Classical Mechanics PHYS 2006 Tim Freegarde 2020 21

Classical Mechanics PHYS 2006 Tim Freegarde 2020 -21 16 Two-body motion

Newton’s law of Universal Gravitation • Exact analogy of Coulomb electrostatic interaction • gravitational force between two masses and • gravitational field • gravitational potential • a spherically-symmetric mass distribution has the same external field as a point mass of equal magnitude at the sphere’s centre • inertial mass = gravitational mass • gravity is a CENTRAL FORCE (acts along line joining masses) • spherically-symmetric central forces are CONSERVATIVE 2

Two body dynamics • We have previously considered translational and rotational motion of rigid bodies and ensembles • Now explore internal motion • Have previously examined kinetic energy of twoparticle system • Now derive response to forces between two particle-like bodies 3

Two particle dynamics • If we have just two particles 1. their position vectors relative to the centre of mass will be antiparallel and in a fixed ratio 2. these positions may therefore be written in terms of the relative position 3. the kinetic energy of the particle pair may be written in terms of the relative velocity, and a scaled mass called the reduced mass i. e. 4

Two body motion 5

Two body motion 6

Two body motion 7

Two body motion • is NOT the position relative to an inertial origin 8

‘Fixed Sun Moving Planet’ approximation 9

Classical Mechanics PHYS 2006 Tim Freegarde