Now that we know what type of motion the planets follow, how do we define properties of an orbit?

To fully define the instantaneous trajectory of a planet or satellite we need 6 parameters. These parameters in *Cartesian coordinates *are:

3 parameters for position

- X
- Y
- Z

3 parameters for velocity

- V
_{x} - V
_{y} - V
_{z}

*However*, there is a more convenient set of parameters which allows us to utilize Kepler’s laws to predict the position and velocity of the orbiting body.

Keplerian Orbital Elements

Two elements to describe the size and shape of an orbit:

- Semi-major axis (a)
- Eccentricity (e)

Three elements to describe the orientation of the orbit in space:

- Inclination (i)
- Right ascension of the ascending node (Ω)
- Argument of perigee (⍵)

One element to describe the location of a satellite within the orbit:

- True Anomaly (𝜈)

A total of 6 parameters in a specified coordinate frame and reference time.

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