comes remotely close to the inner solar system. Can't a comet just be a comet... for once?

Speaking of which, ISON (as I suspected) probably won't live up to the media hype.

 

cosmic

Senior Member
What I mean by that is okay, the title suggests ISON may not be a comet, which is pretty wild, but he does not make any accusation other than taking a view that NASA have treated the image in such a way so as to downplay the appearance of three distinct entities, and in so doing he would seem correct.
There aren't three "entities". There's one object with a slightly different appearance in three separate Hubble exposures due to motion. This had already been explained well in advance of the video being posted. Nobody's trying to downplay anything.

I'm imagining the debate which must've gone on at the NASA photo lab. "Umm, this one looks like three comets in one", says one technician, "Ah, that's just drag, focus and relative positioning, de-contrast it and throw the brightness level up way high to create glare, no one will ever notice", says another.
They already explained their rationale though, so this shouldn't be necessary. It's an example where image processing includes an artistic approach, intended to provide a realistic view of what the comet would look like to our eyes. Some instead seem intent on viewing that as an intention to deceive, and that's unfortunate.
 

Boodles

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He's suggesting that NASA is hiding something from the public...
Omg. They wouldn't.

He lacks expertise, and that's obvious from listening to him speak -- he doesn't have a handle on correct terminology or even pronunciation.
I noted that but it's not particularly relevant.

He can't distinguish between a diffraction spike and a coronal mass ejection.
Okay, I'll take your word on that.

His attempt at analysis is embarrassing to watch.
Subjective. Objectively, his view count is soaring and many memes are breaking out because of that upload.

Can't a comet just be a comet... for once?
Unfortunately no, not when the world is looking to the sky for authentication of millenarian prophesy.
 

Boodles

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There aren't three "entities".
There are, literally, three distinct entities in the image. That is to say discrete, individuated globes of light.

There's one object with a slightly different appearance in three separate Hubble exposures due to motion.
There is one object and three distinct, discrete entities occurring in each of the three separate Hubble colour filtered images due to motion.

This had already been explained well in advance of the video being posted.
I haven't read that.

Nobody's trying to downplay anything... It's an example where image processing includes an artistic approach
It's a painting.

...intended to provide a realistic view of what the comet would look like to our eyes. Some instead seem intent on viewing that as an intention to deceive, and that's unfortunate.
People have various reasons to paint, and various views on the art they observe, I guess.
 
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cosmic

Senior Member
Omg. They wouldn't.
Think about how silly the suggestion is. All the press images, raw imagery and data are publicly available. Through public outreach, they've described everything about the processing for that specific image. When NASA & STScI have covered the matter in such detail, making their intentions known and all the information readily available, how is that a cover-up?

Besides, neither NASA nor HST have a monopoly on cometary observations. Even if ISON isn't the visual stunner the press had hoped for, independent observatories and tons of amateurs are going to be imaging the comet. If there were something funky going on, it would be known about, and nobody can keep such information hidden. Do you think NASA or STScI would fake and distribute imagery, knowing how easily everyone else would notice? o_O

I noted that but it's not particularly relevant.
Sure it is. It indicates his lack of expertise.

Okay, I'll take your word on that.
You don't have to. A number of stars in the image show diffraction spikes -- the cross-like pattern you see here:


So, what's a CME?


At about 4:50 in the "cover up" video, he points to the brightest star in the foreground (at the bottom left) and says it appears to be experiencing a solar flare or CME. There's no way he could know that from just looking at a static image of a star that far away. He also doesn't know enough about what he's seeing to make such determinations.

Subjective. Objectively, his view count is soaring and many memes are breaking out because of that upload.
And Lindsay Lohan has seven million followers on Twitter. Some people just like watching a train wreck, others probably aren't aware of the ignorance involved.

Unfortunately, no; not when the world is looking to the sky for authentication of millenarian prophesy.
Well, ISON is just a comet, so apparently that'll just have to do.

Edited for clarity.
 
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cosmic

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Boodles

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Think about how silly the suggestion is... When NASA & STScI have covered the matter in such detail, how is that a cover-up?
On a Mac it was in the Photoshop tool box (clone tool as an instance) or drop down edit (can't recall) or to transform or filter, or blur, to unsharp mask (that's the nifty one) as examples aside parameters of colour and light to cover up 'stuff'. It's been ages since I used it but I was a dab hand. Crossed purposes? Okay, I'm referring to covering up aesthetic inconsistencies in a picture rather than covering up truths concerning any NEO.
Independent observatories and tons of amateurs are going to be imaging the comet. If there were something funky going on, it would be known about, and nobody can keep such information hidden. Do you think NASA or STScI would fake and distribute imagery, knowing how easily everyone else would notice? o_O
No, do you think I would think that?
You don't have to [take my word on it]. A number of stars in the image show diffraction spikes...
I meant honestly, I will, as it is of no genuine relevance and I'm not seeking to discredit an assertion through subjective interpretation of a given person's level of expertise in unrelated instances.
And Lindsay Lohan has seven million followers on Twitter. Some people just like watching a train wreck... aren't aware of the ignorance involved.
I've no idea who you're referring to...
Well, ISON is just a comet, so apparently that'll just have to do.
I didn't suggest otherwise.
 
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Pete Tar

Senior Member
I'm stealing this post from ATS as it's simple and clear -

So what is the objection to this explanation, which is another way of saying what NASA themselves said?

What is the debunking of the debunk?
 
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Boodles

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So what is the objection to this explanation, which is another way of saying what NASA themselves said?
Yes, an excellent, simple illustrative overlay at the end there, no objection from me, sounds perfectly plausible and incorporates the issues concerning the perception of trajectory due to relative positioning and the velocity of two moving objects in a given direction, as well as lens focus and the time lapse distortion in any given length of exposure.

What is the debunking of the debunk?
I am struggling to keep this phone alive, it's hard to even type let alone expand on anything. As far as I could tell from snatched glances at various things, the supposed debunking of debunking I came across in comments, I think, springs from a misunderstanding of the difference between what NASA has done with the image and what the uploader is saying about it. The image is a composite of three images, the uploader refers to - I think - three different filters. Somehow this is conflated in comments there, or nearby, to mean the same thing.
 
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Pete Tar

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Oh, I was hoping for a real anomaly.
Stupid boring old comet.

It's a bit sad that people's sense of wonder can only be engaged by suggestions of cover-ups, when simple comet's are pretty amazing if you can de-junk your mind of pop-culture and look at them with fresh awe.
 

Boodles

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Oh, I was hoping for a real anomaly. Stupid boring old comet.
Sorry to disappoint you.
Simple comet's are pretty amazing if you can de-junk your mind of pop-culture and look at them with fresh awe.
I didn't realise minds were pop-junked over comets to the extent it prevents awesome stuff. If only city authorities would turn the damn lights out people could appreciate the heavens. Where I live I can barely see a thing, even on a clear night.
 
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Boodles

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I stand by my statement based on the content of his videos.
Fair enough point of view, and entitled, of course. In distinguishing between the two - astronomy and photographic techniques - I only sought to... do that. The Dogon of Mali were ancient, renowned stargazers who displayed uncanny understanding of astronomy without so much as a piece of smoothed concave glass to aid vision, mapping or understanding, so I was just saying I think the misunderstanding is borne of technical issues concerning photo imaging of objects in space and not of a misunderstanding of the objects themselves (I've no idea how much this gentleman knows about space, generally, and am loathe to criticise).
 
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cosmic

Senior Member
Fair enough point of view, and entitled, of course. In distinguishing between the two - astronomy and photographic techniques - I only sought to... do that.
But there's no point in doing so. The person doesn't understand enough about Hubble, its operations, or how returned images are processed to yield anything reasonable or accurate, let alone useful. That's a problem.

The larger issue though is why he's making these videos in the first place -- and it's not because he's keen on space, but because he's a doomsayer, and uninterested in presenting accurate information objectively. Perhaps you've not looked through enough of his material to recognize how skewed it is?

The Dogon of Mali were ancient, renowned stargazers who displayed uncanny understanding of astronomy without so much as a piece of smoothed concave glass to aid vision, mapping or understanding,
I dispute that.

so I was just saying I think the misunderstanding is borne of technical issues concerning photo imaging of objects in space and not of a misunderstanding of the objects themselves (I've no idea how much this gentleman knows about space, generally, and am loathe to criticise).
I don't know how you reach this conclusion. If he actually understood that it's simply a comet and recognized its properties, and also had a realistic grasp on how the Hubble image was assembled, why would he misrepresent it in such a fashion?

His knowledge of astronomy and space are poor, and I've been giving you examples. There are many more. Why are you reluctant to accept that?
 

Boodles

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But there's no point in doing so. The person doesn't understand enough about Hubble, its operations, or how returned images are processed to yield anything reasonable or accurate, let alone useful. That's a problem.
For me there is a clear point and that is to dispassionately address the particular merit, or lack thereof, in what someone has claimed. If a claim can be addressed without personally demeaning an individual or speculating about their expertise, or the lack of it, then that's for the better :)
The larger issue though is why he's making these videos in the first place -- and it's not because he's keen on space, but because he's a doomsayer, and uninterested in presenting accurate information objectively. Perhaps you've not looked through enough of his material to recognize how skewed it is?
As above. I haven't looked through his clips, was passing through. I looked at the upload I brought here, thought it seemed plausible, looked a little deeper, read counter-arguments, decided it wasn't plausible but was a timely case in point of how a simple oversight can lead an internet meme to run amok. There's a whole subset of them now on ISON, as you know. I've no idea what level of interest he - or anyone - genuinely has in objectivity and he is not obliged to strive for it either. I am guessing from his accent and profile name that he is from a Gulf of Mexico state and had an interest in expressing himself concerning the BP oil spill.
That was an off the cuff means to illustrate knowledge of astronomy not being inexorably tied - or at all tied - to knowledge of advanced mechanical technologies. Dogon are a thread unto themselves. The article was okay but was seeking to debunk a fable, my point was not concerned with aliens, useless anthropological methodology, Afrocentric revisionism, or western incredulity to affect superiority, but simply if you spend 40 000 years under a clear Saharan sky you know the cosmos and the way it turns.
I don't know how you reach this conclusion.
It was the only one I needed to reach a conclusion on, I'm trying to be efficient with the use of my brain cells. As far as I could tell - with a perma-flat battery and no signal - he was looking at red, green and monochrome (?) filters of the same composite image and not the three separate exposures, and I have no idea if even the filtered images were genuinely from NASA. It doesn't matter as the problem with the claim was then clear.
If he actually understood that it's simply a comet and recognized its properties, and also had a realistic grasp on how the Hubble image was assembled, why would he misrepresent it in such a fashion?
No idea. He could miss his mother, most probably. Perhaps he's been through an embittered divorce. I could continue speculating... :) I realise that sounds sarcastic but in fact I am trying to reaffirm my position.
His knowledge of astronomy and space are poor, and I've been giving you examples. There are many more. Why are you reluctant to accept that?
It is not a question of my reluctance to accept anything. In fact it is quite simple, firstly, as stated, the claim can be refuted without examining anyone's credentials or reason d'etre. Secondly, it's more to do with my personal desire not to in any sense flame those I do not know over the internet, and particularly not on here, a public forum, where I have no control over what is remained as said, other than at the point at which it is said. When I first joined this site I created a thread on the boy scout's jamboree and I can see that it is now given by Mick as another example of a badly focussed thread and I admit to having not read the rules and posting guidelines before having gone on flights of fancy about a couple of things within it but what I mostly took from that was a sense of regret for having indulged, I think it was Cairenn, in talk of David Lory Van Der Beek being insane. I really regret that and for a number of reasons. So, it is not a personal criticism of your choice to freely express wider criticisms of whoever uploaded the video clip above, it is a simple personal preference of mine to refrain from such wider criticisms.
 
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Pete Tar

Senior Member
For me there is a clear point and that is to dispassionately address the particular merit, or lack thereof, in what someone has claimed. If a claim can be addressed without personally demeaning an individual or speculating about their expertise, or the lack of it, then that's for the better....
It does have relevance to a critical examination of a claim to understand a person's motivations and knowledge or lack thereof.
Though it is perhaps secondary, I think you characterise it as being mean-spirited when it's not.
 

cosmic

Senior Member
For me there is a clear point and that is to dispassionately address the particular merit, or lack thereof, in what someone has claimed. If a claim can be addressed without personally demeaning an individual or speculating about their expertise, or the lack of it, then that's for the better :)
His claim is wrong, and that was the first thing I addressed. This isn't about demeaning anyone, it's about showing, beyond the fact that his claims are wrong, that the claimant lacks the necessary knowledge and understanding to make any of those assertions in the first place. I thought that would be helpful. Apparently not.

As above. I haven't looked through his clips, was passing through. I looked at the upload I brought here, thought it seemed plausible, looked a little deeper, read counter-arguments, decided it wasn't plausible...
It wasn't clear you had ever changed your mind along the way. Frankly, I had a difficult time trying to understand what exactly your thoughts were.

...but was a timely case in point of how a simple oversight can lead an internet meme to run amok. There's a whole subset of them now on ISON, as you know.
People have made far-fetched claims about ISON long before this video was made and uploaded. It's not as if his clips are the catalyst for an entirely new crop. YouTube doomsayers have been making outrageous claims about the comet which predate the Hubble imagery we've examined here.

It was the only one I needed to reach a conclusion on, I'm trying to be efficient with the use of my brain cells. As far as I could tell - with a perma-flat battery and no signal - he was looking at red, green and monochrome (?) filters of the same composite image and not the three separate exposures, and I have no idea if even the filtered images were genuinely from NASA. It doesn't matter as the problem with the claim was then clear.
Whether or not you read through any of the materials or explanations I linked, I still have no idea. If your only access to the forum is through a troubled phone/connection, and that significantly limits your ability to follow URLs or view videos, you should consider communicating that upfront to help avoid confusion. Had I known, I'd have gone out of my way to be explicitly clear and made abundant use of the ex tags.

Despite all the video's flaws, your posts still leave me with the impression that you're giving it undue credit. I'm also left feeling we wasted time and keystrokes in this discussion from not being caught up on the same material.
 

Astro

Senior Member
You have beaten me to it, in his subsequent uploads (I think there are two but haven't seen the third - bandwidth issues) he seeks to address this. It would be more ignorance of photography and certain mechanical or engineering processes than ignorance of astronomy itself.
Actually he sought to discredit the explanation of parallax causing this image.
He is not a trustworthy or credible source, and although he has many viewers this simply indicates his popularity, not his accuracy or expertise. I know Boodles is banned and cannot respond, but for posterity's sake here is a complete calculation of the parallax expected in the ISON images given Hubble's orbit.

The first thing you need are the orbital elements of earth, ISON, and Hubble. Here is a scan of a page containing the orbital elements of earth from the book "Practical Astronomy with Your Calculator" by Peter Duffett-Smith.

http://dropcanvas.com/6eyoa

Earth Orbit Epoch 1990.0
Orbital period Tp 1.00004 (tropical years)
Longitude at epoch E 99.403308
Longitude of perihelion w' 102.768413
eccentricity e 0.016713
semi-major axis a 1 (AU)
inclination i 0
Argument of perihelion O 0

Hubble Space Telescope Orbit (from just before the images were taken - using orbital elements close to the observation point is important due to orbital drag and precession of the orbit over time)

Orbit Epoch (Julain Day) 2456412.251
Orbital period (years) Tp 0.0001821
Longitude at Epoch 358.4212
Longitude of Perigee 59.6612
eccentricity 0.0002971
semi-major axis (km) 6934.189
inclination 28.4694
Longitude of ascending node 230.3343
Argument of perigee 189.3269

C/2012 S1 (ISON) Orbit
Perihelion Date (Julian Day) 2456625.264
Argument of Perihelion w 345.54102
Longitude of Perihelion w' 641.2278526
Longitude of Ascending Node O 295.6868325
Inclination i 62.16095792
Eccentricity e 1
Perihelion Distance (AU) q 0.012466817

The rest is just math. First we need to find the number of days since the epoch of those elements.

The first step is to convert the date and time of when we want to know ISON's apparent position as seen from Hubble to a julian day number.
y = year
m = month
d = day (fraction of a day)
The procedure to convert this to Julian day number format is as follows:
If m = 1 or 2, subtract 1 from y and add 12 to m, otherwise y' = y and m' = m
If the date is > or = 1582 October 15 calculate:
A = the integer part of y'/100
B = 2-A+integer part of A/4
otherwise B = 0
if y' is negative calculate C = integer of ((365.25 x y')-.75)
otherwise C = integer part of (365.25 x y')
D = integer of (30.6001 x (m' + 1))
JD = B + C + D + d + 1720994.5

For calculating the position of earth relative to ISON we also want the JD for 1990.0 (which is the epoch of earth's orbital elements), which equals 2447892.5. Therefore, the days since epoch 1990.0 which we will call D

We will first calculate the position of earth at this timepoint before we do the calculations for ISON.
Mean anomaly = 360/365.242191 * D/Tp + E - W
where
D = days since epoch 1990.0
Tp = Period
E = Longitude at epoch (1990.0)
W = Longitude of perihelion
Refer to the above scanned page for all of these values for Earth. In most cases that will give you a number greater than 360 for any date past 1991 because earth will have gone around the sun more than once, so you need to reduce it down to a value within 360 degrees using the following formula:
d = starting value (8568.4260132099 in this case)
(d/360 - integer of (d/360))*360 = d'
if d' < 0, then 360 + ((d/360 - integer of (d/360))*360) = d'
d' is the new value. This formula will be reused later on, I will simply refer to it as the "360 degree routine."

Next is the true anomaly, v. True anomaly is the angle between the real planet's position and its perihelion position. This calls for an iterative process to solve Kepler's equation (E - e*sin(E)

= M).
We start by making an approximation of E = E0 = M
Find the value of
sigma = E-e*sin(E-M)
where
M = mean anomaly
e = eccentricity
if sigma < 10^-6 radians then take the present value of E as the correct solution, otherwise continue for another iteration
For the next iteration find delta E = sigma/(1-e*cos(E0))
E1 = E0 - delta E
Substitute E1 back in the equation above to find a new value for sigma and repeat this routine as necessary until convering on a solution where sigma < 10^-6 radians.

tan (v/2) = Sqrt((1+e)/(1-e))*tan(E)
where
v = true anomaly
e = eccentricity
E = solution to kepler's equation from the iterative process above

find tan(v/2), take the arctangent and multiply the result by 2. You need to evaluate the numerator and denominator within the arctan function separately in order to do a quadrant disambiguation routine. If the numerator is positive and the denominator negative, add 180 to the result of the arctan function (after converting the result to degrees of course). If the numerator is negative and the denominator positive, then add 360 to the arctan result unless that makes it greater than 360 degrees, in which case add 180 degrees. Finally, if both the numerator and denominator are negative, then add 180 degrees to the result of the arctan function. Otherwise if you have made no other additions and the result is negative, add 180 degrees, or else keep the result of the arctan function without adding or subtracting anything.

Now you have v, the true anomaly.

Now we need to calculate heliocentric longitude, l.
l = (360/365.242191 * D/Tp) + 360/pi * e * sin(360/365.242191 * D/Tp + E - W)
where
D = days since epoch
Tp = Period
e = eccentricity
E = longitude at epoch
W = longitude of the perihelion

Use the 360 degrees routine to get l within 360 degrees.
Now we need the radius vector, that is to say, distance from the sun, r.
r = (a*(1-e^2))/(1+e*cos(v))
where
a = semi-major axis of the orbit
e = eccentricity
v = true anomaly

Now we repeat these calculations for Hubble given the values for Hubble's orbit above.
For Hubble we're dealing with an inclined orbit, so we also need to find the latitude. This is given by
U = Arcsin(sin(L - Omega)*sin(i))
where
L = true longitude of Hubble (same formula as heliocentric longitude for earth)
omega = longitude of the ascending node
i = inclination
Now we need to find the geocentric longitude; true longitude consists partly of values which are inclined to the equator by Hubble's inclination.

L' = v+w'-O
where
v = true anomaly
w' = longitude of perigee
O = argument of perigee
Perform the 360 degree routine on L'
Now we re-orient L' back into the plane of the equator so that we can find the geocentric longitude with respect to the vernal equinox, effectively geocentric right ascension.

geocentric right ascension = arctan((sin(L')*cos(e))/cos(L'))+O
where L' equals the result from above
e = eccentricity
O = argument of perigee
Remember to evaluate the arctan function using the quadrant disambiguation routine described above

Now we need to find the geocentric longitude. We now know the angle of Hubble east of the vernal equinox, but we need to know the number of degrees the vernal equinox is of the 0 line of longitude, the prime meridian, in other words, we need to know Greenwhich mean sidereal time.

GMST = 18.697374558+24.0657098244191*(JD-2451545)
GMST*15 = GMST in degrees
Perform the 360 degree routine on GMST in degrees to get the value within 360 degrees.
Now take the geocentric right ascension and subtract GMST in degrees. This is the eastern

longitude of Hubble. If the value is negative, it's west longitude, if the value is positive it is east longitude. Save this value and the latitude calculated above for later.

Now we need to calculate the position of ISON relative to earth. The orbital elements are listed above. We will approximate ISON's orbit as a parabolic orbit to aid in the ease of calculation.

First find W
W = (0.0364911624/(q*sqrt(q))) * d
where
q = perihelion distance
d = days since perihelion (perihelion date in Julian Days - JD)

Now we need to solve s^3 + 3s - W = 0

First approximate s = s0 = W/3
calculate sigma
sigma = s0^3 +3*s0 - W
if sigma < 10^-6 degrees then take s as the correct value otherwise continue with the iterations and proceed below
s1= (2*s0^3 + W)/(3(s0^2 + 1))
substitute s1 back into the formula above to find sigma and repeat until the value is within the accuracy of sigma <10^-6 degrees. Then take that value of s and proceed
Find the true anomaly
v = 2*arctan (s)
Find the distance from the sun
r = q*(1+s^2)
where
q = perihelion distance in AU
find heliocentric ecliptic longitude
l = v+w'
where
v = true anomaly
w'= longitude of perihelion
find the heliocentric ecliptic latitude
U = Arcsin(sin(l - O)*sin(i))
where
l = heliocentric ecliptic longitude
O = argument of perihelion
i = inclination

Now we need l' which is the heliocentric longitude projected onto the plane of the ecliptic.
l' = arctan((sin(l-O)*cos(i))/cos(l-O))+O
where
l = heliocentric ecliptic longitude
O = argument of perihelion
i = inclination
remember to perform the quadrant disambiguation routine on the arctan function

Now we calculate the geocentric ecliptic longitude (lam) and latitude (beta) of comet ISON. If ISON's radius vector from the sun is less than earth's at the time you are evaluating you can regard it as an inner planet in which case the formula is this:
lam = 180 + Le + arctan ((ri*sin(Le-l'))/(re-ri*sin(Le-l')))
where
Le = heliocentric longitude of earth
re = radius vector of earth
rI = radius vector of ISON
l' = heliocentric longitude of ISON projected onto ecliptic
Note that you need to follow the same quadrant disambiguation routine as listed above for the arctan function in this formula.

If ISON's radius vector from the sun is greater than earth's at the time you are evaluating you can regard it as an outer planet in which case the formula is this:
lam = arctan((re*sin(l'-Le)/(rI-re*cos(l'-Le)))+l'
where
Le = heliocentric longitude of earth
re = radius vector of earth
rI = radius vector of ISON
l' = heliocentric longitude of ISON projected onto ecliptic
Note that you need to follow the same quadrant disambiguation routine as listed above for the arctan function in this formula.

beta is calculated with the following formula:
beta = arctan((r'*tan(U)*sin(lam-l'))/(re*sin(l'-Le))
where
Le = heliocentric longitude of earth
re = radius vector of earth
l' = heliocentric longitude of ISON projected onto ecliptic
U = heliocentric latitude for ISON
r'= radius vector of ISON

Note that you need to follow the same quadrant disambiguation routine as listed above for the arctan function in this formula.

Distance of ISON from earth
reI=sqrt(rI^2+re^2-2*re*ri*cos(l'-Le)*cos(U))
where
Le = heliocentric longitude of earth
re = radius vector of earth
rI = radius vector of ISON
l' = heliocentric longitude of ISON projected onto ecliptic
U = heliocentric latitude for ISON

For the next step we will need the obliquity of the ecliptic. This can be calculated with the following formula, which will need time "t" centuries from 2000.0. We can calculate t thusly:
t = ((JD-2451545)/36525)
where JD = julian day number

Obliquity of the ecliptic (Obl) can then be calculated with this formula:
Obl = 23.43928-0.013*t+0.555*(10^-6)(t^3)-0.0141(10^-8)*(t^4)

Now we just have to convert these coordinates from ecliptic to equatorial and we will have the geocentric equatorial coordinates of ISON at this timepoint.
Right ascension = arctan((sin(lam)*cos(Obl)-tan(beta)*sin(Obl))/cos(lam))
where
lam = geocentric ecliptic longitude
beta = geocentric ecliptic latitude
obl = obliquity of the ecliptic
Note that you need to follow the same quadrant disambiguation routine as listed above for the

arctan function in this formula.

declination = arcsin(sin(beta)*cos(obl)+cos(beta)*sin(obl)*sin(lam))
where
lam = geocentric ecliptic longitude
beta = geocentric ecliptic latitude
obl = obliquity of the ecliptic

Now we have the geocentric coordinates for ISON, but we need to account for the parallax induced by

Hubble's orbit.

First find u
u = atan(0.996647*tan(U))
where U = geocentric latitude of Hubble

Next find p*sin(theta')
p*sin(theta') = 0.996647*sin(u)+(r/6378140)*sin(theta)
where
u = u above
r = altitude of hubble (convert to meters)
theta = geocentric lattitude of hubble

find p*cos(theta')
p*cos(theta') = cos(u)+r/6378140*cos(theta)
where
u = u above
r = altitude of hubble (convert to meters)
theta = geocentric lattitude of hubble

pi = (atan((6378140+r)/149597870700)*3600)/reI)/3600
where
r = altitude of Hubble (in meters)
reI = distance of ISON from earth

LST = (GMST*15)+Lh
where
GMST = Greenwhich mean sidereal time
Lh = geocentric longitude of Hubble
Perform the 360 degree routine to get LST in degrees for the equation below

delta RA = atan((p*cos(theta')*sin(pi)*sin(LST-RA))/(cos(declination)-p*sin(theta')*sin(pi)*cos(LST-RA))
where
RA = geocentric right ascension of ISON declination = geocentric declination of ISON.
Note that you need to follow the same quadrant disambiguation routine as listed above for the arctan function in this formula.

subtract delta RA from the geocentric right ascension of ISON to get the parallax corrected right ascension of ISON which we will call the hubble centric RA

gamma = atan(tan(p*sin(theta')/p*cos(theta'))cos(.5*delta RA)(1/cos(LST-.5*(geocentric RA + hubble centric RA)))

delta declination = (p*sin(theta')*sin(pi)*sin(gamma-geocentric declination))/(sin(gamma)-p*sin(theta')*sin(pi)*cos(gamma-geocentric declination))

subtract delta declination from the geocentric declination to get the parallax corrected declination of ISON which we will call the hubble centric declination. Now we have both the hubble centric RA and hubble centric declination for this point in time. If you repeat these equations over multiple points in time covering the imaging times for the Hubble images (times are listed here: http://archive.stsci.edu/hla/ison/ ) you can generate a list of coordinates for ISON over the imaging session and graph the predicted trail of ISON as seen from Hubble over that period of time. Doing so results in the following graph which matches with the images taken by Hubble:

https://www.metabunk.org/data/MetaMirrorCache/0083999325320aac9955865465be857a.gif
 
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