Ascending and descending nodes

Definition

An orbit inclined to the ecliptic crosses it at two points, the nodes. At the ascending node (symbol ☊) the body passes from south to north of the ecliptic; at the descending node (☋) it goes back from north to south. The straight line joining them through the Sun is the line of nodes: it is the intersection of the orbital plane with the plane of the ecliptic.

The direction of the ascending node is given by the longitude of the ascending node Ω, measured along the ecliptic from the vernal equinox. Together with the inclination i, it fixes the orientation of the orbital plane in space. The descending node lies at Ω + 180°.

Three angles to orient an orbit

Of the six Keplerian elements, three are angles that orient the orbit:

• Ω, the longitude of the ascending node: where the orbit crosses the ecliptic going north.
• i, the inclination: how steeply the orbital plane is tilted around the line of nodes.
• ω, the argument of perihelion: the angle from the ascending node to the perihelion, measured along the orbit.

Meeus often uses the longitude of perihelion ϖ = Ω + ω instead of ω, because it stays defined when the inclination is close to zero. For the Earth's orbit in the ecliptic of date, the inclination is zero and the node is undefined, which is why the Earth's orbit is described by ϖ alone.

Nodes of the planets

The planetary nodes move slowly, by a few tenths of a degree per century, under the attraction of the other planets. In the heliocentric view, switch on the line of nodes and the ascending and descending nodes to see where each orbit pierces the ecliptic plane.

Transits happen in fixed months

Mercury and Venus can only cross the face of the Sun when they are at inferior conjunction close to a node, that is when the Earth is close to their line of nodes. The Earth crosses those directions at the same dates every year, so transits fall in fixed seasons:

Meeus gives a chapter to the passages of the planets through their nodes. It computes the instant directly from the elements: the true anomaly at the node is v = −ω (ascending) or 180° − ω (descending), and Kepler's equation is solved backwards to obtain the time.

The lunar nodes and eclipses

The Moon's orbit is inclined by 5.15°, and its nodes move fast: the Sun's attraction makes the line of nodes regress, westward along the ecliptic, by a full turn in 18.61 years. As a result the Moon returns to the same node after 27.212 days, the draconic month, about 2.6 hours shorter than the sidereal month.

Eclipses happen when a new or full Moon occurs close to a node. The Sun passes a given lunar node every 346.62 days (the eclipse year), so eclipse seasons come about every 173 days, roughly twice a year, and drift about 19 days earlier each year. The famous saros cycle of 18 years 11 days works because 223 synodic months almost exactly equal 242 draconic months: after a saros, the Sun, the Moon and the node are back in nearly the same configuration.

The 18.6-year nodal cycle also drives nutation, the small nodding of the Earth's axis, and the lunar standstills, when the Moon's declination reaches its widest range. In astrology, the lunar nodes are the North and South Nodes, also called the dragon's head and tail, a name that recalls the old idea of a dragon swallowing the Sun during eclipses.

Explore it on AstroAlgos

• Heliocentric view — the nodes and the line of nodes in 3D
• Inclination — the tilt of an orbit
• Nutation — driven by the 18.6-year lunar nodal cycle
• Orbit — the six orbital elements