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By Lawrence

5 minutes

Light Bends Too

The nebula is painted on a box at the edge of the world, and the hole does nothing to it. Mass bends light, so the stars behind a black hole should crowd round it.

How far light bends

Light passing a mass M at a distance b is bent by 4GM/(c²b), twice the angle Newton's physics gives. Stars straight behind the mass are smeared into a ring. Its angle, the Einstein angle θE, grows with √M and shrinks with distance. GravityLens keeps both: θE = strength · √(M/D), where D is the distance from the camera and strength defaults to 0.022.

camera 129.93 from the hole
mass 450      θE = 0.022 · √(450 / 129.93)  = 0.0409 rad     a ring 66 px in radius
mass 1800     θE = 0.022 · √(1800 / 129.93) = 0.0819 rad     133 px

Pixels are per 1000 px of window height. Four times the mass makes twice the ring.

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