proposition A.661 The first-order narrowing

open in the book · appendices/A-long-proofs.tex:32205 · p. 3114

Rests on

depends_on equation 27.39 eq:cfs-apsidal-angle ¶
depends_on lemma A.660 The index in terms of the force ¶
- depends_on definition A.659 Circular orbit and its index ¶
  - depends_on definition A.658 The orbit function ¶
    - depends_on equation 27.30 eq:cfs-binet-u ¶
      - step_from equation 27.29 eq:cfs-binet-phidot ¶
      - step_from equation 27.16 eq:cfs-polar-acceleration ¶
    - depends_on equation 19.4 eq:newt-fma ¶
    - depends_on proposition 27.23 Binet equation ¶
      - depends_on equation 27.20 eq:cfs-angular-momentum-polar ¶
      - depends_on equation 27.16 eq:cfs-polar-acceleration ¶ ↺
      - proves proof ch:10-central-forces-statics@proof-14 ¶
  - depends_on equation A.1050 eq:app-bertrand-orbit ¶
- depends_on equation A.1049 eq:app-bertrand-J ¶
- proves proof app:A-long-proofs@proof-396 ¶
proves proof app:A-long-proofs@proof-397 ¶

Supports

depends_on theorem A.664 Bertrand's condition ¶

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:cfs-apsidal-angle	declared	appendices/A-long-proofs.tex:32224
`depends_on`	→	The index in terms of the force	declared	appendices/A-long-proofs.tex:32224
`depends_on`	←	Bertrand's condition	declared	appendices/A-long-proofs.tex:32355
`proves`	←	app:A-long-proofs@proof-397	declared	appendices/A-long-proofs.tex:32227