# Hour angle for rises and sets

1. Mar 10, 2012

### JeffOCA

Hi,

When you have to calculate the rising or setting time of a celestial body, you have to handle with hour angle and sidereal time.

Sidereal time for the rising is given by T = alpha - H and by T = alpha + H for the setting (alpha = right ascension). Why - H in one hand, and + H on the other hand ?

Maybe because :
1/ hour angle H is computed from east toward west, so H=0 when crossing meridian, in south direction. Before crossing meridian, H = - $\left|H \right|$ so it's negative and it is positive after meridian is crossed H = $\left|H \right|$
2/ we can say that rising and setting are symmetric with respect to meridian transit, which occurs when T = alpha (i.e H=0)... so -H for rising and +H for setting

Which explanation is better ? If none of them, could you explain the right way ?

Thnaks

2. Mar 12, 2012

### Philosophaie

I think you are confusing T with LMST(Local Mean Sidreal Time). The equation goes:

H = LMST - alpha

where H is the Hour Angle and alpha is Right Ascension. Hour Angle does not change signs.

LMST however is made up of time.

LMST = GMST0 + (Hour - timezone - dst + Minute/60)*15 + longitude(East+)

where dst is daylight savings time (1 for on and 0 for off)

3. Mar 14, 2012

### JeffOCA

Hi,

I knew T was LMST, but I don't understand why local mean sidereal time for the rising is given by LMST = alpha - H and by LMST = alpha + H for the setting (where alpha = right ascension). I have some ideas (see my precedent post) but I'm not sure...

Thanks

4. Mar 14, 2012

### Philosophaie

Look more at this equation:

LMST = GMST0 + (Hour - timezone - dst + Minute/60)*15 + longitude(East+)

Hour is in 24hour Time.

5. Mar 14, 2012

### JeffOCA

Ok. I looked at it. So ?

6. Mar 22, 2012

### JeffOCA

Anyone ?

7. Mar 22, 2012

### Philosophaie

The equation is always:

Code (Text):
LMST = alpha - HA
Just the time changes.

JD = 367 * yr - Int(7 * (yr + Int((mo + 9) / 12)) / 4) + Int(275 * mo / 9) + dy + 1721013.5
d = (JDT - 2451545)

GMST0 = 18.697374558 + 24.0657098244191 * d; in hours
GMST0*15; in degrees

8. Mar 25, 2012

### JeffOCA

Hi Philosophaie, hi everyone

For setting, the formula is also : T = alpha - H or, if you prefer : LMST = alpha - HA ? That's it ?
Can you tell me what do you mean with "just time changes" ? JD = julian day ? Why giving me the formula for Greenwich Mean sidereal time ?

9. Mar 27, 2012

### Philosophaie

JD stands for Julian Date. Julian Date is the interval of time in days and fractions of a day since 1-1-4713 BC at Greenwich Noon. This Julian refers to Julius Caesar, who introduced the Julian calendar in 46 BC. This calendar has a regular year of 365 days divided into 12 months. A leap day is added to February every four years. The Julian year is, therefore, on average 365.25 days long.