Calculators: Angular Diameter | Distance to the Horizon | Thumb Method | Height Estimation | Shadow Length
Calculate Angular Diameter
g = real size, r = distance, α = angular diameter or apparent size, parallax
g and r have the same unit, regardless if centimeters or light-years. You can convert length units here.
The unit of the angle is degrees or radiant. You can convert angle units here.
Formulas: g = 2r*tan(α/2) || r = g/(2*tan(α/2)) || α = 2*arctan(g/(2r))
Examples from astronomy: the moon has a size of approximately 3500 km (g) and a distance of 400000 km (r). It has an apparent size of about 0.5 degrees (α). The galaxy M51 is about 31 megalight-years away from us and has an angular diameter of 0.19 degrees, which corresponds to 103000 light-years diameter.
At distances above hundreds of millions of light-years, the curvature of space plays a role, which is neglected here.
Example for a parallax: a mountain in a distance of 50 km, seen from two points 100 m away from each other (line between the points upright to the distance), changes its apparant position for 0.115°.
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