[Tom Bishop]

How is a Columbia University Professor Emeritus of Celestial Mechanics an invalid source? I doubt that your credentials are as good to tell us how this works.

Sounds like a smart guy, but he is beside the point. The point is, these astronomers found, derived, calculated, and predicted a collision with Jupiter, when it would occur, and where it would occur on Jupiter's surface. And it was witnessed.

How does FET account for that? Can FET make such a prediction? If so, how?

FE and RE has nothing to do with it. Astronomers are merely predicting the motion of epicycles. The underlying 'ideal' state on which the deviations differ can be based on anything.

[stack]

How is a Columbia University Professor Emeritus of Celestial Mechanics an invalid source? I doubt that your credentials are as good to tell us how this works.

Sounds like a smart guy, but he is beside the point. The point is, these astronomers found, derived, calculated, and predicted a collision with Jupiter, when it would occur, and where it would occur on Jupiter's surface. And it was witnessed.

How does FET account for that? Can FET make such a prediction? If so, how?

FE and RE has nothing to do with it. Astronomers are merely predicting the motion of epicycles. The underlying 'ideal' state on which the deviations differ can be based on anything.

Wait, so now FET is in agreement with the fact that Jupiter has a diameter of about 88,695 miles which is more than 11 times the diameter of Earth? FET would need to because part of the astronomers' calculations had to take into account the diameter of Jupiter to determine when and where on the planet the debris would hit.

Could FET make the prediction just using an epicycle?

[Tom Bishop]

Wait, so now FET is in agreement with the fact that Jupiter has a diameter of about 88,695 miles which is more than 11 times the diameter of Earth? FET would need to because part of the astronomers' calculations had to take into account the diameter of Jupiter to determine when and where on the planet the debris would hit.

No, they did not take it into account for any meaningful purpose. Once you start adding epicycles, the underlying model is meaningless.

Here is an orbit in the shape of Homer Simpson, based on the Ptolmy's underlying ideal model of a circle with uniform motion:

Could FET make the prediction just using an epicycle?

It can be done with any underlying model. FE does not propose a dogmatic underlying 'ideal' celestial model or force that must be justified and adhered to with intellectually wrong epicycles.

[stack]

Wait, so now FET is in agreement with the fact that Jupiter has a diameter of about 88,695 miles which is more than 11 times the diameter of Earth? FET would need to because part of the astronomers' calculations had to take into account the diameter of Jupiter to determine when and where on the planet the debris would hit.

No, they did not take it into account for any meaningful purpose. Once you start adding epicycles, the underlying model is meaningless.

You are wrong. They most certainly took the known size of Jupiter into account. From the paper I cited before, titled 'Tidal Disruption and the Appearance of Periodic Comet Shoemaker-Levy 9', one of just page after page of calculations used to model/predict the collision:



Note: R3 is Jupiter’s equatorial radius

And that's just scratching the surface, as it where:



https://trs.jpl.nasa.gov/handle/2014/36567

Could FET make the prediction just using an epicycle?

It can be done with anything, and any underlying model. FE does not propose an underlying 'ideal' celestial dogma model or force that must be justified and adhered to with epicycles.

Wrong again. Read the paper I referenced that describes how it was calculated. A massive undertaking.

Bottom line, FET could not have predicted the collision and modern heliocentric calculation could and did.

So again, if "It can be done with anything, and any underlying model," show us how FET could do it. Prove me wrong.

[Tom Bishop]

I did show you to be wrong. I gave you an epicyclic Homer Simpson. The layered corrections made the underlying model of a circle with uniform motion meaningless.

Any paper you present on astrodynamics is going to be peppered with terms like "perturbations" and "Fourier," which are epicyclic theories. The underlying model may be a mass going around another mass, but the epicycle corrections layered upon that make it meaningless beneath.

[stack]

I did show you to be wrong wrong. I gave you an epicyclic Homer Simpson. The layered corrections made the underlying model of a circle with uniform motion meaningless.

Any paper you present on aerodynamics is going to be peppered with terms like "perturbations" and "Fourier," which are epicyclic theories. The underlying model may be a mass going around another mass, but the epicycle corrections layered upon that make it meaningless beneath.

How was the epicycle of the comet derived only having been discovered less than a year before impact and without a complete orbit?

And like I said, the page after page of calculations were not meaningless - They were required to help predict the orbit and time and location on Jupiter of the collision. That much is clear. And part of those calculations took into account the known size of Jupiter as previously shown. Without which the collision could not have been predicted.

So again, if it's just an epicycle as you claim and "It can be done with anything, and any underlying model," as you claim, show us how FET could do it. Prove me wrong.

[Tom Bishop]

How was the epicycle of the comet derived only having been discovered less than a year before impact and without a complete orbit?

The comet was just going in an ellipse, and it was only a portion of the ellipse that needed to be completed, which is a little easier to predict than a Homer Simpson.

Take a look at this simple circular uniform motion:



Is it possible to predict where the body in orbit will be after x amount of time?

And like I said, the page after page of calculations were not meaningless - They were required to help predict the orbit and time and location on Jupiter of the collision. That much is clear.

How is it clear? As soon as you start adding on corrections to your model the underlying model becomes irrelevant. It's no longer your model.

[Tom Bishop]

So again, if it's just an epicycle as you claim and "It can be done with anything, and any underlying model," as you claim, show us how FET could do it. Prove me wrong.

Here you go. I used an epicycle with two terms to make an ellipse. With only these two terms it is possible to predict the path of the orbit and the shape of the ellipse for any given time in the future.



We can see that with a uniform epicycle like this, that you would only need to build a small segment of the ellipse, in order to be able to make a model of the entire ellipse useful for prediction. You only need those two terms.

[JSS]

Sounds pretty clear what the Newtonian Perturbation Theory is to me.

Everything you quoted was simply conjecture, guessing at the methods used, and guessing they were somehow wrong, even though you were shown papers where they described it, even though it worked perfectly.

You can claim it's perturbation this or epicycle that or pattern something, but none of that is evidence at all of anything, let alone evidence against the FACT that they correctly predicted it. You keep ignoring the fact that the math they used WORKS. You can not avoid addressing this and have any argument at all.

You claim that it's all fake math somehow that doesn't represent reality.

You can't do that without showing what this hidden reality looks like. Lets see some equations that predict better than what we have, then we can talk.

[BRrollin]

How is a Columbia University Professor Emeritus of Celestial Mechanics an invalid source? I doubt that your credentials are as good to tell us how this works.

From the paper you posted, in the summary and conclusion section:

In this paper, we derived the Copernican system of epicycles from Newton’s gravitational force law in vector form
via linear perturbation theory in Clifford (geometric) algebra Cl2,0 of the plane.

It says that they derived Copernicus's epicycles with the Newtonian perturbation theory, which we had learned were also epicycles with a gravitational disguise.

Ptolmy's epicycle theory is described as follows:

  “ The circle is the geometric figure possessing perfect symmetry, so Ptolemy and earlier Greek astronomers began with the intuition that celestial bodies orbit in circles at uniform speed. Observations then determined the deviations from the ideal, which Ptolemy modeled using mathematical contrivances unrelated to physical principles (deferents, epicycles, and equants).

...Ptolemy’s science was superficially anti-Platonic in that he emphasized the role of careful observation. However, at a deeper level, his science was a logical application of Platonism; in astronomy and in optics, he started with the “perfect” model and then merely described without explanation the inherently unintelligible deviations from it. ”

Charles Lane Poor says:

"The deviations from the “ideal” in the elements of a planet’s orbit are called “perturbations” or “variations”.... In calculating the perturbations, the mathematician is forced to adopt the old device of Hipparchus, the discredited and discarded epicycle."

Dr. Vijaya said earlier:

"In the process, a new form of theory became popular: Perturbation theory. In this approach, a small approximate deviation from Newton's law is assumed, based on empirical data, and then a rigorous calculation of differential equation is used to nail down the actual value of the deviation. It does not take much to recognize that this was simply the approach taken before Kepler by Copernicus and others for over a thousand years – adding epicycles to make the observations fit. It is the same concept, but now dressed up in gravitational disguise"

Sounds pretty clear what the Newtonian Perturbation Theory is to me.

It does sound clear, I agree. But you interpret the order incorrectly. The Newtonian theory DERIVES the epicycles.

The mathematics in my source has not been disputed.

Rather, you use non-scientific statements from sources to argue the philosophy. The hope is that since the sources used to be scientists, then their opinions will be convincing to an untrained reader. You can do this all day long, but the mathematical model remains unchallenged.

Until the mathematical model is directly challenged, all editorial comments from anyone is anecdotal.

Quoting an emeritus professor’s opinion of the history is an appeal to authority fallacy. His historical opinion is not automatically valid just because of his tenure in another field.

What you are doing is relying on the interpretation of the history by individuals who conclude your desired result.

What you SHOULD do is understand the mathematical model yourself so that you are in a position to debate it. Why don’t you try to do that, if you can.

Oh, by the way, attacking my credentials is an ad hominem fallacy. I would hope you would be better than that, Thomas.

[stack]

So again, if it's just an epicycle as you claim and "It can be done with anything, and any underlying model," as you claim, show us how FET could do it. Prove me wrong.

Here you go. I used an epicycle with two terms to make an ellipse. With only these two terms it is possible to predict the path of the orbit and the shape of the ellipse for any given time in the future.



We can see that with a uniform epicycle like this, that you would only need to build a small segment of the ellipse, in order to be able to make a model of the entire ellipse useful for prediction. You only need those two terms.

'Uniform'?

From 'Lessons from Shoemaker-Levy 9 about Jupiter and Planetary Impacts

Jupiter most likely captured SL9 in 1929 ± 9, and tidally disrupted it during a perijove passage just 0.3 Jupiter radii above the cloudtops on July 7, 1992 (Chodas and Yeomans 1996, see also Chapter 12). Carolyn S. Shoemaker discovered SL9 on March 24, 1993, on a photographic plate that she, Eugene M. Shoemaker, and David H. Levy took with the Palomar 0.46-m Schmidt telescope (Shoemaker et al. 1993, Figure 8.2). On May 22, 1993, Nakano et al. (1993) predicted the impacts.
http://lasp.colorado.edu/home/mop/files/2015/08/jupiter_ch8-1.pdf

Here's what the comet's trajectory was modeled to look like up until impact:



Like I mentioned and cited before, the known size of Jupiter had to be taken into consideration for the calculations to know just when and where on Jupiter the collision would be made. In the Heliocentric world, Jupiter has a diameter of about 88,695 miles. What is the size of Jupiter in FET?

[GreatATuin]

So again, if it's just an epicycle as you claim and "It can be done with anything, and any underlying model," as you claim, show us how FET could do it. Prove me wrong.

Here you go. I used an epicycle with two terms to make an ellipse. With only these two terms it is possible to predict the path of the orbit and the shape of the ellipse for any given time in the future.



We can see that with a uniform epicycle like this, that you would only need to build a small segment of the ellipse, in order to be able to make a model of the entire ellipse useful for prediction. You only need those two terms.

That's nice, but how does that help for predicting a collision? If the orbit is uniform, the comet never collides.

[Tom Bishop]

So again, if it's just an epicycle as you claim and "It can be done with anything, and any underlying model," as you claim, show us how FET could do it. Prove me wrong.

Here you go. I used an epicycle with two terms to make an ellipse. With only these two terms it is possible to predict the path of the orbit and the shape of the ellipse for any given time in the future.



We can see that with a uniform epicycle like this, that you would only need to build a small segment of the ellipse, in order to be able to make a model of the entire ellipse useful for prediction. You only need those two terms.

'Uniform'?

From 'Lessons from Shoemaker-Levy 9 about Jupiter and Planetary Impacts

Jupiter most likely captured SL9 in 1929 ± 9, and tidally disrupted it during a perijove passage just 0.3 Jupiter radii above the cloudtops on July 7, 1992 (Chodas and Yeomans 1996, see also Chapter 12). Carolyn S. Shoemaker discovered SL9 on March 24, 1993, on a photographic plate that she, Eugene M. Shoemaker, and David H. Levy took with the Palomar 0.46-m Schmidt telescope (Shoemaker et al. 1993, Figure 8.2). On May 22, 1993, Nakano et al. (1993) predicted the impacts.
http://lasp.colorado.edu/home/mop/files/2015/08/jupiter_ch8-1.pdf

Here's what the comet's trajectory was modeled to look like up until impact:

The 'final orbit', which is the only orbit that was predicted (a segment of the final orbit), looks pretty symmetrical. It looks something like the symmetrical ellipse I provided. The comet was discovered in its final orbit.

The prior orbits were unobserved, and are presumably based on someone's backwards-in-time orbit project.

Since they only predicted a (portion of a) single symmetrical orbit, it is much less impressive than if they had predicted multiple orbits from the beginning. In this case they did the equivalent of predicting the shape of one of Homer Simpson's epicyclic eyeballs before it was completed.

[BRrollin]

Here is a short animation that depicts how Newtonian robots deliver epicycles as a geometric observational consequence.

https://www.reddit.com/r/Damnthatsinteresting/comments/ga5mn3/dance_of_mars_and_jupiter/

[stack]

So again, if it's just an epicycle as you claim and "It can be done with anything, and any underlying model," as you claim, show us how FET could do it. Prove me wrong.

Here you go. I used an epicycle with two terms to make an ellipse. With only these two terms it is possible to predict the path of the orbit and the shape of the ellipse for any given time in the future.



We can see that with a uniform epicycle like this, that you would only need to build a small segment of the ellipse, in order to be able to make a model of the entire ellipse useful for prediction. You only need those two terms.

'Uniform'?

From 'Lessons from Shoemaker-Levy 9 about Jupiter and Planetary Impacts

Jupiter most likely captured SL9 in 1929 ± 9, and tidally disrupted it during a perijove passage just 0.3 Jupiter radii above the cloudtops on July 7, 1992 (Chodas and Yeomans 1996, see also Chapter 12). Carolyn S. Shoemaker discovered SL9 on March 24, 1993, on a photographic plate that she, Eugene M. Shoemaker, and David H. Levy took with the Palomar 0.46-m Schmidt telescope (Shoemaker et al. 1993, Figure 8.2). On May 22, 1993, Nakano et al. (1993) predicted the impacts.
http://lasp.colorado.edu/home/mop/files/2015/08/jupiter_ch8-1.pdf

Here's what the comet's trajectory was modeled to look like up until impact:

The 'final orbit', which is the only orbit that was predicted (a segment of the final orbit), looks pretty symmetrical. It looks something like the symmetrical ellipse I provided. The comet was discovered in its final orbit.

The prior orbits were unobserved, and are presumably based on someone's backwards-in-time orbit project.

Absolutely, I agree.

Since they only predicted a (portion of a) single symmetrical orbit, it is much less impressive than if they had predicted multiple orbits from the beginning. In this case they did the equivalent of predicting the shape of one of Homer Simpson's epicyclic eyeballs before it was completed.

If you had read the papers I have cited you would see that the predicative efforts were far more complex than the Homer vid and the predictions were correct.

I noticed you didn't answer my question. Like I mentioned and cited before, the known size of Jupiter had to be taken into consideration for the calculations to know just when and where on Jupiter the collision would occur. In the Heliocentric world, Jupiter has a diameter of about 88,695 miles.

What is the size of Jupiter in FET?

[stack]

Since they only predicted a (portion of a) single symmetrical orbit, it is much less impressive than if they had predicted multiple orbits from the beginning. In this case they did the equivalent of predicting the shape of one of Homer Simpson's epicyclic eyeballs before it was completed.

The following from the folks who greatly aided in deciphering and predicting all of the shards that would hit Jupiter, where and when on its surface:

The orbital motion and impact circumstances of Comet Shoemaker-Levy 9
ByPAU L W. CHODAS and DONALD K. YEOMANS Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA

To determine the basic characteristics of SL9's orbit and its impending impact, we quickly modified our software to provide jovicentric information, including position, velocity, and orbital elements as a function of time. It became clear tha t the comet was approaching the apojove of an extremely eccentric orbit about Jupiter, with eccentricity ~ 0.99 and apojove distance ~ 0.33 AU (see Fig. 1). By June 1, we had determined tha t the impact would occur in the mid-southern latitudes of Jupiter, and, unfortunately, on the side of the planet facing away from Earth. We defined impact to occur when the comet reached the one bar pressure level in Jupiter's atmosphere, which we modeled as an oblate spheroid with radius and flattening given by Davies et, al. (1992).

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/7C7A50945B166FCC28D197F3A53EB2D5/S025292110011543Xa.pdf/orbital_motion_and_impact_circumstances_of_comet_shoemakerlevy_9.pdf

As you can see, data was required from a Jovian (Jupiter) perspective in order to predict the orbit and impact. Hence, size and position of Jupiter had to be factored not just through observation, but through calculation as well. And they nailed the prediction.

Which begs the questions: Where and what is the size of Jupiter in Flat Earth Theory?

[Tom Bishop]

Also from the linked paper:

"The need for accurate impact predictions required the modeling of the perturbative effects of the Galilean satellites and Jupiter's oblateness."

"Tidal disruption during an approach to within the Roche limit of a large perturbing body is a common mechanism for cometary splitting."

"In April, we upgraded the dynamical models used in our orbit determinations and impact predictions. Up until this time, we had used only point mass perturbations by the sun and planets, with planetary positions and masses taken from JPL planetary ephemeris DE200 (Standish 1990). But now, we switched to the more accurate planetary ephemeris DE245, and refined our models to include perturbations due to the Galilean satellites and the J2 and J4 zonal harmonic terms of Jupiter's gravity field."

"Our approach was to create a random ensemble of 1000 initial conditions whose statistics matched the actual orbital element uncertainties and correlations. Effectively, a six-dimensional uncertainty ellipsoid in orbital element space was populated with 1000 random points to obtain an ensemble of initial conditions consistent with the actual 6x 6 covariance matrix of the orbital solution. As before, our dynamic model included solar and planetary perturbations, as well as perturbations from the Galilean satellites and Jupiter's oblateness (J2 and J4 terms)."

"Our orbit computations used not only planetary and solar perturbations, but also perturbations due to the Galilean satellites and Jupiter's oblateness."

It sounds like this is based on perturbation theory to me.

As we read previously, perturbations are epicyclic corrections added to make an underlying model match observation.

And they nailed the prediction

Not really that impressive if they resorted to epicycles to make data fit.

Which begs the questions: Where and what is the size of Jupiter in Flat Earth Theory?

FE doesn't have a theory about Jupiter.

[stack]

Also from the linked paper:

"The need for accurate impact predictions required the modeling of the perturbative effects of the Galilean satellites and Jupiter's oblateness."

"Tidal disruption during an approach to within the Roche limit of a large perturbing body is a common mechanism for cometary splitting."

"In April, we upgraded the dynamical models used in our orbit determinations and impact predictions. Up until this time, we had used only point mass perturbations by the sun and planets, with planetary positions and masses taken from JPL planetary ephemeris DE200 (Standish 1990). But now, we switched to the more accurate planetary ephemeris DE245, and refined our models to include perturbations due to the Galilean satellites and the J2 and J4 zonal harmonic terms of Jupiter's gravity field."

"Our approach was to create a random ensemble of 1000 initial conditions whose statistics matched the actual orbital element uncertainties and correlations. Effectively, a six-dimensional uncertainty ellipsoid in orbital element space was populated with 1000 random points to obtain an ensemble of initial conditions consistent with the actual 6x 6 covariance matrix of the orbital solution. As before, our dynamic model included solar and planetary perturbations, as well as perturbations from the Galilean satellites and Jupiter's oblateness (J2 and J4 terms)."

"Our orbit computations used not only planetary and solar perturbations, but also perturbations due to the Galilean satellites and Jupiter's oblateness."

It sounds like this is based on perturbation theory to me.

As we read previously, perturbations are epicyclic corrections added to make an underlying model match observation.

How do "perturbations...make an underlying model match observation."

Are you saying that any underlying model can be fitted to perturbations? Like the FET model (whatever that may be) could be fitted into the perturbations and predicted almost exactly when and where the multitudes of comet debris would hit Jupiter?

 If so, how might FET have done so in this circumstance? How might the underlying model of FET be applied? Do tell.

[stack]

I see you edited your previous post to include this:

And they nailed the prediction

Not really that impressive if they resorted to epicycles to make data fit.

Which begs the questions: Where and what is the size of Jupiter in Flat Earth Theory?

FE doesn't have a theory about Jupiter.

I didn't ask if FE had a theory about Jupiter. I asked "If so, ("perturbations...make an underlying model match observation.") how might FET have done so in this circumstance? How might the underlying model of FET be applied? Do tell.

But, in essence, what you're saying is that FET has no idea where or how large Jupiter is. Therefore, FET could never have predicted the collision, let alone with the accuracy with which these aforementioned calculations did, the when and the where.

Decidedly, here is an example of where modern astronomical predictions based upon observations and calculations eclipses anything that FET could muster. In essence, FET fails to match heliocentricity.

[Tom Bishop]

How do "perturbations...make an underlying model match observation."

As previously discussed, pertubations are calculated on basis of epicycles and are used to make a theory fit observations.

The dynamics of galaxies are also based on epicycles to make a theory fit data:

https://arxiv.org/ftp/arxiv/papers/0911/0911.1594.pdf

Lindblad’s epicycles – valid method or bad science?

In popular culture, epicycles have become almost synonymous with bad science; “adding epicycles” refers to a process of introducing fudges to make a theory fit data, when actually the theory needs to be replaced in its entirety. It is generally believed that epicycles were banished from science when Newton solved his equations of motion and showed that it follows from the inverse square law of gravity that planetary orbits are ellipses. So, it comes as something of a surprise to those unfamiliar with galactic dynamics that the galactic orbits of stars are treated in textbooks using a theory of epicycles revitalized by Bertil Lindblad in the 1920s, and used to introduce density wave theory, which, as reinforced by Lin & Shu (1964), by Lin, Yuan and Shu (1969) and by Kalnajs (1973), has been the leading model of spiral structure for nearly 40 years.

~

Conclusion

The implication to astrophysics is severe. The motions of stars are governed by known mathematical laws. Astrophysics is, or at least it should be, a mathematical science. One should therefore expect that theories in astrophysics are subjected to rigorous mathematical scrutiny. Regrettably, the degree of scrutiny applied to Lindblad’s epicycles and to density wave theory has been seriously lacking. Students should be made aware that these ideas can no longer be considered as science, and authors of textbooks should consider whether they merit anything more than a historical note.

If so, how might FET have done so in this circumstance? How might the underlying model of FET be applied? Do tell.

FE doesn't propose a planetary theory.

FET fails to match heliocentricity.

Interesting that you think that a model with epicycles is valid. However, epicycles do not make a system valid. It is the reason Ptolmy's model was rejected