# FAQ/Sun

## Where does the sun go?

Most people ignore refraction and air density in their arguments. When things get farther from you they appear smaller. And they also appear to descent to the horizon. However the horizon we see is significantly higher than the true horizon. This is because air is not transparent!

When you watch a sunset, you are also looking through 1000s of miles of low, middle and high altitude air. The high altitude air is thinner. That is why clouds float and why helium balloons rise. Due to buoyancy/density. It's also why boats float. So the thin upper atmos forms a wall of air after 100+ miles. This blocks your view of the sun and causes it to get cut off bottom first.

The sun changes color gradually, things get darker before sunset. Also the light curves towards you. This is because light refracts in the upper atmos. You can prove this by looking at examples of "advances sunrise" and "delayed sunset". The sun has been seen to set, then rise again an hour later, then set an hour later and so forth. Wikipedia actually gave this advanced sunrise example.

Light curves up in the upper atmos and down in the lower atmos. This is due to Snells Law. Also the limits of our eyes, curved lenses and perspective play a role in this. Things below you such as the ground converge to the horizon. A curved lense on your eye or camera lense can produce a similar effect. When the sun goes below the horizon, there is still light for a good protion of the day so whether or not it is visible verses whether some of the lights reaches you are decoupled. However the things most people seem to forget about are air density and refraction/Snells Law.

See the online Flat earth map and Sun Position tool ^{[1]}

### Snells Law

Snells Law is a method for calculating refraction. When things go from low refraction to high refraction, light angles down. When things go from high refraction to low refraction light angles up. This bends/changes the angle of light.

Snells Law disproves "far away" stars because light would eventually be bent after millions of miles. The probability is too high that even a 0.0000001 degree chance in angle would cause the light to miss us completely making consistent star trails impossible. Our atmos forms a density gradient. Things that are buoyant rise (like clouds and balloons). Helium and Hydrogen rise, Hydrogen above Helium so for example, when light goes from Hydrogen to Helium light bends up towards you.

Snell's law is given by the following formula: n1sin(θ1) = n2sin(θ2), where θ1 is the angle made between the normal to the boundary and the medium with index of refraction n1. For light travelling in an interstellar perfect vacuum of space, considering any boundary intersected by the light ray's path, n1 = n2 = 1. Thus, sin(θ1) = sin(θ2), and taking the arcsine of both sides gives that θ1 = θ2. In other words, the light ray would not bend in a vacuum. However, outer space is not said to be empty. To have a 0.000 000 1 bend, we can first look at the case where a light ray hits a boundary at a 45 degree angle coming from a vacuum and entering a near-vacuum. In this case, θ1 = 45deg, θ2 = 45deg - 0. 000 000 1deg, n1 = 1, and thus n2 = n1sin(θ1)/sin(θ2). Using trigonometric identities and Taylor series approximations, to a large number of significant figures we have that sin(θ2) = 0.9999999*sqrt(2)/2. Since sin(45deg) = sqrt(2)/2, we have that n2 = 1/0.9999999 = 1.000 000 1 to good approximation. Most gas in outer space is said to be hydrogen, which has a lower index of refraction than air at similar pressure and temperature, thus, if we use the Ciddor equation to estimate the gas density needed for n2, hydrogen gas will require a higher density to achieve the same index of refraction. For example, if we calculate (ignoring the scale of the numbers) using Ciddor that our outer space gas patch requires a density of 0.5atm to bend the light by the given angle, we will actually require a larger density such as 0.6atm. To get in the ballpark of the actual numbers, we can use the Ciddor equation, but we are well outside of the usual values of the input variables, making the Ciddor formula less reliable for our purposes. We get the equation y = (3.37615288E-06)*x+0.99999992 for a trendline when fixing the temperature at -40degC and the relative humidity at 0, and letting x, the pressure in kPa vary, where y is the index of refraction. If y = 1.000 000 1, then the pressure is 0.0533151241658kPa. As mentioned, for hydrogen gas, this would be higher, but this is a ballpark calculation, so we will not alter the required pressure. The pressure in outer space is said to be 1.322E-11 Pa, or 1.322E-14 kPa. We will just look at orders of magnitude. We needed a pocket of gas in space with a pressure of about 1E-2 kPa of pressure, but outer space is said to have a pressure of 1E-14 kPa, which is 10^12, or a trillion times smaller than it needs to be. This all assumes that just one pocket of gas in space causes the light to refract, and likely, a light ray would encounter multiple pockets of gas if any, however, the new direction for the light ray would likely be random. A random walk will need to be defined and studied to determine how a ray will refract through outer space. In summary, it seems unlikely for a light ray to encounter a dense enough patch of interstellar gas to cause a 0.000 000 1deg change in direction. More work will need to be done to determine if Snell's law predicts that the stars' light will miss us. It is also worth noting that a star doesn't emit a single ray of light, but rays of light in all directions. The distance at which light from a given star changes from being a continuous beam of light with some continuous area to a discrete set of photons is not immediately obvious. Thus, perhaps we should not just assume a star only emits one ray of light.

As a rough ballpark calculation, it is possible to use the value of 1.322E-14 kPa for the pressure in space on one side of a boundary, and a pure vacuum on the other side of a boundary, and do a simple calculation using Snell's law to determine the change in angle of the light ray's path.

All chemical/elements have a refractive index so light will always change slightly everywhere it goes. these angular changes become extremely significant over many miles. When combining elements this can greatly exaggerate the refractivity. For example, by placing sugar in water you can see light bend using a laser pointer. Add to this diffusion, reflection and other important things that can happen to light in the atmos which require study.