Why do we need to distinguish between "mean" and "apparent" sidereal time when the telescope is pointed at the same star?
The Earth's rotation gives the general direction, and small changes in the reference zero point of the celestial sphere will also bring about second-level corrections.
In the previous section, I used a fixed window to see the stars move every day. If you want to point more precisely, you must also distinguish between the mean celestial zero point and the true zero point affected by nutation. Two readings describe the same moment, not two clocks suddenly running faster or slower.
Guess first
Mean sidereal time and apparent sidereal time are different, does it mean that the observation occurs at two times?
Show answer and explanation
no — They describe the same instant but use different reference zero points.
Then connect experience and science
At the same instant, calculate the mean sidereal time first
Convert UT1 date to JD and calculate using the average zero point formula in Chapter 12.
θ flat=GMST(JDUT1)
Find small changes in the true zero point
Nutation is calculated based on a given TT time. ΔT is set by you and cannot be changed to a time zone difference.
JDTT=JDUT1+ΔT/86400
plus the equinox equation
Projection of the ecliptic nutation to the equatorial direction gives the difference between mean and apparent sidereal time.
Correction (time seconds) = Δψ cosε / 15
Fine pointing should keep coordinates consistent
Apparent right ascension should match apparent sidereal time; do not add nutation while still using average coordinates.
θ sight = θ plane + Δψ cosε
Expand the calculation
JDTT = JDUT1 + ΔTSecond/86400 ΔθSpend = (Δψarc seconds/3600) cos ε θ视 = θ平 + Δθ Correctiontime seconds = Δψarc seconds cos ε/15
The earth's rotation angle is taken as UT1, and the nutation is taken as TT; the rotation in arc seconds is divided by 3600, and the rotation in arc seconds is divided by 15 in sidereal time seconds. The two conversions cannot be mixed.
give it a try
Dian Yuanshu’s 1987 calculation example. The main picture magnifies the tiny reading differences, and the real correction is only the time seconds marked on the right.
No need to memorize symbols
- Δψ
- Huang Jing chapter movement, arc second
- ε
- True yellow red horn
- GMST/GAST
- Horizontal/apparent Greenwich sidereal time
Algorithm, accuracy and scope of application
Supplement Chapter 12 Equinox equation and mean to apparent sidereal time transformation. The nutation input is TT, and the mean sidereal time input is UT1. Original book 12.a The calculation example that ignores the small time difference is reproduced with dt=0, and the rest is given dt as an assumption.
my understanding check
If the nutation correction Δψ is expressed in arc seconds, how should it be converted into time seconds?
Divide by 15 and multiply by cosε — Distinguish between arc seconds and time seconds.
When pointing with apparent right ascension, should it match?
apparent sidereal time — Coordinate corrections must be consistent across sets.
Can the enlarged deviation in the picture be directly regarded as the real angle?
cannot — Magnification is for clarity only, actual corrections are given by numbers.
Fine pointing at the same instant requires that the average/view coordinates and the time zero point match each other.
Jean Meeus · Astronomical Algorithms, 2nd ed. · No. 12 chapter