<Dl> <Dd> δ = 2 arcsin ⁡ (d a c t 2 D) (\ displaystyle \ delta = 2 \ arcsin \ left ((\ frac (d_ (\ mathrm (act))) (2D)) \ right)) </Dd> </Dl> <Dd> δ = 2 arcsin ⁡ (d a c t 2 D) (\ displaystyle \ delta = 2 \ arcsin \ left ((\ frac (d_ (\ mathrm (act))) (2D)) \ right)) </Dd> <P> The difference is due to the fact that the apparent edges of a sphere are its tangent points, which are closer to the observer than the centre of the sphere . For practical use, the distinction is only significant for spherical objects that are relatively close, since the small - angle approximation holds for x ≪ 1 (\ displaystyle x \ ll 1): </P> <Dl> <Dd> arcsin ⁡ x ≈ arctan ⁡ x ≈ x (\ displaystyle \ arcsin x \ approx \ arctan x \ approx x). </Dd> </Dl>

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