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I am using Stellarium for astronomical data to help in studying celestial navigation. While trying to track down a source of errors in my sextant reading or sight reductions I noticed that the local hour angle (shown HA on Stellarium's ephemera) of Venus varied if I changed the latitude of my location whilst keeping time constant.

Can anyone explain this. I thought the HA would only be a function of time, longitude, and the position of Venus (RA, Dec). Why would my moving north along my meridian affect the HA of a body? Aren't both my meridian and Venus' fixed (time is stopped), so the angle between them wouldn't change?

I noticed that it changed systematically. For the date and meridian in question (16/5/2020; 21:30:00 0° Long.) it varied from 6h 47m 41.86s at both the N and S poles, to 6h 47m 43.78s at the Equator. delta=1.92s

I know it's only a tiny amount, but I would like to understand what the principle behind it is. Everything I found on Google seemed to suggest it shouldn't change. I wondered if it was something to do with parallax changing as I changed position.

Thanks for any help.

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  • $\begingroup$ If you literally tried 90 degrees latitude, the hour angle is undefined in reality, but perhaps it can be calculated mathematically. To avoid a possible issue, what are the results at 80 latitude? $\endgroup$ – JohnHoltz May 17 at 15:33
  • $\begingroup$ Hi, thanks for answering. At 80° both North and South HA = 6h 47m 42.19s $\endgroup$ – richTourist May 17 at 15:41
  • $\begingroup$ You may be correct that the calculation is using the topocentric position (parallax) instead of the geocentric position. However, Venus is currently near 27 degrees declination, so I would expect a slight difference between N and S pole. I would need to pull out a book to confirm that. Someone may provide the "real" answer before I get to that. $\endgroup$ – JohnHoltz May 17 at 15:52
  • $\begingroup$ I can't see why it should make a difference, though. I thought the hour angle was measured between two meridians, not from the observer's point of view. wikipedia: The hour angle of a point is the angle between two planes: one containing Earth's axis and the zenith (the meridian plane), and the other containing Earth's axis and the given point (the hour circle passing through the point). $\endgroup$ – richTourist May 17 at 16:09
  • $\begingroup$ The hour angle is the difference between two right ascension, and the right ascension of Venus changes based on your location due to parallax. The difference would be small, but 2 seconds HA given by Stellarium is also small! $\endgroup$ – JohnHoltz May 17 at 17:11
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I do not have Stellarium, so I cannot confirm what is causing it with 100% certainty. But by using JPL's Horizons website, I can confirm that the position on the Earth's surface changes the apparent Right Ascension (R.A.) and Declination (DEC) of Venus. The following output is for an observer at 80 degrees W longitude and the latitude listed. The time was chosen so that Venus was approximately 7 hours east of the meridian; that is, the hour angle was approximately 7 hours.

Date__(UT)__HR:MN R.A.__(a-apparent)__DEC 2020-May-17 01:00 05 22 07.26 +27 00 24.9 Equator 2020-May-17 01:00 05 22 09.23 +27 00 01.6 North Pole 2020-May-17 01:00 05 22 09.23 +27 00 48.4 South Pole

These results show exactly what you were noticing in Stellarium:

  • The R.A. of Venus changes by approximately 2 seconds from the equator to the poles.
  • The change is the same going to the North or South pole. I thought the values would not be the same because Venus is north of the equator, but the shift is identical in R.A. for those two locations. (Note that the shift in DEC is not the same.)

Observing from the Earth's surface (topocentric position) is important for the Moon if you are looking for occultations or close conjunctions or precise hour angle, but not as important for other objects which are much farther away. Stellarium probably has a setting to change the calculation from topocentric to geocentric, in which case the hour angle discrepancy will disappear.

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  • $\begingroup$ That's great, thanks. I found the setting on Stellarium to set topocentric/planetocentric coordinates, and the discrepancy has gone. Now I need to study the concept of HA a bit more because I thought it was independent of point of view; I thought it was just to do with the meridian of the observer and that of the body. $\endgroup$ – richTourist May 17 at 19:02

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