The Flat Earth Society

Flat Earth Discussion Boards => Flat Earth Theory => Topic started by: Rounder on April 10, 2016, 11:31:44 PM

Title: Evidence for very large, very distant Sun: Infrared Radiation
Post by: Rounder on April 10, 2016, 11:31:44 PM
TL;DR: the small, nearby Sun of the Flat Earth (FE) model could not give Earth the heat and light energy that we actually receive.  Therefore, the Sun is not small and nearby.  The large, far away Sun of the Round Earth (RE) model could give the Earth the heat and light energy we actually receive.

The Long Version.  Quite long, in fact, and I apologize for that.  But in order to adequately make the point, I need to cover a lot of ground that will be unfamiliar to most readers, so please bear with me.  I have broken the monologue up into smaller chunks.  Please, if you are going to quote from a section, EDIT IT DOWN to only the sentence or two you want to talk about, instead of quoting an entire post.
Title: Re: Evidence for very large, very distant Sun: Infrared Radiation
Post by: Rounder on April 10, 2016, 11:32:12 PM
A data gathering technique in which I have some training is called Infrared Thermography.  Colloquially referred to as "thermal imaging" both outside and inside the field, it consists of using cameras sensitive to the near infrared portion of the electromagnetic spectrum instead of the visible light portion of the spectrum.  Oftentimes problems that exhibit no symptoms in the visible light become quite obvious when viewed in the infrared.  Links to some examples: building inspectors can find gaps in insulation ( by seeing hot or cold sections of a wall or ceiling, mechanical inspectors can spot bad bearings, couplings, and air leaks ( by their distinctive thermal patterns, electrical inspectors can find overloaded circuit breakers ( and poorly made connections (, and veterinarians ( and physicians ( can even spot injuries due to the body's immune response leading to increased blood flow to the site of the injury.  Even if you've never seen any of that, you probably HAVE watched police helicopters track a suspect ( in pitch black night.

Title: Re: Evidence for very large, very distant Sun: Infrared Radiation
Post by: Rounder on April 10, 2016, 11:32:39 PM
The Science
Infrared electromagnetic waves occupy the portion of the spectrum at lower energy (lower frequency and longer wavelength) than the visible light spectrum.  The 'infra' portion of the word is from the Latin word for 'below'.  All objects at temperatures above absolute zero emit infrared energy, and they emit across a range of frequencies: very little (essentially zero) energy at some minimum frequency, very little (essentially zero) at some maximum frequency, with a peak intensity somewhere between those two.  The hotter an object is, the more it emits.  This is known as Planck's Law (  "More" in this instance has two meanings: it refers both to intensity (in the same way that a 100 watt bulb is brighter than a 60 watt bulb) and also to energy (in the same way that visible light has more energy than infrared).  The relationship is illustrated by this image:
Each line represents the radiation profile of an object at a certain temperature, in Degrees Kelvin.  You can see that as temperature increases, the intensity (watts per square meter on the Y axis) increases at every wavelength, and you can also see that the curve shifts to the left, reaching its peak at lower and lower wavelengths (micrometers on the X axis).  At a certain temperature, the curve shifts enough to include some radiation in the visible light portion of the spectrum.  Get hot enough, and MOST of the radiation is in the visible spectrum.  You have likely seen this effect yourself on your stovetop.  Turn an electric burner element on low.  You can feel the heat from a few inches away, but the color doesn't change.  Turning it up, you can find a setting where the element begins to glow a dull red.  Turn it up more, and you will see the color (wavelength) shift from red toward orange or even yellow, AND at the same time it will get brighter. 
Title: Re: Evidence for very large, very distant Sun: Infrared Radiation
Post by: Rounder on April 10, 2016, 11:33:09 PM
An infrared camera actually detects TOTAL energy, not the individual wavelengths and their individual intensity.  It is therefore necessary to know exactly how total energy and temperature are related, in order to determine an object's temperature from its infrared energy.  There is a formula for this: the Stefan-Boltzman Law. (–Boltzmann_law#Derivation_from_Planck.27s_law)  Total energy is a function of the fourth power of absolute (Kelvin) temperature.  From this law we can determine the surface temperature of any object by observing the infrared radiation it emits, and at the same time we can determine at what rate it radiates energy.  This is how infrared cameras can “measure” temperature (I put “measure” in quotation marks because there is more to it than that, which we won’t get into here).  We can do the same for very distant objects, like the sun.  For the sun those numbers are: ( 5778 degrees Kelvin, and 63 million watts per square meter.
Title: Re: Evidence for very large, very distant Sun: Infrared Radiation
Post by: Rounder on April 10, 2016, 11:33:37 PM
At the surface of the Earth, we can directly measure how much energy is received from sunlight.  The figure I find quoted most often online is 1000 watts per square meter at high noon, which yields an average daily total between 1000 and 7000 watts per square meter, the variation caused by atmospheric attenuation and the angle of incidence.  As you can see in this image, there is not much cloud cover in the American Southwest, or the Sahara!
Title: Re: Evidence for very large, very distant Sun: Infrared Radiation
Post by: Rounder on April 10, 2016, 11:34:00 PM
We can also calculate the amount of energy arrives at the upper atmosphere using the inverse square law, if we know the distance to the sun and its diameter.  Doing the math for the one spot directly below the sun, and thus receiving the sun’s rays directly perpendicular, we will begin with RE assumptions.  In this model, the energy arriving at earth varies with the distance from earth to sun as we orbit.  The earth is closest to the sun at perihelion in January, when the earth is 147 million kilometers out.  That works out to 211.1 solar radii, which results in an inverse square result of 1414 watts per square meter at the spot directly facing the sun.  The outermost point in the orbit, aphelion, happens in July.  We are at a distance of 152 million kilometers, or 218.3 solar radii.  The inverse square result that day is therefore somewhat less, at 1322 watts.  The quoted average on the internet varies; some sites use 1360 watts per square meter, some use 1370, while Wikipedia settles on the satellite-measured value of 1361.  Next, let’s move away from the subsolar point and consider Portland Oregon, just above the 45th parallel.  On a round earth, Portland will be slightly further from the sun than the equator will be, as curving a little bit around the planet adds a little bit of distance.  That difference is only 1866 km, a vanishingly small fraction of the 5 million kilometer difference between aphelion to perihelion.  Therefore we need only consider the effects caused by the difference in the incident angle of the radiation (which in effect takes a square meter of radiation measured perpendicular to the sun, and spreads it out over a larger surface area due to the curvature of the earth) and a bit more atmospheric attenuation (due to having a longer path through the atmosphere before reaching the ground).  The angle of incidence reduces the energy to 70% of the initial value.  And to my surprise, my searches indicate that the difference between equatorial atmospheric attenuation and higher latitudes appears to be negligible (one source called it “a second-order effect”).
Title: Re: Evidence for very large, very distant Sun: Infrared Radiation
Post by: Rounder on April 10, 2016, 11:34:35 PM
Now, let’s do the math again under FE assumptions.  From the Wiki, we find the distance to the sun to be 3000 miles (4828 km) and the sun’s diameter to be 32 miles (51.5 km).  Thus the spot on the flat earth directly under the sun is 187.5 solar radii from the sun and receives 1792 watts per square meter.  So far, so good: although this number is higher than the RE numbers, I would say it is not enough different to be the breaking point for the FE theory.  Slightly different assumptions about atmospheric absorption and reflection could easily make up the difference.  No, the problem for the FE model comes when you again move away from the subsolar point.  Let us again look to Portland Oregon.  Consider the illustration below. 


Solar radiation that reaches the subsolar point after covering 3000 miles has to cover fully 4242 miles (or 6826.8 km) to reach the 45th parallel, which adds a considerable distance over which the inverse squares rule continues to act.  Solar radiation will be crossing a whopping 265.1 solar radii before reaching Portland, diminishing it to only 896.3 watts per square meter, at the top of the atmosphere.  This would mean Portland gets only half the solar energy that the equator gets. 
Title: Re: Evidence for very large, very distant Sun: Infrared Radiation
Post by: Rounder on April 10, 2016, 11:35:05 PM
Now, before you say “Sure, that sounds about right, Portland is no Ecuador” consider this: on the Summer solstice, the sun is directly above the Tropic of Cancer at 23.5° north, and on the Winter solstice it is above the Tropic of Capricorn at 23.5° south.  The same rules apply.  On a flat earth, the Tropic of Cancer would get only HALF the solar radiation on the Winter Solstice as it did on the Summer Solstice.  (Slightly less, in fact, since the difference is 47° instead of 45° but let’s not quibble.)  Clearly, this is not what is actually observed.
The difference between 23.5° north and 23.5° south on the solstice days (January and July) are clearly not double, nor is the difference between equator and 45° on equinox days (March and September)
Title: Re: Evidence for very large, very distant Sun: Infrared Radiation
Post by: Rounder on April 10, 2016, 11:36:21 PM
(Aside: using the numbers from the wiki, 3000 miles and 32 miles, result in a sun that takes up slightly more room in the sky than what we actually observe.  Wikipedia has the sun’s apparent angular diameter ranging from 31’ 31” to 32’ 33”, but the FE sun dimensions calculate as an apparent diameter of 36’ 40”.  If one changes either the distance to the sun or the diameter of it to actually match the average apparent angular distance of 32’, for example by making it 28 miles across at 3000 miles or keep it 32 miles across and move it to 2763.5 miles away, one gets a distance of 214.6 solar radii and 1367 watts per square meter.)

OK, all done!