# Doubt about hour angle

1. Apr 6, 2015

### Frank Einstein

Hi everybody, I was messing arround with the program stellarium; I decided to check the hour angle of the sun at 10 am on August 12; it was 19h 53 min; then I did the same for september 4th and it was 20h 0 min.
As far as I know it takes 23h 56 minutes to the sun to cross the same point in the sky, so the hour angle varies in about 4 minutes each day; but the hour angle only changes in seven minutes in twenty three days; can someone please tell me why that angle has variated only in seven minutes and not the 92 (23*4) it should have?

Thanks for your anwsers.

2. Apr 6, 2015

### Bandersnatch

Let's start here. The time you specified is for the sidereal day - the time needed for the Sun to get back to the same point in the sky with respect to the so-called fixed stars.
It is NOT the time needed for the Sun to get back to the same 'point' (hour angle) in the sky w/r to the Earth (e.g. cross the meridian). This time is the apparent solar day.
The apparent solar day is not constant in length, due to the Earth's axial tilt and orbital eccentricity. The two effects combine to net a variation that looks like this:

and it's what Stellarium is showing you.
If you take the mean of the apparent solar day, you'll get the mean solar day which is the 24 hours the length of day is defined as.

The 4 minute (-ish) difference between the sidereal day and the mean solar day that you were thinking about adds up to 1 day of difference over a year in very much the same way as the long hand of a clock meets the short hand only 11 times over a 12 hour period, or the protagonists of 'Around the world in 80 days' manage to 'save' a day. This is the effect that makes the Sun pass the signs of Zodiac over the year.
This has no bearing on how long it takes for the sun to get back to where it was on the sky, though.

See here:
http://en.wikipedia.org/wiki/Equation_of_time
for more on the graph you see above.

This wiki entry might be handy as well:
http://en.wikipedia.org/wiki/Solar_time

Last edited: Apr 6, 2015
3. Apr 6, 2015

### Frank Einstein

Then, does the seven minutes difference in the hour anglecomes from the differencie between the mean solar day and the actual one?

4. Apr 6, 2015

Yes.

5. Apr 6, 2015

### Frank Einstein

Thank you very much for your help. Very apreciated.

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