Why do we also need to write the year in the orbital parameters of the planet?
Flip the year and see how the shape and orientation of the average orbit slowly changes.
Planets and Small Solar System Objects
The number of tracks is not a nameplate that will never change. The planets disturb each other, and the parameters describing their average orbits change over time. This lesson turns the coefficient table from the original book into a track record sheet that can turn over years.
Guess first
Orbital parameters usually come with a year as a reminder of what?
Show answer and explanation
Parameters and reference axes may change over time — It is necessary to know the time and reference point corresponding to the parameter.
Then connect experience and science
The average orbit is not an instantaneous precise position
Planets are perturbed by other celestial bodies, and their average orbits use smoothing coefficients to summarize long-term changes. The calculation here is based on Table 31.A/B of the original book, rather than taking the value from the approximate track on the home page.
Each root number=a₀+a₁T+a₂T²+a₃T³
First determine the time and reference points
Position dates and reference axes cannot be confused. The angle coefficients of date equinoxes and J2000 equinoxes are different.
T=(JDE−2451545)/36525
Distinguish between mean longitude and ecliptic longitude
L is measured along the reference plane to the intersection point, and then along the orbit; L cannot be directly regarded as the celestial longitude.
M=L−ϖ；ω=ϖ−Ω
Think of the mean orbit as the starting point
It helps in understanding shapes and changes, but is not a substitute for the periodic ephemeris in the next chapter. The earth's date ecliptic inclination is 0, and the ascending node is conventional at this time.
The average orbit does not include all short-period perturbations
Expand the calculation
T = (JDE−2451545)/36525 元素(T) = a₀ + a₁T + a₂T² + a₃T³ ϖ = Ω+ω；M = L−ϖ；ω = ϖ−Ω
Each element takes a row of coefficients corresponding to its planet, reference frame and element name. The angular element outputs degrees, the semi-major axis outputs AU, and the eccentricity is dimensionless; a₀ and so on here are universal polynomial coefficients, not the semi-major axis a.
give it a try
First fix the year, switch the date minute and J2000 minute; then fix the reference minute to change the year.
No need to memorize symbols
- L / ϖ
- Mean longitude / perihelion longitude
- T
- J2000 onwards Julian century
- a / e / i / Ω
- Semi-major axis, eccentricity, inclination, ascending node
Algorithm, accuracy and scope of application
Realize all eight planetary polynomials in Tables 31.A and 31.B, semi-major axis AU, and angle degrees. Fixed J2000 and date-averaged dynamic ecliptic equinoxes switchable. The earth date plane i=0, Ω does not have unique geometric meaning, and is taken as 0 only for decomposition; the earth's inclination angle in the J2000 table may be a signed small angle, and the coefficient table sign is retained for consistent coordinate rotation. High-precision positions should use Appendix III or complete numerical ephemeris; do not call the JPL approximate formula on the home page.
my understanding check
Is the mean longitude L equal to the ecliptic longitude cast directly onto the ecliptic?
Generally does not wait — The measurement paths of the two are different.
What units are used for semimajor axis?
AU — a is the length, and the other multiple terms are angles or dimensionless.
Can mean orbits replace complete planetary ephemerides?
cannot — It generalizes smoothly changing, periodic perturbations which require a series of calculations in the next chapter.
Let’s talk about dates and coordinate axes first, and then orbit parameters; the average orbit helps to understand, but it does not equal all precision movements.
Jean Meeus · Astronomical Algorithms, 2nd ed. · No. 31 chapter
Planets and Small Solar System Objects · All interactive courses