JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Course Objectives:

• Impart the knowledge in two-body, restricted three-body and n-body problem, Hamiltonian dynamics, canonical transformations, Poincare surface sections.
• Analyze the basic Newtonian dynamics and spacecraft altitude dynamics.
• Provide necessary knowledge to study the satellite and interplanetary trajectories and Formal approaches for handling coordinate transformations.
• Solve the orbital problems related to Earth satellite orbits using Hamilton‘s and generate interplanetary orbits in the frame work of restricted three-body problem.

Course Outcomes:

• Solar Systems and various coordinate systems
• Effect of perturbation on satellite
• Satellite orbits
• Missile trajectory

UNIT - I

Introduction to Space Mechanics: Basic concepts: The solar system, Reference frames and coordinate systems, The celestial sphere, The ecliptic, Motion of vernal equinox, Sidereal time, Solar Time, Standard Time, The earth‘s atmosphere. The many body problem, Lagrange-Jacobi identity. The circular restricted three body problem, Libration points, Relative Motion in the N-body problem.

UNIT - II

The Two Body Problem: Equations of motion-General characteristics of motion for different orbits- Relations between position and time for different orbits, Expansions in elliptic motion, Orbital Elements. Relation between orbital elements and position and velocity: Launch vehicle ascent trajectories, General aspects of satellite injection. Dependence of orbital parameters on in-plane injection parameters, Launch vehicle performances, Orbit deviations due to injection errors.

UNIT - III

Perturbed Satellite Orbit: Special and general perturbations- Cowell‘s Method, Encke‘s method. Method of variations of orbital elements, General perturbations approach. Two-dimensional interplanetary trajectories, Fast interplanetary trajectories, Three dimensional interplanetary trajectories. Launch of interplanetary spacecraft. Trajectory about the target planet.

UNIT - IV

Ballistic Missile Trajectories: The boost phase, the ballistic phase, Trajectory geometry, optimal flights. Time of flight, Re-entry phase. The position of the impact point, Influence coefficients.

UNIT - V

Low-Thrust Trajectories: Equations of Motion. Constant radial thrust acceleration, Constant tangential thrust (Characteristics of the motion), Linearization of the equations of motion, Performance analysis.

TEXT BOOKS:

• 1. J. W. Cornelisse, ―Rocket Propulsion and Spaceflight Dynamicsǁ, Pitman Publishing, London, 1979.
• 2. William E. Wiesel, ―Spaceflight Dynamicsǁ, McGraw-Hill, 3rd Edition, New Delhi, 2010.

REFERENCE BOOKS:

• 1. Vladimir A. Chobotov, ―Orbital Mechanicsǁ, AIAA Education Series, USA, 3rd Edition, 2002.
• 2. Kaplan, Marshall H., ―Modern Spacecraft Dynamics and Controlǁ, John Wiley & Sons, New York, 1976.
• 3. Wiesel, William E., ―Spaceflight Dynamicsǁ, Tata McGraw-Hill Publishing Company Limited, New Delhi, 2nd Edition 2007.
• 4. David A. Vellado, ―Fundamentals of Astrodynamics and Applicationsǁ, Springer, Germany, 3rd Edition, 2007.