Unit 1

Elements of Conics – The n-Body Problem and Reduction to Two-Body Problem – Types of Orbits – Conservation of Energy and Angular Momentum in Orbits – Spherical Trigonometry – Geocentric-Equatorial, HeliocentricEcliptic, Right Ascension Declination, Topocentric-Horizon and Perifocal Co-Ordinate Systems and Transformations between them – Classical Orbital Elements.

Unit 2

Orbital Elements Determination from Position and Velocity at a Point – Determining Position and Velocity from Orbital Elements – Orbit Determinations from a Single Radar Observation, Three Position Vectors and Optical Sightings – Ellipsoidal Earth Model: Geodetic and Geocentric Latitudes – Ground Trace of Satellites – Solar and Sidereal Times – Precession of The Equinoxes – Low and High Earth Orbits: Orbital Perturbations due to Oblateness of Earth – Orbital Maneuvers: General Coplanar Orbit Transfer, Hohmann Transfer, Simple Plane Changes to an Orbit.

Unit 3

Time-Of Flight and Eccentric Anomalies for Elliptic, Parabolic And Hyperbolic Orbits – Kepler’s Problem and Solution Algorithm – Gauss Problem: General Methods of Solution – Intercept and Rendezvous with Examples – Ballistic Missile Trajectories: Effect of Earth Rotation – Interplanetary Trajectories: Spheres of Influence and the Patched Conic Approximation, Synodic Periods – Satellite Attitude Dynamics: Torque Free Motion, Stability of Torque Free Motion, Spin Stabilization, Gyroscopic Attitude Control, Gravity Gradient Attitude Control.

Course Objectives

• To understand the basic conservation laws of specfic energy and specific angular momentum and apply them to orbital maneuvers.
• To understand orbital elements and solve two body problems in orbital mechanics.
• Study various applications of orbital mechanics such as intercept, rendezvous, planetary motions and interplanetary trajectories

Course Outcomes

• CO1: Understand classical orbital elements, physical principles of orbital motion and various coordinate systems used.
• CO2: Orbit element determination from position and velocity vectors. Know effects of perturbations to orbits, know ground trace and basic orbital maneuvers
• CO3: Know Kepler and Gauss problem, ballistic missile trajectories, interplanetary and lunar trajectories and basics of satellite attitude dynamics

CO – PO Mapping

Textbook(s)

• Roger R Bate, Donald D Mueller, Jerry E White And William W Saylor, “Fundamentals of Astrodynamics,” 2^nd edition, Dover, 2015.
• Marshall H Kaplan, “Modern Spacecraft Dynamics and Control,” Wiley, 1976.

Reference(s)

• Howard Curtis, “Orbital Mechanics for Engineers and Scientists,” 3^rd edition, Elsevier, 2010.
• Marcel J. Sidi, “Spacecraft Dynamics And Control: A Practical Engineering Approach,” Cambridge University Press, 1997.

Evaluation Pattern