Einstein Ring & Paczyński Microlensing
This interactive simulator explores Einstein Ring & Paczyński Microlensing in Gravity & Orbits. Point-mass thin lens (weak-field GR): lens equation β = θ − θ_E²/θ gives two images θ_± = ½(β ± √(β² + 4θ_E²)) with magnifications μ_± = ½[(u² + 2)/(u√(u² + 4)) ± 1], u = β/θ_E. Animated source transit at impact parameter u₀ over timescale t_E renders the canonical symmetric Paczyński light curve and the full Einstein ring θ_E = √(4GM·D_LS/(c² D_L D_S)) at perfect alignment. Use the controls to change the scenario; watch the visualization and any graphs or readouts to connect the model with lectures, labs, and homework.
Who it's for: For learners comfortable with heavier math or second-level detail. Typical context: Gravity & Orbits.
Key terms
- einstein
- ring
- paczy
- ski
- microlensing
- einstein ring microlensing
- gravity
- orbits
How it works
Point-mass gravitational microlensing: lens equation β = θ − θ_E²/θ, two-image positions θ_± = ½(β ± √(β² + 4θ_E²)), and the Paczyński light curve μ_tot = (u² + 2)/(u√(u² + 4)) with u = β/θ_E. Animate a straight-line transit at impact parameter u₀ over timescale t_E and watch the Einstein ring of radius θ_E = √(4GM·D_LS/(c² D_L D_S)) form at perfect alignment.
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