My understanding of sidereal time is that the position of a star will be in the same place 4 minutes earlier the next day. So a 20 days later the star will be 1hr 20 mins earlier. So if the star is in the same place it must be a multiple of 4 minutes earlier (and the seconds that I have ignored). So it is not possible for the star to be in the same place and not be that time multiple apart.

Its just that I have some data points where the locations are identical and they are all multiples of 4 mins apart but I am worried that that is not significant because it is inevitable. Is that correct?

  • $\begingroup$ I don't really get the confusion. I don't understand why you are "worried" about this. Suppose it is not significant? why would that be a problem and something to worry about? $\endgroup$ – James K Nov 19 '20 at 0:04
  • $\begingroup$ @ James K I suppose you are right. The fact that multiple data points map to the same location is more informative. $\endgroup$ – user36093 Nov 19 '20 at 20:14

Let's start with a description of sidereal time. From my knowledge, sidereal time at any location can be described as:

the right ascension currently at the zenith

Here are the definitions of zenith and right ascension, if you need them.

So, if the sidereal time at some location is 12 hours, 0 minutes, and 0 seconds, the right ascension directly above that location at that time will be 12:00:00. So, one sidereal day is the time it takes for the sidereal time at any location to "repeat itself" - i.e., the time between one 00:00:00 and the next 00:00:00. This means that one sidereal day is the time it takes for Earth to rotate 360 degrees.

The time that full rotation takes - i.e., one sidereal day - has been calculated to be roughly 23 hours and 56 minutes, or 1436 minutes. Since you're measuring your time in solar time, you would expect to see this 4-minute discrepancy in a lot of places, because, well, 23 hours and 56 minutes is 4 minutes less than a full solar day of 24 hours. From one day to the next, most objects (the Moon is a notable exception) will rise 4 minutes earlier.

So, yes, your analysis is correct - this daily 4 minute change is not really "significant" since it is a consequence of the Earth's rotation around the Sun, and you should expect to see that.

A side note:

Additionally, we can see that the time it takes Earth to rotate one full degree is:

$\dfrac{1436\: \rm{minutes}}{360 \: \rm{degrees}} = 3.99 \dfrac{\rm{minutes}}{\rm{degree}}$

So, this 4-minute daily change is also a nearly 1-degree daily change.


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