- Mayur Pawar

# Do you know: What is Orbital Dynamics?

Since humans started looking up towards the sky, they have been fascinated with the stars, the planets and space in general. In the old times, the Earth was supposed to be the centre of the universe and everything else revolved around it. However, in the 16th century, this view was challenged by Copernicus and the heliocentric definition of the Solar system came into existence. Then at the beginning of the 17th century Johannes Kepler came up with the three basic laws to define the motion of planets around the solar system and these laws with Newton's law of gravitation have come to be the basis of all orbital dynamics.

**Orbital mechanics** or **astrodynamics** is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. The motion of these objects is usually calculated from Newton's laws of motion and law of universal gravitation. Orbital mechanics is a core discipline within space mission design and control.

Celestial mechanics treats more broadly the orbital dynamics of systems under the influence of gravity, including both spacecraft and natural astronomical bodies such as star systems, planets, moons, and comets. Orbital mechanics focus on spacecraft trajectories, including orbital manoeuvres, orbital plane changes, and interplanetary transfers, and is used by mission planners to predict the results of propulsive manoeuvres. General relativity is a more exact theory than Newton's laws for calculating orbits and is sometimes necessary for greater accuracy or in high-gravity situations (e.g. orbits near the Sun).

The fundamental laws of astrodynamics are Newton's law of universal gravitation and Newton's laws of motion, while the fundamental mathematical tool is differential calculus.

Every orbit and trajectory outside atmospheres is in principle reversible, i.e., in the space-time function, the time is reversed. The velocities are reversed and the accelerations are the same, including those due to rocket bursts. Thus if a rocket burst is in the direction of the velocity, in the reversed case it is opposite to the velocity. Of course in the case of rocket bursts, there is no full reversal of events, both ways the same delta-v is used and the same mass ratio applies.

Standard assumptions in astrodynamics include non-interference from outside bodies, negligible mass for one of the bodies, and negligible other forces (such as from the solar wind, atmospheric drag, etc.). More accurate calculations can be made without these simplifying assumptions, but they are more complicated. The increased accuracy often does not make enough of a difference in the calculation to be worthwhile.

Kepler's laws of planetary motion may be derived from Newton's laws when it is assumed that the orbiting body is subject only to the gravitational force of the central attractor. When an engine thrust or propulsive force is present, Newton's laws still apply, but Kepler's laws are invalidated. When the thrust stops, the resulting orbit will be different but will once again be described by Kepler's laws. The three laws are:

The orbit of every planet is an ellipse with the sun at one of the foci.

A line joining a planet and the Sun sweeps out equal areas during equal intervals of time.

The squares of the orbital periods of planets are directly proportional to the cubes of the semi-major axis of the orbits.

The Keplerian laws can most easily be derived by considering a two-body problem and it was first solved by Sir Isaac Newton. If the central body is considered to be much larger than the body orbiting it, then the mass of the other body can be neglected. In addition to the negligible mass, the force exerted on the satellite always points towards the centre of the central body because the applied force is always anti-parallel to the position vector thus eliminating any acceleration perpendicular to the plane, hence its orbit is always conned to a plane at all times.