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What you are looking for is called the "galactic size-mass relation" for galaxies dominated by disks. Theres an interesting research paper by Rebeca Lange and others where this relation (equation 3 in the paper) has the form $R = \gamma M^{\alpha}(1+M/M_0)^{\beta-\alpha}$ Where $R$ is the radius of the galaxy in kiloparsecs ($1$ kpc $= 3260$ light ...

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The answer below is a combination of the first answer with a cross-check from Wikipedia (for the obliquity of the ecliptic plane specifically) and here (the formula for ecliptic longitude of the Sun in the first answer uses 0.918994643 to multiply sin(2 * g * pi) in the final term instead of 0.020, so I used the factor below, but I am not sure which is ...

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The Earth's surface which is visible when you look at the planet from a certain distance is a spherical cap in terms of geometry. Here it is, in blue: $A$ is the position of the observer, $H$ is the distance from the observer to the surface of the sphere, $O$ is the center of the sphere,$r$ is the radius of the sphere, $AB$ is the distance to the true ...

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If I understand correctly, you are trying to create a realistic looking view of the stars rendered (in the game) on a dome surrounding the game play area. So you don't need to fly through the stars or interact with them in a 3D environment, is that right? If so, it isn't the star size you want to reproduce - it is the brightness. We can't see the width of ...

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For that specific E-mode map we have applied a Wiener filter to highlight the high SN modes (those "rings"). I also further apply the following filter: $((1 + (kx/5)^{-4})^{-1}) * ((1 + (k/150)^{-4})^{-1})$. This second filter gives the "hole" and a "thin" vertical line in your 2D PS. The image above is just for PR purposes. In ...

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Having now looked at the paper by Aiola et al. (2020), it emerges that for that map, they filtered the data to exclude low frequency multipoles with $|l|<150$, corresponding to about 1 degree. This filtering was done to all the maps in the paper and will be responsible for the dramatic "hole" in your Fourier transform. As for the high frequency ...

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