The same window, the same hour, why do the stars move every few days?
Take photos at the same location and at the same time every day, and let the window frame remember the position of the stars for you.
At eight o'clock tonight, a star is exactly in the middle of the window. A week later, you still stand in the same place and look again at eight o'clock, but it has moved to one side. The windows didn't move, the clock didn't break: the Earth rotated a little more than a full revolution each day relative to the distant star.
Guess first
Will the starry sky seen one week apart at the same place and at the same time be exactly the same?
Show answer and explanation
There will be a little movement — The earth rotates and revolves at the same time, and the direction of the stars corresponding to the same solar clock changes slightly every day.
Then connect experience and science
Convert fixed hours to JD
Fixed UT1 20:00 every day, only the day number changes. The first day is 1987-04-10, the location and star declination remain unchanged.
JD = JD₀ + days
Find the mean sidereal time for each day
Equation (12.4) gives the Greenwich mean sidereal time at this instant of the day, and the result is in degrees.
T = (JD − 2451545.0) / 36525
minus the direction of the first night
After subtracting the same hour points and processing the entire circle, there is approximately 0.986° more local hour angle per day; change it to local coordinates and draw it into the window.
ΔH = θ(JD₀ + days) − θ(JD₀) (normalized)
Convert direction difference into advance time
Divide the direction difference by the earth's average rotation speed relative to the star to get how long it takes to return to the original direction.
Minutes ahead ≈ ΔH / 360.98564736629 × 1440
Expand the calculation
T = (JD − 2451545.0)/36525 θ = 280.46061837 + 360.98564736629(JD − 2451545.0) + 0.000387933T² − T³/38710000 θ圈内 = θ mod 360°
θ is expressed in degrees, normalized to 0° to 360°. The input JD uses UT1; it rotates about 0.986° more at the same time every day, not just this point.
give it a try
Watch "First Night" first, then "One Week Later." The gold color is the current position of the star, and the hollow outline remembers the first night.
No need to memorize symbols
- θ
- GMT mean sidereal time in degrees
- JD₀
- 1987-04-10 UT1 20:00 Julian Day
- ΔH
- The hour angle added to the same hour relative to the first day
- days
- The whole number of days since the first day
Algorithm, accuracy and scope of application
Reuse existing calculations from Chapters 7, 12, and 13. The fixed location is 0° east longitude and 40° north latitude; the fictitious star has a declination of 20° and a right ascension equal to the mean sidereal time at 20:00 UT1 on the first day, so that it is in the midheaven on the first day. It only demonstrates the comparison of 0-30 days at the same time, does not read the real star catalog, and does not predict urban observation conditions. Minutes in advance are approximately converted using the average stellar speed in the book, and independently verified using numerical roots. This lesson does not treat UT1 as being exactly the same as UTC, nor does it include nutation, precession, aberration, refraction, or the moon.
my understanding check
Want to see the same star return to its original position in the window after a few days?
Watch earlier — The moment when the same star passes in the same direction occurs approximately 4 minutes earlier each day.
What conditions remain the same when comparing two photos here?
place and hour — The date changes, but the place of observation, perspective, and hour of the day remain the same.
Does this mean the clock at home is running 4 minutes slower every day?
No, it’s because the two day calculations have different references. — The solar day on which the clock is based is different from the period in which the direction of the stars is repeated, and the difference cannot be regarded as a clock malfunction.
The stars in the sky pass in the same direction about 4 minutes earlier every day; if you take pictures at a fixed time, the position changes will accumulate day by day.
Jean Meeus · Astronomical Algorithms, 2nd ed. · No. 12 chapter