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The Eddington luminosity is the ideal limit where radiation pressure on matter balances spherical gravity.
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Formula
LE in W; G in m3/(kg·s2); M in kg; c in m/s; κ in m2/kg
| Symbol | Meaning | Unit |
|---|---|---|
| Eddington luminosity in the model | W | |
| Gravitational constant | m3/(kg·s2) | |
| Central mass | kg | |
| Speed of light | m/s | |
| Mass opacity for the relevant radiation transport | m2/kg |
L_E=\frac{4\pi GMc}{\kappa}In stationary spherical balance, outward radiation force per unit mass κF/c equals gravitational acceleration GM/r2, yielding LE=4πGMc/κ. The limit assumes a defined opacity and coupling between radiation and matter. Geometry, accretion disc, spectrum and time-dependent outflow alter real systems. Exceeding LE does not mean every mass flow is impossible.
In stationary spherical balance, outward radiation force per unit mass κF/c equals gravitational acceleration GM/r2, yielding LE=4πGMc/κ. The limit assumes a defined opacity and coupling between radiation and matter. Geometry, accretion disc, spectrum and time-dependent outflow alter real systems. Exceeding LE does not mean every mass flow is impossible.
The relation LE=\frac{4\pi GMc}{\kappa} connects the quantities defined in the variable list. Its form follows from the underlying astronomical model; it is not a universal rule outside the stated assumptions.
Defining relation
This is the documented defining relation. Rearrange it only when the requested quantity can be isolated unambiguously.
Check the worked example for Eddington luminosity for constant opacity: For one solar mass and electron-scattering opacity κ≈0.034 m2/kg, LE≈1.47·1031 W, about 3.8·104 solar luminosities.
Substitute quantities in the documented order, keep units consistent and compare the result with the check stated in the example.
Applying an approximate relation to real measurements without checking its model range.
Check the measurement definition, assumptions and units before interpreting the result physically.
Formula cluster
Compare radiation pressure with gravity in stars and accretion systems.
For one solar mass and electron-scattering opacity κ≈0.034 m2/kg, LE≈1.47·1031 W, about 3.8·104 solar luminosities.
Compare radiation pressure with gravity in stars and accretion systems.
Here is how to work through a typical Eddington luminosity for constant opacity (LE = 4πGMc/κ) task step by step:
Task
Check the worked example for Eddington luminosity for constant opacity: For one solar mass and electron-scattering opacity κ≈0.034 m2/kg, LE≈1.47·1031 W, about 3.8·104 solar luminosities.
Solution path
Substitute quantities in the documented order, keep units consistent and compare the result with the check stated in the example.
The equation describes a specific relation among astronomical quantities; it supports a reliable conclusion only when measurements match the variables’ definitions. Start by identifying each quantity, unit and reference frame. The relation LE=\frac{4\pi GMc}{\kappa} organizes those values mathematically, while the physical model determines whether it applies to the situation. A number alone does not establish that. Record assumptions, signs and any approximations. This keeps separate what follows directly from calculation and what requires interpretation. Compare the scale with the system being studied, and report uncertainty or systematic effects whenever they matter.
The relevant limits are stated in the subject background: In stationary spherical balance, outward radiation force per unit mass κF/c equals gravitational acceleration GM/r2, yielding LE=4πGMc/κ. The limit assumes a defined opacity and coupling between radiation and matter. Geometry, accretion disc, spectrum and time-dependent outflow alter real systems. Exceeding LE does not mean every mass flow is impossible. Read them before substitution because ideal geometry, small angles, constant properties or a particular cause of motion may be part of the derivation. Measurement uncertainty is also distinct from model validity: a precise measurement does not make an unsuitable approximation correct. Check that quantities use consistent conventions. If the assumptions fail, use a more suitable model or explicitly report the result as an estimate rather than an exact measurement. Compare the scale with the system being studied, and report uncertainty or systematic effects whenever they matter.
Use the documented worked example as a calculation check: For one solar mass and electron-scattering opacity κ≈0.034 m2/kg, LE≈1.47·1031 W, about 3.8·104 solar luminosities. Carry units through the arithmetic rather than handling numbers alone. Do they combine into the unit of the requested quantity? A dimensional mismatch often reveals a conversion error or swapped variables. If possible, substitute the result back into a rearranged original relation. Finally compare its order of magnitude with familiar astronomical scales; plausibility is not proof, but it is a useful error check. Compare the scale with the system being studied, and report uncertainty or systematic effects whenever they matter.
Read the exponents and placement of quantities in LE=\frac{4\pi GMc}{\kappa}: direct proportionality behaves differently from an inverse or power relation. Mentally double one input at a time and infer how the requested quantity changes. In observational data, a small relative uncertainty can matter greatly when a relation uses a small angle, a difference or an inverse quantity. Distinguish this sensitivity from measurement precision: the equation describes error propagation, not how well an instrument measures. Compare the scale with the system being studied, and report uncertainty or systematic effects whenever they matter.
State the numerical value with its unit, the input measurements and the main model assumption. If using an approximation, label the result as an estimate and say which effects were ignored. Avoid conclusions beyond the equation: a geometric or photometric quantity is not automatically a complete description of a star or galaxy. When measurement errors are known, do not report more precision than the data support. This concise record makes both calculation and interpretation traceable and reproducible. Compare the scale with the system being studied, and report uncertainty or systematic effects whenever they matter.
Quanta exam set
Curated exam set for "Eddington luminosity for constant opacity":
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Which formula describes Eddington luminosity for constant opacity?
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How do you rearrange Eddington luminosity for constant opacity for Defining relation?
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Which common mistake happens with Eddington luminosity for constant opacity?
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