Will the "coordinate ruler" of the starry sky sway slightly on its own?
See clearly the average direction and small periodic changes of the earth's axis, and distinguish between "the stars are moving" and "the ruler is moving".
Sky coordinates and observations
If you repeatedly measure the same star with a telescope, the coordinate numbers will change slightly. In addition to the motion of the stars themselves, the coordinate datum defined by the Earth's axis of rotation also changes. Here we zoom in on the very small nutation to see how it affects the coordinate ruler we use.
Guess first
If there is a small change in the coordinates of a star, does it mean that the star itself must be moving rapidly?
Show answer and explanation
Not necessarily, the coordinate datum will also change. — Changes in the direction of the earth's axis will affect the reference grid, so it is necessary to distinguish between the coordinate datum and the motion of the celestial body itself.
Then connect experience and science
First distinguish between long-term drift and small swings
The main trend of long-term slow changes in the direction of the earth's axis is called precession; the periodic changes around the mean direction are called nutation. They change the basis from which we draw the sky coordinate grid.
Nutation is divided into Δψ (yellow longitude) and Δε (intersection angle)
Change the date, see two small corrections
Here, add up all the 63 periodic terms in Table 22.A in the book. The numbers are only in the order of arcseconds. The picture on the right is enlarged to a clear scale and does not mean that the Earth's axis is shaking significantly.
Δψ=Σ(A+B T)sin(argument)；Δε=Σ(C+D T)cos(argument)
The average angle of intersection does not include nutation
The ecliptic angle is the angle between the equatorial plane and the ecliptic plane. "Average" excludes nutation, and "true" angles add back the day's Δε.
εtrue = εaverage + Δε/3600
Connect it back to the star catalog and telescope
When the coordinate datum changes slightly, the coordinate numbers of the star will also change; this change cannot be said to be entirely due to the movement of the star itself.
The input time is TT; the output Δψ, Δε are arc seconds
Expand the calculation
argᵢ = dᵢD + mᵢM + m′ᵢM′ + fᵢF + ωᵢΩ Δψarc seconds = Σᵢ[(Aᵢ+BᵢT) sin argᵢ]/10000 Δεarc seconds = Σᵢ[(Cᵢ+DᵢT) cos argᵢ]/10000 ε真 = εaverage + Δεarc seconds/3600
The five integer multipliers of argᵢ and the coefficients A, B, C, and D are taken from Table 22.A row by row, and the coefficient unit is 0.0001 arc seconds; where Dᵢ is different from the basic angle D. The complete summation structure is shown here without listing the 63 coefficients line by line. T is the TT Julian century from J2000 onwards.
give it a try
First read the calculation example from 1987 in the original book, and then switch the date. The enlargement in the picture is a small correction, and the yellow-red angle on the left is still in real degrees.
No need to memorize symbols
- Δψ
- Huang Jing chapter movement, arc second
- Δε
- Yellow-red horn nutation, arc seconds
- ε
- Yellow-red intersection angle, degrees
- TT/JDE
- Time scales and consecutive days used to calculate geodynamic phenomena
Algorithm, accuracy and scope of application
Implement all 63 terms of Table 22.A and the five basic angle polynomials; each coefficient unit is 0.0001 arc seconds. We provide Equation 22.2 cubic average intersection angle and Equation 22.3 Laskar tenth degree formula; the teaching control range is 1900–2100. Although the Laskar formula itself has a longer applicable range, it does not extrapolate the entire nutation table to the same length. True intersection angle = selected average intersection angle + Δε/3600. Example 22.a of the original book is compared with the local AA+ grid; AA+ MeanObliquity uses the Laskar formula, and the same method is clearly selected when comparing.
my understanding check
What is the difference between average yellow and red angles and true yellow and red angles?
Whether to add nutation correction for the day — The true angle of intersection is the average value plus the nutation of the yellow-red angle of intersection Δε.
In the picture on the right, the arcsecond correction is drawn very large. Does this mean that the earth's axis is really that large?
No, the picture is enlarged separately — You must look at the marked arcsecond scale, and do not take the enlarged picture as a true spatial scale.
Can the 63 results in this course be directly called the modern IAU 2000A results?
Can't — It is a truncated table of the IAU 1980 theory in the book. The model age and number of terms must be clearly stated.
When measuring stars, you also need to know how the "coordinate ruler" changes: precession is a long-term trend, and nutation is a superimposed small periodic change.
Jean Meeus · Astronomical Algorithms, 2nd ed. · No. 22 chapter