# Finding Hour Angle

1. Jan 22, 2010

### dacruick

Hi. I want to be able to find the hour angle at each day of the year. Wikipedia sent me on a wild goose chase of Julian Day Numbers and some useless formulas that place solar noon at the same time every day. For those who may be used to different terms, hour angle is the amount of time (in degrees) that a position on earth is away from solar noon. Ideally I would like to be able to find the hour angle, but finding solar noon will also be acceptable as well, as I can find the hour angle from that.

One site suggested that my hour angle is equal to the local sidereal time subtract the right ascension. The problem with this is I don't know how to calculate sidereal time, or right ascension. If anyone could shed some light for me(no pun intended), it would be much appreciated

2. Jan 22, 2010

### Borg

The Wikipedia article on http://en.wikipedia.org/wiki/Sidereal_time" [Broken] should help.

Also, this site can calculate it for you based on your location - http://tycho.usno.navy.mil/sidereal.html" [Broken].

Last edited by a moderator: May 4, 2017
3. Jan 22, 2010

### Yeti08

Find solar time:

$$Solar\ Time = Standar\ Time + 4\left(L_{st}-L_{loc}\right)+E$$

where Lst is the standard meridian for the local time zone, Lloc is the longitude of the location, and E is defined by:

$$E=229.2\left(0.000075+0.001868\ cosB-0.032077\ sinB-0.014615\ cos2B-0.04089\ sin2B\right)$$

where B is

$$B=\left(n-1\right)\frac{360}{365}$$

and n is the day of the year.

To get hour angle from time, multiply hours from noon times 15 degrees per hour (negative for before noon, positive for after). For example if solar time is 10:30 am, this is 1.5 hours before noon, so the hour angle would be -22.5 degrees.

4. Jan 22, 2010

### dacruick

when you say Lst is the standard meridian for the local time zone, what does that mean.

5. Jan 22, 2010

### Yeti08

It is the longitude that corresponds with your time zone. Examples in the US would be Eastern - 75oW, Central - 90oW, Mountain - 105oW, and Pacific - 120oW.

6. Jan 22, 2010

### dacruick

I though Lloc was the longitude corresponding to my time zone.

7. Jan 22, 2010

### Bob S

If you photograph the position of the Sun at noon (not daylight savings time) every day for a year, you will get an analemma in the sky. See

http://www.1worldglobes.com/analemma.htm

The analemma used to be shown on world globes, usually in the Pacific Ocean, west of South America.

Bob S

8. Jan 22, 2010

### Yeti08

That's your actual longitude for the location. That difference in that equation is to correct for your actual location - while your "normal" time will stay the same while traveling across several degrees of longitude, your solar time will change.

9. Jan 22, 2010

### dacruick

I apologize, I don't think I understand what you are saying. I live in Toronto, so my Lloc would be approximately 79 degrees. But you are saying my Lst will be 75 degrees because I'm in the eastern time zone? So my difference will be -4 degrees correct?

10. Jan 22, 2010

### dacruick

Furthermore, I am doing this to calculate solar time, but I do not know what solar time is. Is the solar time equal to solar noon?

11. Jan 22, 2010

### Yeti08

Yes, that is correct.

For solar time, noon corresponds to solar noon. I stated in my first post how to convert solar time to hour angle.

12. Jan 22, 2010

### dacruick

So my standard time must be measured in degrees as well?

13. Jan 22, 2010

### Yeti08

Yes, I should have said before that all the equations I listed use degrees, not radians.