theorem 52.2 Virial theorem for a self-gravitating sphere

open in the book · parts/05-general-relativity-cosmology/11-stellar-structure-nucleosynthesis.tex:91 · p. 1388

Rests on

depends_on equation 52.2 eq:stellar-hydrostatic ¶
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 ¶
proves proof ch:11-stellar-structure-nucleosynthesis@proof-2 ¶

Supports

depends_on phenomenon 52.4 The Sun has shone for billions of years ¶
- depends_on phenomenon 52.23 The Sun's energy budget audited reaction by reaction ¶
depends_on proposition 52.18 Schönberg–Chandrasekhar limit ¶

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
`depends_on`	→	eq:stellar-hydrostatic	declared	parts/05-general-relativity-cosmology/11-stellar-structure-nucleosynthesis.tex:100
`depends_on`	→	Hydrostatic equilibrium of a self-gravitating sphere	declared	parts/05-general-relativity-cosmology/11-stellar-structure-nucleosynthesis.tex:100
`depends_on`	←	The Sun has shone for billions of years	declared	parts/05-general-relativity-cosmology/11-stellar-structure-nucleosynthesis.tex:153
`depends_on`	←	Schönberg–Chandrasekhar limit	declared	parts/05-general-relativity-cosmology/11-stellar-structure-nucleosynthesis.tex:1273
`proves`	←	ch:11-stellar-structure-nucleosynthesis@proof-2	declared	parts/05-general-relativity-cosmology/11-stellar-structure-nucleosynthesis.tex:103