Magnitude measures brightness backwards: smaller numbers are brighter, negative numbers are very bright, and each step of 1 is about 2.5 times dimmer.
Astronomers have measured brightness in magnitudes for a very long time, and the scale runs the ‘wrong’ way. A star of magnitude 1 is brighter than a star of magnitude 2. Very bright objects get zero or negative numbers.
The modern scale is defined so that a difference of 5 magnitudes is exactly a factor of 100 in brightness. One magnitude is therefore a factor of about 2.512. A magnitude 1 star is 100 times brighter than a magnitude 6 star.
Why backwards? The scale grew out of old star rankings in which the brightest stars were ‘first magnitude’ and the faintest visible ones ‘sixth magnitude’. The modern scale keeps that order and simply extends it past 1 into zero and negative numbers for brighter objects.
Indian cities are not dark. Street lights and haze hide the faintest stars, so this site counts a satellite as naked-eye visible only if its estimated magnitude is 4.5 or brighter.
Use the list to place a satellite. A magnitude −1 pass is as bright as Sirius. A satellite at magnitude 4 is 5 magnitudes fainter — 100 times dimmer — and is hard to pick out from a city.
Each pass card shows mag and a plain label based on the brightest point of the pass:
A magnitude here is an estimate. Real satellites tumble, flash and change angle, so one may look half a magnitude brighter or fainter than predicted. Treat it as a guide, not a promise.
Each pass card's Brightness line shows ‘mag’ with a number and a label — compare a Very bright ISS pass with a Faint one. See satellites visible tonight
Magnitude is logarithmic: m₁ − m₂ = −2.5 log₁₀(F₁ / F₂), where F is the light received. Check: F₁/F₂ = 100 gives m₁ − m₂ = −5.
For satellites, observers quote a standard magnitude: the brightness of the satellite half-lit (phase angle 90°) at a range of 1,000 km. The phase angle is the Sun–satellite–observer angle; 0° means the lit face points straight at you.
This site turns a standard magnitude m_std into a predicted apparent magnitude with a diffuse-sphere model:
m = m_std + 5 log₁₀(ρ / 1,000 km) − 2.5 log₁₀(π · F(φ))
where ρ is the range and F(φ) = [sin φ + (π − φ) cos φ] / π is the light reflected by a matte sphere at phase angle φ. The first correction is the inverse-square law (light falls off with the square of distance, hence 5 log₁₀ rather than 2.5 log₁₀). The second is normalised so that it is zero at φ = 90°.
Worked example: the ISS, m_std = −1.3, passing at 420 km range with φ = 90°: m = −1.3 + 5 log₁₀(0.42) ≈ −1.3 − 1.88 ≈ −3.2 — Very bright. At 10° elevation the range is about 1,490 km: m ≈ −1.3 + 5 log₁₀(1.49) ≈ −1.3 + 0.87 ≈ −0.4, still Bright.
The site only uses known standard magnitudes for its bright-pass list; objects with a guessed (category-default) value are kept out of the full pass search so it does not promise passes it cannot back up.
The difference is 5 magnitudes, which is exactly a factor of 100.
The one at −0.5. Smaller (and negative) magnitudes are brighter.
By 5 log₁₀(2) ≈ 1.5 magnitudes, because brightness falls with the square of distance.