Kepler’s laws and Newton ’s derivation of Keplerian orbits. Energy and angular momentum related to orbital geometry. Velocity and mission planning. Time along orbit – Kepler’s problem, mean and eccentric anomalies. Groundtracks, Molniya, geosynchronous and resonant orbits, LEO and sun synchronous orbits.
Coordinate Systems and Time:
Equinoxes, solstices, first point of Aries, precession of the nodes.Earth’s mean equator, the obliquity of the ecliptic. Local topographic frames, hour angles, latuitude and longitude. Perifocal coordinates and local satellite coordinates.Solar time, sidereal time, universal time and atomic time. Julian date and MJD. Polar motion. Earth’s nutation and precession.
Dynamics of a Rigid Body:
Rotating frames of reference. Coriolis theorem. Moments of Inertia, principal axes, Euler’s equations. Kinematics, Euler angles, roll, pitch and yaw. Kinematic equations, integrals of the motion – rotational energy, total angular momentum. Motion of the angular momentum vector, torques.
Rotation states of triaxial satellites, precession and nutation with methods of control. Attitude sensors and actuators. Attitude solution from vector observations
Gyroscopic torques and momentum bias. Internal momentum storage devices. Control moment gyroscopes, gravity gradient booms, momentum wheels.
Detumbling of a spacecraft on separation. Magnetic control in LEO, Y-Thomson spin.