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-postulate 2: a star's apparent luminosity is directly related to its size in one's sky (the closer one is to such star, the bigger the latter will seem, and thus the brighter it will shine),
So, before I address your theory any further, can you please explain postulate 2 in further depth?
The inverse square law is extremely easy to measure in the lab, and can be analyzed with corrections for detector shape. I know this because Iv done it
Over stellar distances astronomers have a few tricks up their sleeves, many stars can have their distances determined via parallax
-postulate 2: a star's apparent luminosity is directly related to its size in one's sky (the closer one is to such star, the bigger the latter will seem, and thus the brighter it will shine),
Can you elaborate on how you're getting the result of 32.828063? In your 2D example, you give a luminosity of 360/2pi*r. What luminosity and area are you using to get 32.828063 in 3D?
originally posted by: swanne
This is important to consider when we compute the star's apparent luminosity. Now to find the area of a disk, we need to multiply the square of its diameter by 0.785398. As such, a disk with a diameter of 5.7 degrees will appear to have an area of 25.783095 square degrees in the sky. Similarly, a 1-degree large disk will cover 0.785398 of a square degree in your sky.
But this is where the mainstream F=L/A formula gives a different result. After setting everything on 3 dimensions, one gets the result of 32.828063 for 10 AU and the result of 1 for 57.295779 AU.
though from the looks of your thought pattern in postulate 2, I must currently presume that your calculations also fail to account for relative size, distance and luminosity.
What luminosity and area are you using to get 32.828063 in 3D?