
Obduction Backer 
Joined: Fri Apr 30, 2010 7:11 pm Posts: 30 Location: Czech Republic

I am going to prove that there is no realistic astrophysics involved in Teledahn
First, let's establish the facts we may assume.
 By observation, the sun's height above the horizon does not change. It is clear if you look at it through the "solar telescope".
 The period of the sun is about 66.7 seconds.
 The gravitation at the site seems to be at least roughly similar to Earth's
Realistically, we should assume that the planet orbits the sun, like it is everywhere else in the universe The sun should be of giant proportions, reasonable density and we are reasonably far away from it, so the day cycle is caused by the planet's rotation (I will return to these later). The fact that the sun's height on the sky does not change, has only one explanation: we are situated on a pole. Let's prove this. In the planetary reference frame (nonrotating), let's formulate the "zenith vector" as a unit vector pointing upwards to zenith. We place the planet's rotation axis on the Zaxis. Therefore, we have the zenith pointing in the direction specified by coordinates (X,Y,Z):
T is the period and Θ is latitude. The sun has a fixed position relative to our reference frame, given by an angle relative to the planetary rotation axis, which has the Zdirection. Without loss of generality, we can place the sun on XZ plane.
Now the relative angle of these two must be constant, which means that the sun does not change its angle relative to our zenith (and horizon). If we calculate the dot product, we obtain only one term which is timedependent. Its coefficient must be therefore zero:
This provides us with two options. The second cosine could be zero, which would mean that the planet's rotation axis points directly at the sun. In that case, the sun would stay at one point in the sky no matter where we are on the planet. So we are left with the other cosine, which tells us that our geographical position is at one of the poles. Given this, we can calculate the planet's tilt relative to the sun by measuring how far above the horizon the sun is. We cannot do that precisely, but we can see that the planet's rotation axis is almost perpendicular to the orbital plane.
Now, this is all marvelous, because if we are on the pole, we feel no centrifugal force. And if the planet is roughly spherical, we should examine its maximum radius, which means that at the equator, the centrifugal force should be smaller than gravity. Or else everything would fall in the sky there If we calculate this, given that there is earthly gravitation on the pole and there is 66.7 s period, we arrive at maximum radius of 1.1 kilometers, which is clearly nonsense. The planet simply cannot be turning that fast. Not even if we assume very elliptical shape of the planet.
Another possibility is sun orbiting the planet. We would still have to be on a pole and the sun has constant velocity, therefore circular orbit. We don't know the planet's mass, but in order to preserve Earth's gravity, we must increase the planet's radius with the increasing mass. Simultaneously, we have to keep the sun in orbit, so depending on the planet's mass, not only can we calculate the planet's radius, but the sun's distance from the planet's center as well. For nonbelievers, spherical objects have the same gravitational pull as if the mass would be concentrated in their center. Clearly, the sun's orbit radius cannot be smaller than the actual radius of the planet Also, the sun's mass is much smaller than the planet's or else there would be problems about different centrifugal pulls around the planet. Here's a plot:
The blue line is planet's radius and the orange line is the sun's distance from the planet's core. Horizontal axis represents planetary mass in kg, vertical represents radius in meters. Clearly, if we'd have a planet only like a kilometer wide, the sun (or light) would be about 100 m above the surface. This is clearly nonsense.
A third and last possibility is that the daily cycle would be caused by the planet's orbit. The planet would not rotate at all, just revolve around the sun. In order for this to work, the planet would have to be very far from the sun, which would mean that the sun would have to have enormous mass and therefore unrealistic density.
In conclusion, I don't think we should analyse fictional worlds which were created by graphic designers in order to be fun and pretty, not realistic.

