# What is the relationship between longitude of ascending node and argument of perihelion?

May 18, 2017

Longitude of ascending node and argument of perihelion are two of the six orbital elements required to describe an orbit.

#### Explanation:

The orbit of a planet, moon or other body requires six parameters to describe it. These are know as orbital elements or Keplerian elements after Johannes Kepler who first described orbits with his three laws.

The first two elements and the eccentricity e and semi-major axis distance a which describes the shape of the ellipse. Kepler's first law states that orbits are ellipses.

To describe the other elements we need a frame of reference. The plane of the ecliptic is the plane of Earth's orbit. All orbits are measured relative to this.

We also need a direction which is 0 degrees in the plane. This is the Vernal Equinox. The Vernal Equinox is the moment when the Sun crosses the equator heading North which occurs around 20 March. The direction from the centre of the Earth to the point where the Sun crosses the equation is the reference direction. As the equinoxes precess, an epoch is defined. J2000 is often used. It is the direction of the Vernal Equinox on 1 January 2000 at 1200.

The inclination i is the angle the orbit makes to the ecliptic. For Earth it is always 0 degrees.

The longitude of ascending node $\Omega$ is the angle from the Vernal Equinox to the point where the orbit crosses the ecliptic heading North - the ascending node.

The argument of perihelion $\omega$ is the angle from the longitude of ascending node to the perihelion.

Finally the true anomaly $\nu$ is the angle the planet makes from perihelion to its position at a particular time.

So, the longitude of the ascending node defines the direction in which the orbit intersects the ecliptic. The argument of perihelion defines the angle from the direction of the ascending node to the direction of perihelion, the closest point to the body being orbited around.