Black Hole Gravitational Lensing Simulator Independent Toy Model

At mass 10, the displayed Schwarzschild scale is about 29.53 km. Doubling mass to 20 doubles it to about 59.07 km because r_s = 2GM/c². At the same mass and launch offset, changing the ring parameter from 0 to 0.99 changes its radius from 1.50 to 1.30 r_s, while every ray coordinate stays identical. This isolates a decorative change from a modeled trajectory change.

Jeremy Schnittman’s NASA visualization models the apparent disk around a black hole. Curved spacetime redirects disk light, producing multiple distorted views. This page is an independent sketch; it does not reproduce that simulation or its data. NASA: Visualization Shows a Black Hole’s Warped World

NASA distinguishes the event horizon from its larger apparent shadow and describes Doppler beaming: material moving toward an observer appears brighter and bluer. Here the disk consists of symmetric fixed-color arcs. Neither that brightness effect nor the observer’s shadow is calculated. NASA Science: Anatomy of a Black Hole

Hold mass and offset fixed while changing the ring parameter, then compare JSON ray samples: they should match. Change mass or offset to explore the toy rule. The launch offset is a screen-coordinate parameter, not physical b/r_s. Dragging vertically mirrors the start below center and clamps it to the slider range; horizontal dragging does not alter launch direction.

JSON records the parameters, scope and first 50 primary-ray positions, not a full validated orbit. PNG captures the canvas alone. The direction display is the absolute difference between initial and final velocity angles, so angle wrapping can inflate it; it is not total orbital winding or an observer’s image position. Reset restores baseline mass, ring parameter and launch offset; grid and ray-bundle toggles retain their current settings.

• NASA: Visualization Shows a Black Hole’s Warped World

  Schnittman’s actual visualization and gravitationally distorted disk appearance.

• NASA Science: Anatomy of a Black Hole

  Horizon, apparent shadow, disk images and Doppler beaming; not this toy integrator.

This independent sandbox is not N A S A code or a validated general relativistic ray tracer. It computes the physical Schwarzschild length from two G M divided by c squared, but its ray capture test uses a separately chosen screen boundary. Start mass at ten solar masses. Physical length is about twenty nine point five three kilometers. The toy boundary is point zero eight normalized screen units. The left circle uses three pixels per kilometer; the right uses one thousand pixels per normalized unit. Their sizes are not a common physical scale. Increase only mass from ten to twenty solar masses. Both circles grow in proportion to that parameter, following their separate exact source formulas. The physical length uses gravitational constant, solar mass and light speed. The screen boundary uses point zero eight times mass divided by ten. These share proportionality, but that does not make the screen boundary a validated physical shadow, apparent image or event horizon measurement. Hold mass at twenty solar masses. Physical Schwarzschild length is about fifty nine point zero seven kilometers, twice its initial value. The toy boundary is point one six screen units, also twice its initial value. Both circles stop while the numbers are spoken. A computed physical length does not validate the unrelated ray acceleration and capture rules. Entering the drawn boundary means captured under the toy test only. Restore mass to ten solar masses. The source parameter labeled spin does not enter its ray integrator. It changes an illustrative ring ratio, one point five minus point two times the parameter. Start that parameter at zero. The ring ratio is one point five and the corresponding toy ring radius is point one two screen units. The fixed inner capture reference has radius point zero eight. This diagram uses one thousand pixels per normalized screen unit. Increase the ring parameter from zero to point nine five. The outer circle follows the unrounded arithmetic ratio one point five minus point two times the current input. The actual page rounds that ratio to two decimals before drawing its ring, so its displayed changes are quantized. Changing this parameter leaves ray coordinates unchanged when mass and launch inputs are held fixed. The decreasing circle is a decorative model rule, not a calculation of Kerr frame dragging or a spinning black hole photon sphere. Hold the parameter at point nine five. The ratio is one point three one, giving a toy ring radius point one zero four eight. The outer circle is now one hundred four point eight pixels in radius, while the inner capture reference remains eighty pixels. Both stop during these numbers. The page disk arcs and fixed forty one point two zero degree reference are drawn decorations. They do not provide radiative transfer, observer images or measured light bending. Inspect one algebraic term from the toy integrator rather than a complete ray history. Its acceleration magnitude is one point five times screen boundary radius times angular momentum squared, divided by distance to the power four point five. Hold the boundary at point zero eight and angular momentum at one in source normalized units. Start distance at one. This isolated expression evaluates to point one two. The horizontal coordinate is distance and the vertical coordinate is the authored acceleration coefficient. Increase distance from one to two while holding those other two quantities fixed for this mathematical comparison. The marker follows the inverse power formula. It decreases much faster than an inverse square relation. In an actual source run, position and velocity also change, angular momentum is recomputed and speed is normalized back to one at every step. This isolated curve is therefore not a solved trajectory, a conserved angular momentum claim or a Schwarzschild geodesic. Hold distance at two. The coefficient is about point zero zero five three zero three, or the initial value divided by about twenty two point six three. The marker remains fixed during the comparison. The source uses steps of point zero one five and an authored capture boundary. Its endpoint direction difference is not an observer image angle or accumulated orbital winding. Original presets, all sliders and toggles, emitter drag, learning details and actual J S O N and P N G exports remain available above the video.