ISCO & Photon Sphere (V_eff)
This interactive simulator explores ISCO & Photon Sphere (V_eff) in Gravity & Orbits. Schwarzschild effective potential V_eff(r) for massive (timelike) and photon (null) test particles in geometric units. Sliding angular momentum L collapses the stable / unstable circular pair into the innermost stable circular orbit r_ISCO = 6M (the inner edge of accretion discs); for photons the unstable photon sphere r = 3M defines the inner ring of black-hole shadow images. 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
- isco
- photon
- sphere
- eff
- isco photon sphere
- gravity
- orbits
How it works
Schwarzschild effective potential V_eff(r) for massive (timelike) and photon (null) geodesics, in geometric units G = c = M = 1. Slide angular momentum L to watch stable / unstable circular orbits collide at the innermost stable circular orbit r_ISCO = 6M; for photons the unstable photon sphere sits at r = 3M, the inner ring of black-hole shadows.
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