[Author Prev][Author Next][Thread Prev][Thread Next][Author Index][Thread Index]
Re: [ATM] Converting ALT and AZ to RA and DEC
I took me a while to find it and make it work.
In the Transform of Coordinates in Astronomical Algorthms uses:
L Latitude of Observation
h Altitude above Horizon + if above, - if below
A Azimuth measured clockwise from South. if from the North add 180deg
>From these are computed the:
D Declination and the
H Local Hour angle in radians.
You will also need to know your Local Sidereal Time to get the Right
Ascencion from.
tan(H) = sin(A)/(cos(A)*sin(L)+tan(h)*cos(L))
arctan(tan(H)) will an hour angle in radians that will need to be corrected
for quadrant issues.
convert to degrees and correct for quadrant issue:
if A from south >180 then H - 180deg =H
now convert to hour angle at 15 degrees per hour H/15= H in decimal hours.
You could use the atan2 function as in Excel atan2(x,y) to get quadrant
correct.
so now you would have:
atan2(cos(A)*sin(L)+tan(h)*cos(L),sin(A))
to this you would do the divide by 15 to get the Local Hour Angle in decimal
hour format.
Right Ascencion is Local Sidereal Time minus the Local Hour Angle
RA=LST-LHA
if RA >24hours then RA=RA-24hours
sin(D)=sin(L)*sin(h)-cos(L)*cos(h)*cos(A)
declination D=asin(sin(D))
Example data from MICA for Capella at my home in Klamath Falls, Or.
the following is a cut and paste headache:
Capella
Date Time Zenith Azimuth
(UT1) Distance (E of N)
h m s ° °
2007 Dec 05 22:57:31.0 85.64911 25.14596
Date Time Local Hour Declination
(UT1) Angle
h m s h °
2007 Dec 05 22:57:31.0 - 9.493909 + 46.00763
Date Time Right Ascension Declination
(UT1)
h m s h °
2007 Dec 05 22:57:31.0 5.2886255 + 46.007630
SIDEREAL TIME
Greenwich Local
Equation
Date Time Sidereal Time Sidereal Time of
the
(UT1) Mean App. Mean App.
Equinoxes
h m s h m s s h m s s s
2007 Dec 05 22:57:31.0 3 54 57.3524 57.7804 19 47 40.5524 40.9804
+0.4280
Altitude h is 90 deg - the from Zenith Distance 90deg- 85.64911d=4.35089 deg
or 0.075937356 radians
Azimuth is from the North so add 180 deg 25.14596deg+ 180 = 205.14596deg or
3.580472449 radians
Latitude used is: north 42d13m12s so 42+13/60+12/3600=42.22deg or 0.73687801
radians
Using The Local Mean. Sidereal Time 19h 47m 40.5524s so
19+47/60+40.5524/3600 = 19.79472hr
h=0.075937356 radians
A=3.580472449 radians
L=0.73687801 radians
LST= 19.79472 hr
tan(H) = sin(A)/(cos(A)*sin(L)+tan(h)*cos(L))
TAN(H)=SIN(3.580472449)/(COS(3.580472449)*SIN(0.73687801)+TAN(0.075937356)*COS(0.73687801))
TAN(H)= 0.769863756
ATAN(TAN(H))= 0.65609318radians or 37.5913702deg
since A>180 then 37.5913702 deg-180 deg = -142.4086298 deg
-142.4086298deg/15 deg per hr = -9.4939086 Local Hour Angle
ATAN2 Method:
atan2(cos(A)*sin(L)+tan(h)*cos(L),sin(A))
ATAN2(COS(3.580472449)*SIN(0.73687801)+TAN(0.075937356)*COS(0.73687801),SIN(3.580472449))=
-2.485499473
radians or -142.4086298deg
-142.4086298deg/15 deg per hr = -9.493908653 Local Hour Angle
LST-LHA=RA
19.79472-(-9.493908653)= 29.28862543 hrs
if RA >24hours then RA=RA-24hours
29.28862543 hrs-24hr=5.288625431 hrs
RA=5.288625431 hrs
Close to MICA's 5.2886255 hrs
sin(D)=sin(L)*sin(h)-cos(L)*cos(h)*cos(A)
SIN(D)=(SIN(0.73687801)*SIN(0.075937356)-COS(0.73687801)*COS(0.075937356)*COS(3.580472449))
SIN(D)= 0.719432281
ASIN(SIN(D))= 0.802984596radians or 46.00762838deg
DEC=46.00762838 deg
Good match for MICA output
You may also want to look at:
http://star-www.st-and.ac.uk/%7Efv/webnotes/index.html
I hope this does more than confuse. Who knows what the email format will do
to this.
Virgil Johnson
Raider of the Lost Dark
----- Original Message -----
From: "G Gagne" <gagne51@clearwire.net>
To: "atm" <atm@atmlist.net>
Sent: Sunday, December 02, 2007 5:13 AM
Subject: [ATM] Converting ALT and AZ to RA and DEC
>I have programmed my telescope computer to convert RA and DEC to ALT and
> AZ for controlling the axes of my dob telescope. However, when manually
> slewing the telescope I often find interesting objects that I would
> like to track. What I need now are the reverse equations for RA and DEC
> of the new found object as a function of ALT and AZ derived from the
> encoders.
>
> Can anyone point me an appropriate reference?
> _______________________________________________
> ATM mailing list http://www.atmlist.net/
>
_______________________________________________
ATM mailing list http://www.atmlist.net/