theorem 27.30 Reduction of the two-body problem

open in the book · parts/03-classical-mechanics/10-central-forces-statics.tex:957 · p. 936

Rests on

depends_on equation 19.38 eq:newt-cm-position ¶
depends_on equation 19.4 eq:newt-fma ¶
depends_on postulate 19.48 Newton's third law ¶
- depends_on definition 19.2 Interaction ¶
  - depends_on definition 18.3 Particle ¶
  - depends_on postulate 19.1 Inertia ¶
    - depends_on definition 18.8 Inertial frame of reference ¶
      - depends_on definition 18.7 Frame of reference ¶
      - depends_on definition 18.6 Free particle ¶
    - depends_on definition 18.3 Particle ¶ ↺
- depends_on postulate 19.8 Newton's second law ¶
  - depends_on definition 19.5 Linear momentum ¶
    - depends_on definition 18.10 Velocity ¶
      - depends_on definition 7.26 Derivative of a function at a point ¶
      - depends_on definition 18.9 Position ¶
      - depends_on definition 13.9 Tangent vector to a curve ¶
    - depends_on definition 19.3 Mass ¶
      - depends_on definition 18.3 Particle ¶ ↺
      - depends_on postulate 19.1 Inertia ¶ ↺
  - depends_on postulate 19.6 Newton's first law ¶
    - depends_on definition 18.8 Inertial frame of reference ¶ ↺
    - depends_on definition 19.5 Linear momentum ¶ ↺
proves proof ch:10-central-forces-statics@proof-18 ¶

Supports

depends_on phenomenon 27.32 Kepler's first law: bound orbits are closed ellipses ¶
depends_on phenomenon 27.35 Kepler's third law ¶
- depends_on phenomenon 50.5 Black-hole masses from gravitational waves ¶
- depends_on phenomenon 50.1 Dark companions too massive to be neutron stars ¶
- depends_on phenomenon 50.2 Four million solar masses inside the orbit of a single star ¶
depends_on phenomenon 50.1 Dark companions too massive to be neutron stars ¶ ↺
depends_on phenomenon 50.2 Four million solar masses inside the orbit of a single star ¶ ↺

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:newt-cm-position	declared	parts/03-classical-mechanics/10-central-forces-statics.tex:982
`depends_on`	→	eq:newt-fma	declared	parts/03-classical-mechanics/10-central-forces-statics.tex:982
`depends_on`	→	Newton's third law	declared	parts/03-classical-mechanics/10-central-forces-statics.tex:982
`depends_on`	←	Kepler's first law: bound orbits are closed ellipses	declared	parts/03-classical-mechanics/10-central-forces-statics.tex:1053
`depends_on`	←	Kepler's third law	declared	parts/03-classical-mechanics/10-central-forces-statics.tex:1215
`depends_on`	←	Dark companions too massive to be neutron stars	declared	parts/05-general-relativity-cosmology/09-exp-black-holes.tex:388
`depends_on`	←	Four million solar masses inside the orbit of a single star	declared	parts/05-general-relativity-cosmology/09-exp-black-holes.tex:530
`proves`	←	ch:10-central-forces-statics@proof-18	declared	parts/03-classical-mechanics/10-central-forces-statics.tex:985