Sorry but there is a simple effect that when we observe at a low angle across a planar surface we see a bump in the middle. It's an optical effect. This can be seen looking across a floor or table. What you have here is not a proof of the shape of the ground beneath us, or its placement into "outer space".
The Earth is not a spinning space ball. You would need to account for oceans sticking to a ball in a vacuum by demonstrated experimentation.
We did take refraction into account. Refraction was always so that it bent light down, never the other way around. So if the earth were flat, we would not observe a bump, but a concave surface. There were never conditions observed where light could bend upwards so that a flat earth would look like a globe.
Did you miss the part where we measured the targets and water levels with differential GPS? This are geometrical measurements, not optical. We measured geometrically curved water and ice! And the measured geometrical curvature has a radius of about 6400 km.
The shape of the earth does not depend on whether we can make an experiment or not. The experiment you request is physically impossible to execute on earth. To demonstrate water holding to a shpere we have to switch off earths gravity and use a planet sized sphere to get enough mass to hold water on it. There are things that don't scale. But you can go to space and observe the globe earth rotate. And we have plenty photographs from a time where no CGI was invented, so that argument is lame.
The following website serves as a digital repository for the hand-held camera photography captured during the Mercury, Gemini, and Apollo programs, which flew between 1958 and 1972. NASA team members at Johnson Space Center scanned the films in an ongoing effort to preserve, share, and commemorate some of the greatest historical achievements of humankind.
Following the completion of each mission, master duplicates were produced and the original flight films were placed into archival storage. These galleries are digital scans of the original films – and the first instance in which they have been provided on the Internet.
What a wonderful resource you have provided. The simulations are quite spectacular, and the analysis is top-notch. The knowledge and care you put into this work is easy to see.
I apologize for posting this comment on the Rainy Lake page, and it has more to do with your View Geo Data page - but I didn't see comments turned-on anywhere else. The lake experiment with time lapse is very compelling, and I shared it with the flat earth guy that posts the oil rig platform videos on YouTube.
Can you provide more information on how to obtain X, Y, Z data using GPS for someone that's looking at logging data on a trip? I've found some resources that might help me process a dateset with Log, Lat, and Elev. but would prefer to find a way to record those coordinates directly using an app or cloud based resource.
I have not found any commertial GPS device or App yet that does not convert the intern calculated ECEF x,y,z coordinates into latitude, longitude and elevation. GPS tracker and Apps can often export lat,long,elev in KML files, which kann be plotted in many Apps like Google Earth.
But survey grade GNSS receivers do record the raw GPS satellite data and x,y,z coordinates and export them in the so called RINEX data format for later postprocessing. This way using the method of Differential GPS they can achieve much better accuracy down to mm level.
I got such data from Jesse Kozlowski, not only from the Rainy Lake experiment, but also from the Causeway, the Bonneville Salt Flats, the State Kansas, NGS CORS, the UNAVCO reference stations and more. Jesse has software that reads and processes RINEX data and can export the x,y,z or lat,long,elev data in many other formats, like CSV textfiles, which I can import into my Display Geo Data App and plot.
I have programmed a converter that can parse some KML formats and transform the lat,long,height data back to ECEF x,y,z coordinates:
There is also programmed a page that can convert between ECEF and geodetic coordinates individual points back and forth:
Note that this converter requires the ellipsoid height, not the geoid height to calculate the original x,y,z coordinates. GPS receivers usually calculate the geoid height. But often the small difference is irrelevant.
To convert between ellipsoid height and geoid height you need some software I don't have. You can probably find some free software online. The geoid databases can be downloaded for free and you may probably find some software to use it there too:
If you are interested in building your own receiver and find out how to calculate the ECEF coordinates from the satellite measurements and data, see here:
I appreciate the detailed reply and your explanations.
My attempt to use the data from GPS Logger (Android) didn't work very well. I used this input from the KML I was able to export from the Android cellphone:
But the "Convert <Placemark>" button only yields this output:
It seems to only see the first line of data in the list of coordinates. Do I need to post-process the data, adding the right XLM tags on every line?
You made a claim, that is not true: "There were never conditions observed where light could bend upwards so that a flat earth would look like a globe."
In normal conditions (temperature decreasing with height) light always bends upwards in a horizontal measurement near the ground (or water) surface. Light bends downwards ONLY in temperature inversion with the same setup.
Here is abpicture I took on my 2016 Balaton laser experiment, showing the laser beam bending UPwards. https://images.app.goo.gl/dsQpCMCaEA1VniKGA
You have an other claim: that light bends towards the denser medium. The problem here, is that Snell's law (and Edlèn or Ciddor calculations) refer to OPTICAL density and not volume density. This is a common mistake, so you have to understand the difference. They are not equivalent.
Nice image, really! (Discussion on Metabunk).
I know that light can bend upwards near the ground when the ground is warmer than the air, specifically if the temperature gradient is less than −0.034°C/m. I was talking about the Rainy Lake Experiment over frozen water, where we could never see such an effect. Upwards bending of light is real and a daily event. It happens always while the sun is heating up the ground and the air is still colder. It creates inferior mirages and the exchange between rising warm and falling cool air is responsible for the blurriness of such images.
But the point is, this effect happens only in a small layer above the ground and can never make a flat earth appear as a globe above the ground layer, see Refraction Coefficient as a Function of Altitude. Why? Because if the ground is warmer than the air, the air gets heated up by the ground, raises and gets quickly replaced by cooler sinking air from above. A temperature gradient, that can bend light upwards, cannot be maintained to arbitrary heights. It only happens directly over the ground (or maybe in a layer higher up in very exteem conditions, which would easily be recognized as a refracted image).
No, not always and not at all in normal (standard) conditions. It only happens if the temperature gradient is steeper than −0.034°C/m. In normal conditions (ground and air temperature are about the same), the Temperature Gradient is only about −0.007°C/m. By far not enough to bend light upwards. Normal conditions bend light downwards in a radius of curvature of about 38,000 km. The globe earth appears 7/6R bigger.
In fact at night (laser test time) it is almost always exactly the opposite and light bends stronger than the curvature of the earth. The temperature gradient for such conditions is about 0.13°C/m or more, which is easily achieved in a small layer above cooling ground and still warm air above. A laser aimed at the horizon will enter this layer and be conducted along the curved surface of the earth like in a fibre optic cable to any distance until it gets too faint to be recognized. Such conditions are documented in the Rainy Lake Experiment, see Strong Refraction at Bedford Targets.
I don't know whether you intend to claim that light gets bent upwards in normal conditions in any altitude. Anyway, I will explain why light gets always bent down above the ground layer where strong heat exchange happens.
Light always bends towards the denser medium, that is the medium with the higher refractive index or refractivity. The refractivity of the air is directly proportional to the density of the air. The curvature of light is directly proportional to the refractivity gradient and hence to the density gradient.
Deriving Equations for Atmospheric Refraction
This implies that not the density itself is responsible for the bending, but the change in density. The stronger the density gradient (the change in density), the stronger the bending of light, always towards more density. The fact that the bending is caused by the density gradient, not the absolute density, is the reason, why even a light ray gets bent, that starts horizontal, because the gradient is never zero along this path. So it's not the curvature of the earth or atmospheric layers that is causing this. It would even happen on a flat earth. There are fibre optic cables that make use of this fact.
Now we can use the Calculator for Refractivity based on Ciddor Equation to calculate refractivity from the wavelength of light and atmospheric conditions like pressure, absolute temperature, humidity and CO2, where the last 2 have only negligible influence on refractivity. If we use the standard atmosphere model and the ideal gas law, we can calculate the density of the air depending on pressure and temperature, which both depend on the altitude, and we can calculate the density gradient and from that the refractivity gradient which is responsible for the curvature of light.
If we do so, see Deriving Equations for Atmospheric Refraction, we can derive the following predictions:
Light bending depends only marginal on Pressure and absolute Temperature. It mostly depends on the Temperature Gradient, the change in temperature with altitude.
The equation to calculate the curvature of light from Pressure, absolute Temperature and the Temperature Gradient is:
To get upwards bending, i.e. a negative radius of curvature, the temperature gradient has to be smaller than (more negative than) −0.0343°C/m. The absolute temperature and pressure does not change this. They have only a minor effect on the strength of the curvature. Mainly the Temperature Gradient determines the direction of the bending and the strength of the bending. The influence of humidity and CO2 concentration is neglegtable for an accuracy of less than about 5%.
The Temperature Gradient in standard conditions, i.e. above the ground effect layer, is about −0.005°C/m to −0.01°C/m. This is way too less to get upwards bending. Only very near the ground, where heat exchange happens, can the Temperature Gradient be strong enough to invert the density gradient, and hence the refractivity gradient, and bend light upwards. Above the ground layer air is always mixed well and there is no strong enough temperature gradient to bend light upwards, see Refraction Coefficient as a Function of Altitude.
To bend light upwards, so that the flat earth appeard like a globe as we can observe (horizon drops), the upwards radius of curvature has to be at least −7400 km. From the equation above we can calculate that this corresponds to a Temperature Gradient of at least −0.17°C/m. This gradient has to be maintained as high as we can go, because the curvature drop of the horizon can be observed from any altitude above the ground layer. Now this is physically impossible. The temperature would have to decrease 170°C or more every km up to any reachable altitude. We can use refraction measurements as a method of Determining the Shape of the Earth with Zenith Angle Measurements.
This math model is proven correct by uncountable observations, measurements and experiments. It is based on basic laws of physics (Fermat's principle, ideal gas law, fluid dynamics in a gravitational field) and empirical data (Ciddor equation and standard atmosphere).
You must never apply Snell's law to a non-isotropic medium like the atmosphere!
You have to apply Fermat's principle to calculate how light behaves in an non-isotropic medium. Again see Deriving Equations for Atmospheric Refraction how this is done properly.
The connection between your so called optical density (I think you mean the optical properties of air like the speed of light in the air) and volume density is made by the Ciddor Equation, which gives the index of refraction or refractivity as a function of the wavelength of the light ray and the air density, implicitely defined by the pressure, absolute temperature, humidity and CO2 concentration via the ideal gas law.
So if we know the index of refraction of air from the Ciddor Equation, we know how fast light travels in the air at certain conditions: v = c/n, where v is the speed of light in the medium, c the speed of light in vacuum and n the index of refraction. From the change of the speed of light with altitude, i.e. the refractivity gradient, applying Fermat's principle and using Calculus we can derive how much light gets bent and in what direction in a density gradient. The density gradient on the other hand can be derived from measurable values like Pressure, absolute Temperature and most importantly the Temperature Gradient. The result is equation (RayCurvature).