From the NEODyS data set (http://newton.dm.unipi.it/neodys/index.php?pc=5), we can take the computed values of proper elements for the NEOs, that is, the precession rate g of perihelion (the frequency of perihelion), that is equal to the sum of changes in the argument of perihelion, [omega], and in the longitude of the ascending node, [OMEGA], of the orbit of the asteroid, expressed in arc seconds per year and the precession rate s of the ascending node (the frequency of the ascending node), that is equal to the change in the longitude of the ascending node, [OMEGA], of the orbit of the asteroid, expressed in arc seconds per year.
A particular secular resonance occurs when the frequency of time-variation of the longitude of perihelion, g, or the longitude of the ascending node, s, of an asteroid becomes close to the orbital frequency of a planet.
Optimal Control Law for the Rate of Change of Ascending Node
. The procedure is the same as in optimal control law for inclination
But because there may be either one or two transits at each node, other intervals are possible; for instance when series B ends there will be just one transit at the ascending node
giving the sequence 129 1/2, 8 and 105 1/2 years.
In comparison with the best area coverage result in Case 7, it can be seen that, by introducing v as an optimized variable in Case 12, the satellites' ascending node
in the same orbit plane (satellite 1 and 2) is separated up to 264[degrees].
Argument of perihelion 43.63720 [degrees] Longitude of ascending node
126.37563 [degrees] Eccentricity 0.5147984 Inclination 19.81182 [degrees] Currently the ascending node
is between the orbits of Mercury and Venus, and the descending node between the orbits of Earth and Mars.
Argument of perihelion, [Omega] 130.296 [degrees] Longitude of ascending node
, [Omega] 188.156 [degrees] Inclination, i 124.650 [degrees] Sky & Telescope columnist John Bortle is more optimistic.
Because the Moon is headed north of the ecliptic, it is called the ascending node
. Nothing actually marks this spot in the sky, but we can keep track of its position with respect to the background stars.
Eccentricity, e 0.9953 Argument of perihelion, [ohms] 130.57 [degrees] Longitude of ascending node
, [ohms] 282.47 [degrees] Inclination, i 89.43 [degrees] If the comet does brighten significantly, eclipse chasers in Mongolia and eastern Siberia may see Hale-Bopp with the naked eye 46 [degrees] from the Sun during the total eclipse on March 9, 1997, along with Mercury, Venus, Jupiter, and Saturn.
1.49226 TT (ET), perihelion distance q = 1.3651154 a.u., eccentricity e = 0.6228036, inclination i = 30 [degrees].27061, argument of perihelion [Omega] = 353 [degrees].35863, longitude of ascending node
[Omega] = 75 [degrees].42389 (2000.0).
Levison and Stern claim Pluto avoided this fate because something knocked it solidly into the orbital resonance, in such a way that its perihelion and ascending node
remained far apart as well.
The "splash" points, where the fish enters and leaves the water, are, respectively, the descending and ascending nodes
-- points where the Moon passes through the Earth's orbital plane.