I have two or more sets of dates and times for which I am interested in the location of the Zenith at my location and whether they are coinciding. So far I have been comparing pairs of them on two Stellarium windows with the azimuthal grid but its laborious. Can any one tell me of an easier way. I expect I could do it in excel with a bit more knowledge.
Technically, the location of the zenith is constant: 90 degrees altitude, undefined azimuth. :-) I assume that you want it in terms of the coordinates declination and right ascension instead of altitude and azimuth. Declination and Right Ascension are the coordinate system used to locate objects in the sky. They are similar in concept to latitude and longitude. The difference is that one is "locked" to the sky, and the other is "locked" to the Earth.
- The declination of the zenith is the same as the observer's latitude. If your location is the same, then the declination is the same. (If the latitude is different, the coordinate of the zenith is different.)
- The right ascension of the zenith can be calculated by using the formulas for the local sidereal time (LST or LMST for the mean local sidereal time.) See the post Local Sidereal Time.
What @JohnHoltz says is correct. If you need a cook book formula for 2020: The vernal equinox starts the year at 100.1167 degrees greenwich hour angle (GHA). Every second after that it's 0.0041780744757 degrees greater. The sidereal hour angle (SHA) of your zenith is your west longitude minus the GHA of the vernal equinox. If you're an excel user you probably know how to convert D-M-S to decimal degrees, and handle modulo arithmetic. If you're only interested in comparing times, the SHA of your zenith repeats every 86164.0935534009 seconds, so, if the difference in time is an integer multiple of that (plus/minus some tolerance) the zeniths are coincident.
Making a spreadsheet: Start with a column of all the date/times you want to compare. (You might find it easier to have separate date/time columns, if that's the way your data is given.) Make a column of time differences. One way to do that would be to calculate the elapsed time in seconds for each date/time since the start of 2017. Make another column calculating the time difference mod 86164. (The Excel formula would be "=MOD([cell number],86164)", where the cell number would be for the adjacent cell in the time difference column) Then sort the entire spreadsheet on that column. ("Sort" is one of the choices in the "Data" pull-down menu.) At this point you're done. The times with the same zeniths will be bunched in adjacent rows.