DIZZZYLABS / TOOL BENCH
Practical tools for difficult scales.
Translate unfamiliar astronomical quantities into usable decisions, from light-travel perspective to horizon scale and night-sky exposure limits.
Light-Travel Explorer
How long has the light been on its way?
DECIMALS AND SCIENTIFIC NOTATION ARE SUPPORTED
You see the light that had time to reach you.
At the average Earth–Moon distance, you see the Moon as it was when its light began the crossing—not its unknowable present state.
Numerical precision+
- SECONDS
- 1.282220382
- KILOMETERS
- 384,400
- LIGHT-YEARS
- 4.06311121e-8
- INPUT UNIT
- km
How this works+
Light travels through a vacuum at exactly 299,792.458 kilometers per second.
Travel time is distance divided by the speed of light. Internal values remain precise; the main answer is rounded for readability.
Distant light left before you received it, so observation shows an earlier state. It does not reveal what the object is doing “right now.”
The path graphic is conceptual. Solar System presets marked as variable are representative scales, not live astronomical positions.
Sources & approximation notes+
Astrophotography Exposure Planner
Start with a shutter time and understand the limiting constraint.
Advanced sensor and sky inputs+
- LIMITING FACTOR
- Apparent star motion
- WHY
- At this focal length, aperture, pixel scale, and declination, longer fixed-tripod exposures increasingly turn point stars into elongated trails.
- NEXT ADJUSTMENT
- If the image is too dark, first consider a wider usable aperture, higher practical ISO, or stacking more frames before extending shutter time far past the calculated star-motion limit.
arcseconds / pixel. Smaller values reveal trailing sooner.
Why this mattershorizontal x vertical angular field of view in degrees.
Why this matterscomplete NPF limit using Balanced.
Why this mattersapproximate pixel displacement during the preview shutter.
Why this mattersThis is a lightweight concept view, not a simulated astrophotograph. It links exposure duration, focal length, pixel scale, and declination to likely elongation.
11 s
Complete NPF: k x (16.9N + 0.1F + 13.7P) / (F x cos declination). V1 maps pinpoint, balanced, and maximum-light to k=1, 2, and 3.
11.6 s
Simplified NPF comparison: (35N + 30P) / F. It is shown for education, not as the primary recommendation.
20.8 s
500 divided by full-frame-equivalent focal length. It ignores pixel pitch and is often too generous for modern high-resolution sensors.
Exposure guidance notes+
ISO does not collect more photons. Use it as a practical gain setting; useful ranges depend on read noise, highlight headroom, sky brightness, and processing workflow.
A wider aperture gathers more light, but many lenses improve star shape, coma, and vignetting when stopped down slightly.
Tracking reduces star motion as the dominant limit. It does not remove mount accuracy, polar alignment, periodic error, wind, guiding, sky brightness, or saturation limits.
Calculated values come directly from supplied inputs. Estimated values are model-dependent. Recommended values add practical assumptions.
Black Hole Explorer
Mass translated into event-horizon scale for a Schwarzschild black hole.
NON-ROTATING / UNCHARGED / CLASSICAL SCHWARZSCHILD MODEL
- MODEL
- Non-rotating, uncharged, classical Schwarzschild black hole.
- INPUT MASS
- 1 M_sun
- MEANING
- This is the event-horizon radius: the center-to-horizon scale in the simplified model.
- PRESET
- 1 solar mass is exact for this reference input.
event-horizon diameter, equal to 2 x Schwarzschild radius.
Why this mattershorizon-radius light-crossing time: t = r_s / c.
Why this mattersdiameter crossing time: t = 2r_s / c. This is a scale time, not escaping light.
Why this mattersmass divided by the Euclidean volume inside r_s; not a local interior density.
Why this mattersRadius grows linearly with mass. The marker is logarithmic so sub-meter, stellar, and supermassive horizons can share one compact rail.
4.64e-4 Earth diameters
Event horizon vs Earth. The event-horizon diameter is still smaller than Earth.
4.64e-4 Earth radii
Radius vs Earth. Radius is measured from the center to the Schwarzschild event horizon.
Black-hole model notes+
V1 assumes a non-rotating, uncharged black hole described by the classical Schwarzschild solution. Rotation, charge, accretion disks, mergers, and ray tracing are outside this model.
The density number is mass divided by an ordinary spherical volume using r_s. Because r_s grows with mass, that conceptual density drops quickly for larger black holes.
The event horizon is the boundary in this calculation. The observed black-hole shadow is larger because strong gravity bends light around the horizon.
At stellar masses, horizon-scale tidal gradients can be extreme because the event horizon is compact.
Quantities become decisions.
This bench keeps scientific and practical models compact enough to explore in the field without replacing deeper planning tools.