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Last updated:

September 21, 2022


Unlimited Duration


This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration


This course covers the fundamentals of astrodynamics,

focusing on the two-body orbital initial-value and boundary-value problems with applications to space vehicle navigation and guidance for lunar and planetary missions, including both powered flight and midcourse maneuvers. Other topics include celestial mechanics, Kepler’s problem, Lambert’s problem, orbit determination, multi-body methods, mission planning, and recursive algorithms for space navigation. Selected applications from the Apollo, Space Shuttle, and Mars exploration programs are also discussed.

Course Curriculum

  • The two-body problem Unlimited
  • The two-body problem (cont.) Unlimited
  • Barker’s equation and Kepler’s equation Unlimited
  • The initial-value problem Unlimited
  • Euler angles Unlimited
  • The orbital boundary-value problem (BVP) Unlimited
  • Optimum orbital transfer Unlimited
  • Analytical and geometric properties of the BVP Unlimited
  • Lambert’s theorem and the Lagrange time equation Unlimited
  • Transformation of the BVP Unlimited
  • Hyperbolic orbits Unlimited
  • Patched conics and planetary flybys Unlimited
  • Gauss’s method for the time-constrained BVP Unlimited
  • Hypergeometric functions and continued fractions Unlimited
  • The fundamental ellipse of the BVP Unlimited
  • Non-singular “Gauss-like” method for the BVP Unlimited
  • The Battin-Vaughan algorithm for the BVP Unlimited
  • Preliminary orbit determination using Taylor series Unlimited
  • The state transition matrix Unlimited
  • Powered flight guidance Unlimited
  • Space navigation: the position fix Unlimited
  • The covariance, information, and estimator matrices Unlimited
  • Estimation of position and velocity in space navigation Unlimited
  • Basic elements of the three-body problem Unlimited
  • The restricted problem of three bodies Unlimited
  • The Clohessy-Wiltshire equations of relative motion Unlimited
  • Variation of parameters Unlimited
  • Effect of atmospheric drag on satellite orbits Unlimited
  • The disturbing function and Legendre polynomials Unlimited
  • Effect of J2 on a satellite orbit of the Earth Unlimited
  • The calculus of variations and lunar landing guidance Unlimited
  • Powered flight guidance to maximize final energy Unlimited
  • Runge-Kutta method of numerical integration Unlimited

About the instructor

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Massachusetts Institute of Technology