With the same comet orbit, why do the numbers change when I change the star map?
What is being changed is the coordinate ruler, not moving the comet's orbit elsewhere.
Sky coordinates and observations
The same street may have different coordinates on the two maps. The reference direction of astronomical coordinates will also change with precession: if a set of orbital roots is changed to another equinox, the direction angle needs to be recalculated, but the orbit itself is still the same.
Guess first
Does just changing the reference equinox of the orbit mean that the comet has actually moved to that year?
Show answer and explanation
no — The coordinate reference has changed, but the effective epoch of the original orbital root number has not changed.
Then connect experience and science
The same road can be marked with different coordinate networks
Changing the coordinate grid of the map will not make way for the real move. It has the same meaning when converting the orbital root number to the reference point.
a, e remain unchanged; what changes is i, ω, Ω
Change only the three items describing the direction
Orbital inclination, ascending node longitude and perihelion argument are all defined relative to a reference plane/direction. Precession changes these references.
Calculate η, Π, p from the initial equinox
See the readings of the comet example in the original book
Comet 1744 changed the same group of roots from B1744 to B1950, and the three direction angles changed, but the shape of the orbit did not change.
Formula (24.1)–(24.3)
Changes in equinoxes do not equal orbital evolution over time
Also distinguish between FK4 and FK5 system conversion. In the case of Comet Encke, the effective epoch of the orbital root number is still 1990, not 2000.
Coordinate reference change ≠ dynamic deduction
First calculate η, Π, and p based on the starting and ending points, and then rotate the orbital plane to obtain new i, Ω, and ω. The semi-major axis a and eccentricity e remain unchanged; the reference axis is changed during this process, and the perturbation of the real orbit is not extrapolated.
give it a try
First compare the "original coordinate network" and "switch to B1950", and then check the difference between the two system conversions of Comet Encke.
No need to memorize symbols
- i
- The inclination of the orbital plane relative to the reference ecliptic plane
- Ω
- ascending node longitude
- ω
- perihelion argument
- B / J
- Bezier/Julian Year Reference Equinox Markers
Algorithm, accuracy and scope of application
Implement the general point conversion (24.1)–(24.3) of Chapter 24, the equivalent general formula route from B1950/FK5 to J2000/FK5, and the Yeomans’ FK4 B1950→FK5 J2000 conversion at the end of the book. Refer to AAEclipticalElements and check the values with Example 24.a/b/c. The inclination angle uses atan2(sin i, cos i) to maintain the retrograde orbit quadrant; when the new orbit is exactly located on the reference plane, the ascending node and argument are split and degraded, and null is returned. The interface only shows non-degenerate cases in the original book; there is no orbital perturbation or orbital evolution over time.
my understanding check
Which two items remain unchanged after changing the reference point?
Semimajor axis and eccentricity — a and e describe the scale and shape of the same orbit, which do not change with this reference conversion.
From B1950 to J2000, do we just need to add 0.7° to all angles mechanically?
no — The inclination angle and perihelion argument also need to be calculated according to the spatial rotation relationship, and constants cannot be added uniformly.
Are equinox transitions and orbital dynamics evolution the same thing?
no — The former requires changing the coordinate ruler, while the latter requires calculation of real motion and perturbation.
First check which equinox and system the coordinates belong to, and then compare the numbers; changing the coordinate network does not mean allowing celestial bodies to travel through time.
Jean Meeus · Astronomical Algorithms, 2nd ed. · No. 24 chapter