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fagricipni
2015-Sep-11, 10:04 PM
I think that the ascending and descending must be separated by exactly 180 degrees with respect to the central body, when both exist. It is possible for a hyperbolic orbit to have only one node; and it is theoretically possible for a parabolic orbit to have only one node, but the perihelion must be perfectly aligned with the existing node. This assumes that the orbiting body has a negligible mass in regards to the central body and perturbations can be ignored. The problem is that I don't know if my assumptions are correct.

grapes
2015-Sep-11, 11:12 PM
The nodes are defined when the orbit crosses the reference plane, whatever that reference plane is. For the earth, the orbit is in the ecliptic, so the reference frame is the equatorial plane. For the moon, the reference frame is the ecliptic.

The nodes can precess, so they don't have to be 180 degrees apart.

ETA: I'm totally not sure of that

fagricipni
2015-Sep-11, 11:18 PM
I'm assuming a Newtonian system, so relativistic orbital precession can be ignored.

grapes
2015-Sep-12, 09:18 AM
Relativistic precession is a thousand times smaller than ordinary precession. The nodes of the moon precess completely around the orbit every 18.6 years I think.

antoniseb
2015-Sep-12, 11:39 AM
Relativistic precession is a thousand times smaller than ordinary precession. The nodes of the moon precess completely around the orbit every 18.6 years I think.
In case it isn't obvious from what grapes has posted, most precession comes from the context of the orbit not being a purely two body system. Gravity from the Sun is a big contributor to the Moon's precession. Jupiter is a big contributor to Earth's precession around the Sun. Going back to the OP, if you looked at a circular orbit in a two-body system, the nodes would be 180 degrees apart. In a three body system with precession, if you looked at the orbit instantaneously and asked where the nodes were they would be very close to 180 degrees apart. If you looked at the location of where ascending and descending took place in one orbit, they would be close, but not as close to 180 degrees apart. In a case like the Moon, they'd be about 179 degrees apart.

fagricipni
2015-Sep-12, 12:53 PM
if you looked at a circular orbit in a two-body system, the nodes would be 180 degrees apart.

Just circular orbits? How about elliptical orbits or open orbits?

ETA: I want to clarify that I mean 180 degree separation with regard to the central body, not with regard to the center of the ellipse.


I do thank you for telling where the precession of Luna's orbit comes from; that really had me questioning my understanding -- I thought of Jupiter and inhomogeneities in Earth and Luna, and neither seemed to be enough to explain such a rapid precession, but I didn't think of Sol.

antoniseb
2015-Sep-12, 01:20 PM
Just circular orbits? How about elliptical orbits or open orbits?

ETA: I want to clarify that I mean 180 degree separation with regard to the central body, not with regard to the center of the ellipse.
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Sure, in a two body system where the second body has negligible mass, you can draw a straight line from ascending node to descending node, and it will go through the center of mass of the massive object, regardless of eccentricity of the orbit.