## Frequently Asked Questions and Comments --- ## FAQ ## Negative Angles Obs at the beach looking at water. The horizon merges the ground. Over the hump of water between him and where the celestial horizon actually meets the equator ## "Where is the star?" --- ## Comments from YouTube > Your presentation is based on deliberate lying about basic atmospheric optics and geometry. Bold claim. Let's go through your analysis and see if you were able to address anything with specifics. Hopefully you didn't just use ChatGPT to recite a non-refutation in the form of "nu-uh". > The repeated claim that “astronomical refraction is always half the distance angle” is simply wrong. Refraction depends on the vertical gradient of the refractive index of air, not on the distance to the object. You're confusing astronomical refraction with terrestrial. They don't know the vertical gradient beyond the boundary layer. That's why they require the assumption of Laplace's theorem to justify their strictly static modeling conditions to facilitate the exact amount of astronomical refraction. > Near the zenith, the effect is only a few arcseconds, whereas at the horizon it reaches 35 arcminutes. I agree with the zenith and disagree with the 35' at the horizon. That figure would come out of the empirically derived formula, not from actual atmospheric conditions, which is what is in contention. No value higher than 14' at the horizon, with an observer 6m above sea has ever been measured. The lowest elevation to a peak that was measured was 45' with an observer alt of 2072m. The refraction correction there (predicted by formulae) is 23'. The measured difference was 13'. For an observer at 6m above sea level at an angle of 53', the refraction was 14', not the predicted 26'. > It is never a constant fraction of any distance angle. It's always compensating for ~half the drop. The entire was going over slides showing that relationship. Mike showed it another way by doing 1/2 180xdist/2pir, but I have to learn more about that one. > You also artificially separate “terrestrial” and “astronomical” refraction as if they were unrelated phenomena. In reality, both are manifestations of the same physical law: light bends when passing through layers of air with different densities. The only difference is the length of the path and the atmospheric conditions along it. They are unrelated. The cause (following Snell's law) is the same, but mechanistically they are not produced by the same conditions and because of that, they have different effects on the path of light. Terrestrial refraction is governed by the boundary layer. Thermal conditions effect the temp and pressure gradient throughout the day, causing a uniform vertical profile that lifts objects 1:1. It's that uniform gradient that allows refracted images to preserve their shape when they're lifted up. Astronomical refraction doesn't have a vertical temp profile to uniformly create lift. Changes in the gradient above the boundary layer govern here. To this day it is not tell know and the conditions are modeled out assuming Laplace's theorem is correct so they can make static, smooth gradients that extend radially outward from a sphere. Astronomical refraction causes deformation and magnification of objects. Further, one of the our measurements at Mount Rosa was only 30'' different from the peak. Meaning there was almost no refraction at that time for the occlusion. Terrestrial refraction at that location was 2'. If terrestrial refraction effected the measurements in the way you suggest, any measurement sub 2' would be impossible. > Bennett’s formula is not a “scam” but an empirically validated approximation derived from real measurements. It has been used successfully for decades in astronomy and navigation. > If it were wrong, astronomical almanacks and satellite tracking would not work. The formulae provided work with the model because it explains why the stars aren't following 15°/h. It maintains internal consistency. I'm not saying that moving the star to that location doesn't fix the problem for the globe, the globe is entirely dependent on that relationship to give that appearance that it works. > Your treatment of star consultations behind mountains also confuses apparent and true positions. The apparent position (what we see) is shifted by refraction relative to the true geometric position. Ignoring this distinction leads you to false conclusions. This is why you should never let a machine do your bidding. Your conclusion is my premise. > Likewise, claiming that negative altitudes are “illusions” is incorrect: negative apparent altitudes are standard in astronomy, which explains why the Sun remains visible after it is geometrically below the horizon. Mixing two arguments. The negative angle in question regarding occlusions, is created by the occluding peak not actually being the horizon. There's a horizon behind that peak. Your elevation difference in combination with the previous creates that that illusion. It's asserted that a sunset for an obs on the ground, not occluding by an object, but the "Earth, rather, would be a physical angle, if the object were actually beneath our feet. A hypotheses that can't be confirmed by simply watching a sunset. If the Earth were a globe and the Earth were occluding the sun (stars, etc), then the fraction wouldn't be 1:1. As shown by all 50 some measurements, the sun would linger at the horizon and the immediately vanish once it was too far below the horizon. In instances where the astronomic refraction would have kept the stars above the peak, it still occluded well before any of the prescribed astronomical refraction amounts and that never happens. > In short, your model ignores key atmospheric variables, misuses formulas, and replaces physics with rhetoric. That is why your conclusions do not match reality. We quantify the empirically derived formulas are incorrect. They work entirely off a curve fit based on models with as much assumptions built into them as one can assume. Your analysis was insufficient to refute the null hypothesis, the methodology or any of the contentions we brought up. Farewell. --- ## FAQ Rollin's Questions --- `stellarium uses the distances to stars. you'd have to show me explicitly where in the code it is placing the stars on a "celestial sphere" and where in the code it is using flat observation plane.` Stellarium doesn't use distances to the stars. Nothing in the world functions on "true distances" to the stars. Stellarium works off the the two sphere model (celestial sphere and terrestrial sphere). The apparent position of a star is what's called topocentric. That's where the observer is located (surface of earth). In order to relate a star to a geographic position (GP) on earth, you need to a geocentric transformation. The geocentric transformation moves the observer to the center of the Earth and the star to the surface. All that's really being done here is astronomical refraction is being subtracted out and you're left with the star's "true position". By doing this, the GP is established via angle at that time, which gives you the circle of equal altitude for cel nav. None of the so-called "distances to stars" is used for anything. Everything in the sky is treated as an equidistant web fixed a sphere of radius 6371 km that rotates around the observer in the center. If the star's "true distance" mattered, they all wouldn't follow the same 60 NMi/° @ 15°/h. `where in the code it is using flat observation plane.` Any transformation that relates celestial coordinates to geodetic must do this. You can find directional vector transformations here: https://discord.com/channels/1142257006795825153/1417114351130640515/1462857684683591924 Section 192 - 208. `i think they are unfounded and wrong. "celestial sphere" is really just a convenient abstraction, not a real model in itself.` The celestial sphere is an abstraction, however to use it, you must also introduce another abstraction, which is the terrestrial sphere. These completes the two sphere model. The two sphere model was given to us through the historical narrative of Ptolemy in his book Geographia where he explains how to use the two sphere model. This is the same model used today that defines the globe. Nothing has changed. The celestial sphere is a sphere of infinite radius (effectively flat) if you want to use it, you must do a geocentric transformation and put the observer in the center of earth. This is what binds the assumed linear relation of 60 NMi/° of angular drop to the star relative to the center of Earth to give it a GP. To learn more about the geocentric to topocentric transformation, I would recommend this celestial navigation guide by Umland. He just tells it like it is without any additional fluff and has awesome diagrams. Umland, Henning. _A Short Guide to Celestial Navigation_. 2015. From the first two pages lay it out clearly with these quotes: *"The apparent position of a body in the sky is defined by the horizon system of coordinates. In this system, the observer is located at the center of a fictitious hollow sphere of infinite diameter, the celestial sphere, which is divided into two hemispheres by the plane of the celestial horizon (Fig. 1-1)."* *In reality, the observer is not located on the plane of the celestial horizon. Fig. 1-2 shows the three horizontal planes relevant to celestial navigation.* *"Calculations of celestial navigation always refer to the geocentric altitude of a body, the altitude measured by a fictitious observer being on the plane of the celestial horizon and at the center of the earth which coincides with the center of the celestial sphere."* ![[96_FAQ.png]] ![[96_FAQ-1.png]] `i don't know why you are testing a two-sphere model when that is definitely not the globe model, even geometrically.` The two sphere model is the globe model, even geometrically. It would be a helluva coincidence for them to be unrelated yet share the same radius value and define the GP of stars to the same locations on Earth. Stellarium is just a real-time Almanac. `what is this "two-sphere model"? The two sphere model as presented to us from the historical narrative of Ptolemy is how one relates the positions of the stars to geographic positions on Earth. Shane may have a spare copy of an English translation of the Geographia if you care to read it. The two sphere is the globe that you think you live on. `i'm assuming you mean the earth sphere and the celestial sphere, but the celestial sphere isn't a model, its just an abstraction. there are estimated distances to the stars and they don't all lie on the surface of a second sphere. that is certainly not the globe model, so falsifying that won't falsify the globe... why not just use the full globe model with the estimated distances to the stars? `there are estimated distances to the stars and they don't all lie on the surface of a second sphere. that is certainly not the globe model` Riddle me this: Do you think it necessary to know the true distance (or estimated distance) of a star to do celestial navigation? The only unit of distance you'd need is an is the distance to the center of the terrestrial sphere, which is 6371 km, which establishes the 60 NMi/° @ 15°/h relationship. That is the globe. Otherwise a star's true position would have no physical meaning to the latitude and longitude system which uses it. `so falsifying that won't falsify the globe... On the contrary. The two sphere model *is* the globe. Falsifying the conceptual model would prove that the Earth is not a globe. The geographic positions are calculated based on the assumed 60 NMi/° @ 15°/h relationship. If the two sphere model is correct by virtue of Earth truly being a globe, then these occlusions would occur at an earlier time that matches the observer location geometric intersection. That's the only time that the star would be aligned to the peak for the observer on a globe, which would occlude the star as occlusions are a physical process between light source and occluding objecting. `why not just use the full globe model with the estimated distances to the stars?` I am using the full globe model. And RE: the so-called true (estimated) distance to the stars, because the established estimated distances aren't even used in the way you think they are. In fact, supplemental parallax measurements only changed the true positions by microarcseconds. A deviation no human on earth would ever be able to confirm or make use as it's smaller than what we can make use of on the ground. Typical viewing conditions are 2 - 3 arcseconds (or greater). So none of the 'estimated distances' or .000001 change in position in establishing that distance is relevant. `i'm having trouble parsing what you wrote here and above, because it seems like it has geometric (no refraction) mixed in with optical (refraction).` We compare geometric intersections, no astronomical refraction or terrestrial. We're dealing with an occlusion which is geometric by definition. Any comparison of refracted positions of the star is done to to show the globe enthusiasts that refraction doesn't explain the occlusion timing difference either because in almost every scenario the refracted position is above the peak. But as I said, that's just to show people who are unaccepting of our use of the true position, even though it's the backbone of the two sphere model. Carroll, Michael Dale. _Occultation Observation Methods._ 1968 ![[96_FAQ-2.png]] The same goes for conjunction predictions as well: ![[96_FAQ-4.png]] `Also it seems to have receding stars mixed half mixed in with globe model or celestial sphere half mixed in with flat earth stuff. To be extremely clear: the globe (otherwise known as the two sphere model) makes the prediction that the star's true position is following this relationship: 60 NMi/° @ 15°/h at every conceivable angle, at any time. The celestial theodolite measurements show that the stars don't following that linear relationship at the horizon, which is geometrically impossible because there's no mechanism for their rate of angular descent to change. ` consequently, it is really hard for me to sort out for any given statement what is the model, what is the prediction, and what is the observation. ` The globe predicts observer based occlusions using the geocentric position of the star at observer location. Flat Earth predicts from the crosshair of the celestial theodolite (the mountain) relative to the observer's location. I have a full write up and examples here of what the globe predicts vs what FE predicts and why: https://publish.obsidian.md/spaceaudits/Celestial_Theodolite/Why_the_Globe_Predicts_an_Earlier_Time `i don't have the long history looking at this that you do though, and you might just be using shorthand that i am not following` No worries. I'll clarify anything you need. `. i'm still trying to reverse engineer the cel theo with rigor, and for that i need to cleanly separate the model being used and the reference frame being used` As previously stated: globe makes the prediction from the observer location, FE checks with the occluding mountain peak. The goal is to relate the occlusion time (and thus the angle of the occluded star's true position) from star -> peak -> observer. The globe predicts this will occur earlier as predicated by the geocentric position of the star relative to the observer and the mountain peak which accounts for drop over distance. You see, if the occlusion occured at the globular predicted time, when we go to the peak to check, the true position should be ~ approximately whatever the rise/run - drop of distance angle relative to the observer was. If the Earth is flat, the angle at the time of occlusions will be approximately rise/run to the peak. `then (and only then, really) can i work out what is predicted, and finally pull up all the observations and see how the population of predictions compare. Hopefully this helps clear things up. `i still have not been able to cleanly sort out the various models in play here, for example full globe model, with distance to stars, your two-sphere model, receding stars, refraction, perspective, and etc` I don't have a two sphere model. That's what the globe is. "Distances to stars" is irrelevant and plays no meaningful part in either model. Refraction isn't considered when predicting occlusions, as noted by all of astronomy books. You could introduce it after the fact, but no one is saying that after introducing a correction, you couldn't make it fit. We're testing what is given to us as is. The only thing you really need to grasp here is why the globe predicts an earlier time vs flat earth, which hopefully the above mentioned link will assist with. Once you get that, everything else should fall into place. It's a simple concept. Try not to overthink it.