Gravitational Lensing Simulator
Point mass & binary lens — observer’s sky view
Light
Click/drag canvas to reposition source • Press P to play/pause
Side-View Geometry
Source
Position \(\beta/\theta_E\)
2.00
Direction \(\phi\)
0°
Disk radius \(\rho = r/\theta_E\)
0.15
Finite-source \(\mu\) (disk of radius \(\rho\), not a point)
Lens Display Scale
\(\theta_E\) ring size (px)
95
Transit Animation
Play
Reset
Impact param \(b/\theta_E\)
0.00
Time \(t/\theta_E\)
-4.80
Speed
3
Binary Lens (Planet)
Enable planet (binary lens)
Caustics (source plane)
Critical curves (image plane)
\(\log_{10}(q)\) mass ratio
1.0e-3
Separation \(d/\theta_E\)
1.20
Angle \(\phi_p\)
0°
Display
Angle annotations \((\theta_+, \theta_-, \beta)\)
Einstein ring \(\theta_E\)
True source position
Transit path
Angular scale rings
Galaxy source (exponential profile)
Tangent lines from lens to source
Lensing effect
Physical Scale
Star
Stellar BH
Galaxy
Cluster
\(\log_{10}(M/M_\odot)\)
11.0
\(D_L\)
1000
\(D_S\)
2000
\(\theta_E\) =
—
Magnification Curve
log
290 px
+
\(\beta/\theta_E\):
—
\(\mu_\text{total}\):
—
Images:
—
\(\theta_+\):
—
\(\theta_E\)
\(\theta_-\):
—
\(\theta_E\)
Einstein Ring