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2

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 ...


2

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 ...


2

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 ...


20

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 ...


22

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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