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Is there a formula for calculating the size of a galaxy or even a nebula if you have the Angular Size. For example, M31 has an angular size of 199.53 70.79 35 (Opt) D

M31 should be 200,000 light Years or Whirlpool Galaxy 10.00 7.59 163 (Opt) D should equate to 30,000 Light Years.

Or Even the Orion Nebula 5.5 5.5 90 (Rad) D to be 12 Light Years.

The angular sizes come from Simbad as sources.

https://simbad.u-strasbg.fr/simbad/sim-id?Ident=Andromeda%20Galaxy
https://simbad.u-strasbg.fr/simbad/sim-id?Ident=Whirlpool%20Galaxy
https://simbad.u-strasbg.fr/simbad/sim-id?Ident=Orion%20Nebula

Any help on the formula if there is one or if not, is it based on observation? Thanks in advance

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    $\begingroup$ Errrr, you multiply by the distance. $\endgroup$
    – ProfRob
    Commented Oct 28, 2021 at 13:11

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The transverse size is the angular size in radians times the distance, or $\frac{π}{10800}$ times the angular size in arc minutes times the distance. (The values you quoted are in arc minutes.) The radius is half that.

Technically you should probably take the tangent of the angular radius, but for the sizes encountered in astronomy, it's unnecessary. Even for Andromeda, the difference is less than 0.1%.

Technically the distance you should use is the angular diameter distance, but the distinction between that and any other distance measure is less than 1% at distances under 100 million light years.

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  • $\begingroup$ Would you mind giving an example of a calculation please? $\endgroup$
    – MiscellaneousUser
    Commented Oct 30, 2021 at 17:35

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