Aero-Quantum

I thought to write something about the orbital mechanics that I know so far. This would be a revision for me as well as chance to realize new things and come up with new questions to ask for myself.

The celestial mechanics or the orbital mechanics is the study of dynamics of satellites and planets in their orbit around bigger masses. For example, the moon and artificial satellites such as GPS, International Space station, etc. revolve around the earth in their orbit while the planets revolve around the sun in their orbit. The orbit around the sun is called helical orbit while the orbit around the earth is named as geo-orbit.
 
Nomenclature: It is important to understand the terminologies used to define the characteristics of orbit. In the demonstration figure below a mass is revolving around a bigger mass in its orbit. When the smaller body is at the closest distance with the bigger body (at position 2), its position is called as the periapsis. On the other hand, when the body approaches the farthest point (at position 1), its position is called as the apoapsis.

If the center body is sun, the closest and farthest positions are called perihelion and apohelion position respectively. Similarly, if the center body is earth, the closest and farthest position are called apogee and perigee respectively.See table below for more terms of apogee and perigee.

Body	Farthest approach	Closest approach
General	Apogee	Perigee
Sun	Apihelion	Perihelion
Earth	Apogee	Perigee
Mercury	Apohemion	Perihermion
Venus	Apocyterian	Pericytherian
Mars	Apoareion	Periareion
Jupiter	Apozene	Perizene
Saturn	Aposaturnium	Perisaturnium
Uranus	Apouranion	Periuranion
Neptune	Apoposeidion	Periposeidion
Pluto	Apohadion	Perihadion
Star	Apoastron	Periastron
Galaxy	Apogalacticon	Perigalacticon
Black Hole	Apobothra	Peribothra

Obviously, you must have noted that the periapsis is equal to the apoapsis for a circular orbit. The circular orbits can be seen in case of artificial satellites only. By nature, each and every cellestial body revolves in an elliptical path. The Keplers law define these kind of properties of properties of planets around the sun.

Kepler's law:
1. The orbit of each planet is an ellipse with the sun occupying the focus (center object).
2. The line joining the sun to a planet sweeps out equal areas in equal intervals of time
3. A planets orbital period is proportional to the mean distance between the Sun and the planet raised to the power 3/2.

First law	Picture owned by Gary M. Winter
Second law
Third law

Helical Orbits: