## Wednesday, November 8, 2017

### Characteristics of Orbits

The science behind the legion of satellites and spacecraft which humanity launches and uses right now is at the same time both complicated and simple, and is surprisingly also very old, much older than spacecrafts and indeed, flight itself.

An orbit is the path a body takes around another. There are several shapes of orbits, from elliptical to circular to hyperbolic. Orbits have many properties, but only 6 of them are required to completely describe them mathematically. They are the semi-major axis, the eccentricity, the inclination, the argument of periapsis, the time of periapsis passage and the longitude of the ascending node.

Semi-major axis: The semi-major axis of an orbit is the average distance of an orbiting body from the body it is orbiting (its primary). For elliptical orbits, the semi-major axis is half the length of the ellipse's major axis, which is the longest line that can be drawn inside an ellipse which goes through a focus. For a circular orbit, the semi-major axis is the radius of the circle.

Eccentricity: The eccentricity of an orbit is a measure of how elliptical it is. It is defined as the ratio of the distanced between the two foci of an orbit to its semi-major axis. For circles, this number if zero; for ellipses, between zero and one; for parabolas, one; and for hyperbolic orbits, greater than one.

Inclination: The inclination of an orbit is the angle between the orbit and the equatorial plane of its primary. An inclination of 0 degrees indicates and equatorial orbit in the direction of the primary's rotation, while an inclination of 180 degrees indicates an equatorial orbit in the opposite direction to the primary's rotation.

Time of periapsis passage: The time for periapsis passage is the amount of time an orbiting body takes to pass through its periapsis, which is defined as the point on the orbit closest to the primary.

Argument of the periapsis: The argument of the periapsis is the angular distance from the ascending node of the orbit to the periapsis of the orbit. The ascending node of an orbit is the place where the orbit crosses the equatorial plane of the primary.

Longitude of ascending node: The longitude of the ascending node of an orbit is the celestial longitude of the ascending node as measured in the celestial positioning system.

With these 6 parameters, one can calculate almost all of the other parameters of that orbit, of which there are many.

(Below): The picture below shows the parameters described above graphically.