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0542-4527

Satellite orbital mechanics

Also listed as: מכניקת המסלולים של לוויינים

Astrodynamics from the two-body problem to rendezvous and interplanetary transfer. The mathematical half of the space track, and the part that transfers straight to guidance work.

Semester
Semester B
Weekly hours
4h
Counts as
Department electives
Interest areas
Aeronautics and space

Comes after

  • Rigid body dynamics

Opens up

  • Astrodynamics and GNC research

What it covers

Orbits

  • Two-body problem, energy and angular momentum, conic orbits, orbital elements
  • Position against time, Kepler's equation, universal variables
  • Orbits in three dimensions, coordinate transforms, ground tracks
  • Perturbations: J2 oblateness, nodal regression, apsidal rotation, drag

Manoeuvres and relative motion

  • Orbit determination: Gibbs, Gauss, Lambert's problem
  • Manoeuvres: Hohmann, bi-elliptic, plane changes, phasing
  • Relative motion and rendezvous, Clohessy–Wiltshire equations
  • Interplanetary trajectories, patched conics, gravity assists
  • Introduction to attitude dynamics

Results worth carrying out

  • Vis-viva

    v2=μ(2r−1a)v^2 = \mu\left(\frac{2}{r} - \frac{1}{a}\right)

  • Kepler's equation

    M=E−esin⁡EM = E - e\sin E

  • J2 nodal regression

    Ω˙=−32J2(Rep)2ncos⁡i\dot{\Omega} = -\frac{3}{2} J_2 \left(\frac{R_e}{p}\right)^{2} n \cos i

  • Clohessy–Wiltshire, in-plane

    x¨−3n2x−2ny˙=0,y¨+2nx˙=0\ddot{x} - 3n^2 x - 2n\dot{y} = 0, \qquad \ddot{y} + 2n\dot{x} = 0

Figures worth knowing

  • Conic-orbit geometry
  • Ground-track plots
  • Hohmann transfer diagram
  • Porkchop plots

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