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AST-07

Magnitude difference

m₁ − m₂ = −2.5 log₁₀ (F₁/F₂). Pogson's scale.

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RadiationPogson

Governing equation

m1−m2=−2.5log⁡10(F1/F2)m_1-m_2=-2.5\log_{10}(F_1/F_2)

F1∈[1×10−6,100]F_1 \in \left[1\times 10^{-6}, 100\right]

where

F_1
Flux 1 (—)
F_2
Flux 2 (—)
\Delta m
Magnitude difference (mag)

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AST-07 · star
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①

Governing law — red

m1−m2=−2.5log⁡10(F1/F2)m_1-m_2=-2.5\log_{10}(F_1/F_2)

F1∈[1×10−6,100]F_1 \in \left[1\times 10^{-6}, 100\right]

F1=1×10−6F_1 = 1\times 10^{-6}Δm=16\Delta m = 16

②

Domain of the variable — blue

F_1_{\min} = 1\times 10^{-6},\quad F_1_{\max} = 100

F1∈[1×10−6,100]F_1 \in \left[1\times 10^{-6}, 100\right]

F1=1×10−6F_1 = 1\times 10^{-6}F1=1×10−6F_1 = 1\times 10^{-6}

③

Response curve — green

m1−m2=−2.5log⁡10(F1/F2)m_1-m_2=-2.5\log_{10}(F_1/F_2)

F1∈[1×10−6,100]F_1 \in \left[1\times 10^{-6}, 100\right]

F1=1×10−6F_1 = 1\times 10^{-6}Δm=16\Delta m = 16

④

Rate of change — amber

dΔmdF1\frac{\mathrm{d}\Delta m}{\mathrm{d}F_1}

F1∈[1×10−6,100]F_1 \in \left[1\times 10^{-6}, 100\right]

F1=0.629F_1 = 0.629Δm′=−12.12\Delta m^{\prime} = -12.12

Lecture brief

Historical brief

Hubble expansion, Jeans collapse, Eddington luminosity, Bondi accretion and Stefan–Boltzmann stars are the first astrophysical budgets. The sheets scale a star, a cloud and a horizon. This sheet (AST-07 — Magnitude difference) is the form associated with Pogson. Working symbols: F1F_1, F2F_2 →\rightarrow Δm\Delta m. Five magnitudes are a factor 100 in flux. Absolute M is m at 10 pc.

Purpose

Purpose: compute Δm\Delta m from F1F_1, F2F_2 in Astrophysics via m1−m2=−2.5log⁡10(F1/F2)m_1-m_2=-2.5\log_{10}(F_1/F_2) m₁ − m₂ = −2.5 log₁₀ (F₁/F₂). Pogson's scale. Use it when a real astrophysics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given F1=1.000 —F_1 = 1.000\,\mathrm{—}, F2=2.512 —F_2 = 2.512\,\mathrm{—}, the governing relation m1−m2=−2.5log⁡10(F1/F2)m_1-m_2=-2.5\log_{10}(F_1/F_2) yields Δm=1.000 mag\Delta m = 1.000\,\mathrm{mag}. Two stars, two fluxes, a Δm. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Outputs

  • Magnitude difference \Delta m1.000 mag
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AST-07 · star
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Narration of this film

Two stars, two fluxes, a Δm.

Five magnitudes are a factor 100 in flux. Absolute M is m at 10 pc.

Reading speed

Watch on YouTube