Scroll down for explanations of the Keplerian Orbital Elements Framework
Orbital Elements and Key Concepts
Semi-major axis (a)
Half the longest diameter of the elliptical orbit. It determines the orbit's size and is directly related to the orbital period.
$$T = 2\pi\sqrt{\frac{a^3}{\mu}}$$
Where T is the orbital period and μ is the gravitational parameter.
Eccentricity (e)
Describes the orbit's shape, ranging from 0 (circular) to 1 (parabolic). Values between 0 and 1 represent elliptical orbits.
$$e = \sqrt{1 - \frac{b^2}{a^2}}$$
Where b is the semi-minor axis.
Inclination (i)
The angle between the orbital plane and the reference plane. Ranges from 0° to 180°.
$$\cos i = \frac{\mathbf{h} \cdot \hat{\mathbf{z}}}{|\mathbf{h}||\hat{\mathbf{z}}|}$$
Where h is the angular momentum vector and ẑ is the unit vector of the reference plane's normal.
Right Ascension of Ascending Node (Ω)
Angle from the reference direction to the ascending node, measured in the reference plane. Ranges from 0° to 360°.
$$\tan \Omega = \frac{\mathbf{n} \cdot \hat{\mathbf{y}}}{\mathbf{n} \cdot \hat{\mathbf{x}}}$$
Where n is the node line vector, and x̂ and ŷ are unit vectors in the reference plane.
Argument of Periapsis (ω)
Angle from the ascending node to the periapsis, measured in the orbital plane. Ranges from 0° to 360°.
$$\cos \omega = \frac{\mathbf{n} \cdot \mathbf{e}}{|\mathbf{n}||\mathbf{e}|}$$
Where e is the eccentricity vector.
True Anomaly (ν)
Angle from the periapsis to the orbiting body's current position, measured in the direction of motion. Ranges from 0° to 360°.
$$\cos \nu = \frac{\mathbf{e} \cdot \mathbf{r}}{|\mathbf{e}||\mathbf{r}|}$$
Where r is the position vector of the orbiting body.
Reference Plane
The light blue plane in the visualization, representing the fundamental plane of the coordinate system (e.g., Earth's equatorial plane).
Orbital Plane
The light orange plane containing the orbit. Its orientation is defined by the inclination and RAAN.
Line of Nodes
The intersection of the orbital plane and the reference plane. It connects the ascending and descending nodes.
$$\mathbf{n} = \hat{\mathbf{z}} \times \mathbf{h}$$
Where n is the node line vector, ẑ is the reference plane normal, and h is the angular momentum vector.
Periapsis
The point of closest approach to the central body in an elliptical orbit. Marked by a dashed white line in the visualization.
$$r_p = a(1-e)$$
Where rp is the periapsis distance.