phenomenon 52.12 The mass–luminosity relation

open in the book · parts/05-general-relativity-cosmology/11-stellar-structure-nucleosynthesis.tex:600 · p. 1393

phenomenon-tested: no experiment declares a \tests edge to it and it is not listed in untested.txt

Rests on

depends_on equation 52.2 eq:stellar-hydrostatic ¶
depends_on equation 52.17 eq:stellar-radiative-gradient ¶
depends_on proposition 52.1 Hydrostatic equilibrium of a self-gravitating sphere ¶
- depends_on proposition 31.16 Hydrostatic balance ¶
  - depends_on definition 31.1 Fluid ¶
    - depends_on theorem 30.18 Cauchy: the stress tensor exists ¶
      - depends_on definition 30.17 Traction ¶
      - depends_on definition 13.5 Tensor under orthogonal transformations ¶
      - proves proof ch:13-continuum-elasticity@proof-7 ¶
  - depends_on theorem 30.21 Cauchy's equation of motion ¶
    - depends_on theorem 7.133 Gauss ¶
      - depends_on definition 7.127 Simple regions ¶
      - depends_on remark 7.128 What the derivations below take as given ¶
      - depends_on theorem 7.43 Fundamental theorem of calculus, II ¶
      - proves proof ch:05-real-analysis@proof-79 ¶
    - depends_on theorem 30.18 Cauchy: the stress tensor exists ¶ ↺
    - proves proof ch:13-continuum-elasticity@proof-9 ¶
  - proves proof ch:14-fluid-dynamics@proof-7 ¶
- proves proof ch:11-stellar-structure-nucleosynthesis@proof-1 ¶
depends_on proposition 52.9 Radiative diffusion ¶
- depends_on equation 68.2 eq:bb-stefan-boltzmann ¶
- proves proof ch:11-stellar-structure-nucleosynthesis@proof-6 ¶
proves proof ch:11-stellar-structure-nucleosynthesis@proof-8 ¶

Supports

depends_on phenomenon 52.17 The Hertzsprung–Russell diagram ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`cites`	→	On the Relation between the Masses and Luminosities of the Stars.: (Plate 8.)	derived	parts/05-general-relativity-cosmology/11-stellar-structure-nucleosynthesis.tex:609
`depends_on`	→	eq:stellar-hydrostatic	declared	parts/05-general-relativity-cosmology/11-stellar-structure-nucleosynthesis.tex:615
`depends_on`	→	eq:stellar-radiative-gradient	declared	parts/05-general-relativity-cosmology/11-stellar-structure-nucleosynthesis.tex:615
`depends_on`	→	Hydrostatic equilibrium of a self-gravitating sphere	declared	parts/05-general-relativity-cosmology/11-stellar-structure-nucleosynthesis.tex:615
`depends_on`	→	Radiative diffusion	declared	parts/05-general-relativity-cosmology/11-stellar-structure-nucleosynthesis.tex:615
`depends_on`	←	The Hertzsprung–Russell diagram	declared	parts/05-general-relativity-cosmology/11-stellar-structure-nucleosynthesis.tex:1176
`proves`	←	ch:11-stellar-structure-nucleosynthesis@proof-8	declared	parts/05-general-relativity-cosmology/11-stellar-structure-nucleosynthesis.tex:619