## Emergence vs Occlusion: Why Refraction Cannot Save the Globe Of the 18 celestial theodolite observations, 11 are occlusions and 7 are emergences. This split creates a test with only one honest standard: the star's true position. True positions produce a clean geometric result. If one model is correct, its residual vanishes. If it's wrong, the residual equals the full curvature drop. There's no middle ground. Nothing to adjust. Nothing to invoke after the fact. Refraction destroys this cleanness. It introduces an atmospheric correction that varies unpredictably across observations, shows no proportionality to the geometric quantities it's supposed to explain, and produces contradictory results depending on whether the star is appearing or disappearing. The predicted refraction amount is what it is. You can't cut it short when it overshoots. You can't add more when it falls short. And it does both, with no pattern. The emergence observations are: | Peak | Star | Distance | Type | |:--|:--|--:|:--| | Old Blyn | HD206088 | 22.1 km | Emergence | | Old Blyn | HD207098 | 22.1 km | Emergence | | Hounds Tooth | HD199828 | 8.8 km | Emergence | | Ediz Blyn | HD187663 | 40.9 km | Emergence | | Ediz Blyn | 3 Cap | 40.9 km | Emergence | | Lucky Peak | HD 76600 | 5.6 km | Emergence | | Lucky Peak | HIP 45592 | 5.6 km | Emergence | --- ## The clean test: true positions Both models predict the angle at which a star intersects a peak. FE computes rise over run on a flat baseline. GE subtracts the curvature drop (γ/2) from the FE prediction, lowering the expected angle. The algebra is simple: $\theta_{GE} = \theta_{FE} - \theta_{drop}$ $\Delta_{GE} = \Delta_{FE} + \theta_{drop}$ If FE is correct, ΔFE is near zero. The star intersects where flat geometry predicts. The GE residual equals the drop, because the curvature correction was applied to a surface that didn't need it. If GE is correct, ΔGE is near zero. The star intersects where curved geometry predicts. The FE residual equals the negative drop, because FE failed to account for curvature. One model zeroes out. The other absorbs the full drop as error. That's the test. No atmospheric corrections. No assumptions about light bending. Just geometry. ### Occlusions | Peak | Star | ΔFE | ΔGE | Drop | FE off by | GE off by | | :------------ | :----------- | -----: | -----: | ----: | --------: | --------: | | Pikes Peak | 39 Aquarii | -0.03° | +0.19° | 0.23° | 11 sec | 63 sec | | Blodgett Peak | LP Aquarii | +0.09° | +0.25° | 0.16° | 27 sec | 76 sec | | Cheyenne Mtn | Mu Fornacis | +0.09° | +0.28° | 0.19° | 37 sec | 115 sec | | Blue Mtn | HD 32515 | +0.06° | +0.29° | 0.22° | 27 sec | 121 sec | | Mount Rosa | HD 17320 | +0.01° | +0.23° | 0.21° | 5 sec | 84 sec | | Green Mtn | HD 28388 | +0.02° | +0.26° | 0.24° | 8 sec | 102 sec | | North Peak | HD55892 | -0.23° | +0.35° | 0.59° | 197 sec | 307 sec | | Getaway Peak | HD102928 | +0.12° | +0.35° | 0.22° | 41 sec | 115 sec | | Varley SE | Regulus | +0.08° | +0.16° | 0.07° | 31 sec | 59 sec | | Puhitampi | Baten Kaitos | +0.20° | +0.40° | 0.23° | 67 sec | 134 sec | | Puhitampi | 53 Cet | +0.23° | +0.42° | 0.25° | 76 sec | 140 sec | **Occlusion mean |ΔFE|: 0.105° (48 sec)** **Occlusion mean |ΔGE|: 0.289° (120 sec)** ### Emergences | Peak | Star | ΔFE | ΔGE | Drop | FE off by | GE off by | |:--|:--|--:|--:|--:|--:|--:| | Old Blyn | HD206088 | +0.21° | +0.31° | 0.10° | 85 sec | 125 sec | | Old Blyn | HD207098 | +0.22° | +0.32° | 0.10° | 86 sec | 127 sec | | Hounds Tooth | HD199828 | +0.05° | +0.09° | 0.04° | 19 sec | 32 sec | | Ediz Blyn | HD187663 | +0.20° | +0.38° | 0.18° | 77 sec | 144 sec | | Ediz Blyn | 3 Cap | +0.24° | +0.42° | 0.18° | 90 sec | 159 sec | | Lucky Peak | HD 76600 | +0.16° | +0.18° | 0.03° | 53 sec | 61 sec | | Lucky Peak | HIP 45592 | +0.15° | +0.18° | 0.03° | 51 sec | 59 sec | **Emergence mean |ΔFE|: 0.176° (66 sec)** **Emergence mean |ΔGE|: 0.269° (101 sec)** FE is closer on both event types. The identity $\Delta_{GE} = \Delta_{FE} + \theta_{drop}$ holds across all 18 observations. The drop is the extra error. The curvature correction doesn't remove a discrepancy. It creates one. This is the FE-correct scenario. ΔFE is small. ΔGE equals the drop stacked on top of ΔFE. If the globe were correct, these roles would reverse: ΔGE would be small and ΔFE would equal the negative drop. That's not what happens. Not once across 18 observations. --- ## The refraction defense Globe proponents don't accept the true position comparison. They argue that the star's apparent position (refracted) is what matters, not its true geometric position. Atmospheric refraction bends light upward, lifting the star above where it truly is. On a globe, this lift is supposed to account for the gap between the FE and GE predictions. Refraction is the explanation for every angular discrepancy at the horizon. If this is the explanation, it must be exact. Not approximate. Not close enough on average. Exact. Because refraction is invoked to do a specific geometric job: compensate for the curvature drop that separates the two models. The drop is a fixed geometric quantity for each observation. The refraction is a predicted atmospheric quantity of a specific amount. If refraction is doing the work of curvature, the measured refraction must match the drop. It doesn't. Across the 18 observations, the ratio of measured astronomical refraction to the half central angle (γ/2) ranges from 0.69 to 5.02. There is no consistent proportionality. At Lucky Peak (5.6 km), refraction is 5 times the half central angle. At North Peak (131 km), it barely reaches 69% of it. The refraction amount is decoupled from the geometric quantity it's supposed to explain. But even setting proportionality aside, the GE Hypothetical tests the refraction defense directly. It uses the star's measured apparent position on a curved baseline to predict when the star appears or disappears. If refraction truly compensates for curvature, the GE Hypothetical should nail every observation. --- ## The GE Hypothetical: what refraction actually does ### Occlusions | Peak | Star | FE off by | GE off by | GE Hyp off by | |:--|:--|--:|--:|--:| | Pikes Peak | 39 Aquarii | 11 sec | 63 sec | 10 sec | | Blodgett Peak | LP Aquarii | 27 sec | 76 sec | 15 sec | | Cheyenne Mtn | Mu Fornacis | 37 sec | 115 sec | 15 sec | | Blue Mtn | HD 32515 | 27 sec | 121 sec | 17 sec | | Mount Rosa | HD 17320 | 5 sec | 84 sec | 14 sec | | Green Mtn | HD 28388 | 8 sec | 102 sec | 28 sec | | North Peak | HD55892 | 197 sec | 307 sec | 46 sec | | Getaway Peak | HD102928 | 41 sec | 115 sec | 12 sec | | Varley SE | Regulus | 31 sec | 59 sec | 4 sec | | Puhitampi | Baten Kaitos | 67 sec | 134 sec | -2 sec | | Puhitampi | 53 Cet | 76 sec | 140 sec | -9 sec | **Occlusion GE Hypothetical mean |Δt|: 16 sec** ### Emergences | Peak | Star | FE off by | GE off by | GE Hyp off by | Apparent at emergence | |:--|:--|--:|--:|--:|:--| | Old Blyn | HD206088 | 85 sec | 125 sec | -13 sec | 2' above peak | | Old Blyn | HD207098 | 86 sec | 127 sec | -13 sec | 2' above peak | | Hounds Tooth | HD199828 | 19 sec | 32 sec | +7 sec | 1' below peak | | Ediz Blyn | HD187663 | 77 sec | 144 sec | -17 sec | 3' above peak | | Ediz Blyn | 3 Cap | 90 sec | 159 sec | -8 sec | 1' above peak | | Lucky Peak | HD 76600 | 53 sec | 61 sec | -19 sec | 3' below peak | | Lucky Peak | HIP 45592 | 51 sec | 59 sec | -17 sec | 3' below peak | **Emergence GE Hypothetical mean |Δt|: 13 sec** The refracted globe is close. Mean 16 seconds for occlusions, 13 seconds for emergences. Closer than FE on both event types. But closeness is not correctness. --- ## Why closeness is not correctness ### The refraction must be exact Refraction is not a statistical tool. It's a physical explanation. Globe proponents invoke it as the reason stars at the horizon appear where they do. It is the correction that makes the globe model match reality. If it works, it must work precisely, because the geometric job it's doing is precise. The curvature drop is a fixed number for each distance. The refraction must compensate for exactly that amount. Not half. Not double. Not close on average. Across 18 observations, the GE Hypothetical uses the full measured refraction from Stellarium. No approximations. No truncation. The full atmospheric correction applied to a curved baseline. And the result is a scatter of residuals that overshoot and undershoot with no systematic pattern. ### The sign problem For **occlusions**, 9 of 11 observations show the refracted globe predicting the star should still be visible when it has already disappeared. The apparent position is above the peak. The star is gone, but the refracted model says it's still there. Refraction overshot. Two observations (Puhitampi, both stars) show the opposite: the refracted globe predicts the star should already be gone, but it's still visible. Refraction undershot. For **emergences**, 4 of 7 observations show the apparent position already above the peak at the moment of emergence. Old Blyn (both stars) and Ediz Blyn (both stars) have the refracted globe placing the star 1 to 3 arcminutes above the peak. It should already be visible. But it isn't. The peak is still blocking it. Refraction overshot. Three observations (Hounds Tooth and Lucky Peak, both stars) show the apparent position still below the peak at emergence. The refracted globe says the star hasn't cleared the peak yet. But the star is already visible. At Hounds Tooth, the observer would have had to wait another 7 seconds for an emergence that already happened. At Lucky Peak, 17 to 19 seconds. Refraction undershot. Overall: 13 of 18 observations overshoot. 5 undershoot. The refraction amount is not doing the job it's supposed to do. It doesn't consistently lift the star by the right amount. It lifts too much most of the time, and sometimes not enough. You can't cut refraction short to fix the overshoots without breaking the undershoots. You can't add more to fix the undershoots without making the overshoots worse. The measured refraction is the measured refraction. It's a single physical quantity for each observation. It either explains the discrepancy or it doesn't. And it doesn't. ### Two wrongs blurring together The GE Hypothetical is close because two corrections are fighting each other. On a flat baseline, the star's true position aligns with the peak at the FE-predicted angle. Star, peak, observer are geometrically collinear. The FE residual is whatever measurement error exists. Curve that baseline into an arc. The collinearity breaks. The peak drops by γ/2 relative to the observer's tangent plane. The GE prediction is now off by the drop on top of the measurement error. Now add refraction. Refraction lifts the star's apparent position, partially undoing the depression caused by curving the baseline. The two effects push in opposite directions. Curvature depresses the peak. Refraction lifts the star. They work against each other, and the GE Hypothetical residual sits in the middle of that fight. When refraction roughly compensates for the drop, the GE Hypothetical lands close to reality. When refraction exceeds what's needed, it overshoots. When it falls short, it undershoots. The GE Hypothetical averages out to being close not because the geometry is correct, but because two competing corrections partially cancel. This is not a physical explanation. This is two errors blurring together. On FE, there's no crossfire. No curvature to correct for. No refraction needed to undo the correction. The residual is the residual. Rise over run. Star clears the peak or it doesn't. --- ## The only consistent standard The true position comparison is the only test that produces a clean geometric verdict. ΔFE is small. ΔGE is large. The difference is exactly the drop. The curvature correction introduces the error. Every time. Both event types. All 18 observations. Refraction is supposed to be the answer. It's the explanation invoked for every discrepancy between globe predictions and horizon observations. But the measured refraction doesn't match the drop. It overshoots 13 times and undershoots 5. It has no proportionality to the geometric quantity it needs to compensate. And it can't be adjusted, because it's a measured atmospheric value. You can't use 70% of the measured refraction for one observation and 130% for another. The FE model uses one geometry for everything. True position of the star. Physical elevation of the peak. Rise over run on a flat baseline. The same math handles occlusions and emergences. It doesn't care which direction the star is moving. It doesn't need an atmospheric correction to reconcile two competing angular references. The intersection happens when the star crosses the peak elevation angle. That's it. The globe model needs the curvature drop to account for the curved baseline. Then it needs refraction to undo the damage the drop caused. Then it needs to explain why the refraction sometimes undoes too much and sometimes not enough. Then it needs to explain why this pattern changes between locations, between event types, and between paired observations at the same site. Remove the curvature. Remove the refraction. The geometry works. --- | Model | Occlusions (11 obs) | Emergences (7 obs) | |:--|:--|:--| | FE (true pos, flat) | 48 sec mean | 66 sec mean | | GE (true pos, curved) | 120 sec mean | 101 sec mean | | GE Hyp (apparent pos, curved) | 16 sec mean | 13 sec mean | The GE Hypothetical is closest in absolute timing. But it achieves this by pitting curvature against refraction and hoping they cancel. They don't cancel cleanly. The sign flips. The proportionality breaks. And the physical mechanism requires the atmosphere to perform a different correction at every distance, every altitude, and every location to mask a curvature that the true position comparison says isn't there. FE doesn't need refraction to be close. It's already there with true positions and flat geometry. The residual is measurement error. Not a correction. Not a compensation. Just the natural scatter of aligning a star with a mountaintop through a theodolite. --- See also: [[Refraction_and_Half_Gamma]], [[Refraction_and_Gamma]], [[85_Inscribed_Angle_Residual]]