Calculation of Right Ascension and Declination

The real-time position of any celestial body can be calculated using some parameters called Orbital Elements.

Nov 7, 2016

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Code snippet #4

text

1        Days to beginning of month
2
3        Month   Normal year    Leap year
4        Jan         0             0
5        Feb        31            31
6        Mar        59            60
7        Apr        90            91
8        May       120           121
9        Jun       151           152
10        Jul       181           182
11        Aug       212           213
12        Sep       243           244
13        Oct       273           274
14        Nov       304           305
15        Dec       334           335
16
17        Days since J2000 to beginning of each year
18
19                  Days
20        1999     -366.5
21        2000       -1.5
22        2001      364.5
23        2002      729.5
24        2003     1094.5
25        2004     1459.5
26        2005     1825.5
27Similarly,
28        2013     4747.5
29        2016     5842.5

        Days to beginning of month

        Month   Normal year    Leap year
        Jan         0             0
        Feb        31            31
        Mar        59            60
        Apr        90            91
        May       120           121
        Jun       151           152
        Jul       181           182
        Aug       212           213
        Sep       243           244
        Oct       273           274
        Nov       304           305
        Dec       334           335

        Days since J2000 to beginning of each year

                  Days
        1999     -366.5
        2000       -1.5
        2001      364.5
        2002      729.5
        2003     1094.5
        2004     1459.5
        2005     1825.5
Similarly,
        2013     4747.5
        2016     5842.5

Code snippet #21

text

1    Xq = X'
2    Yq = Y' * cos(ec) - Z' * sin(ec)
3    Zq = Y' * sin(ec)  + Z' * cos(ec)
4
5    Xq are the equatorial coordinates
6    X' are the geocentric  ecliptic coordinates      
7    ec is the obliquity of the ecliptic 
8

    Xq = X'
    Yq = Y' * cos(ec) - Z' * sin(ec)
    Zq = Y' * sin(ec)  + Z' * cos(ec)

    Xq are the equatorial coordinates
    X' are the geocentric  ecliptic coordinates      
    ec is the obliquity of the ecliptic

Code snippet #11

text

1v = M + 180/pi * [ (2 * e - e^3/4) * sin(M) + 5/4 * e^2 * sin(2*M)
2                             + 13/12 * e^3 * sin(3*M)........ n terms ]
3
4         v is true anomaly
5         M is mean anomaly
6         e is eccentricity
7         pi is 3.14159...
8
9         e^3 means the third power of e. Note how  the third
10         power is involved the first term as well as the last.
11
12
13A  more expanded series can give a better result so this is what i have used 
14in  my code :
15
16
17 v = m + (2 * e - 0.25 *pow(e,3) + 5/96 * pow(e,5)) * sin(m)  +
18 (1.25 * pow(e,2) - 11/24 * pow(e,4)) * sin(2*m) + 
19(13/12 * pow(e,3) -  43/64 * pow(e,5)) * sin(3*m) + 
20103/96 * pow(e,4) * sin(4*m) + 1097/960 * pow(e,5)  * sin(5*m);
21
22
23

v = M + 180/pi * [ (2 * e - e^3/4) * sin(M) + 5/4 * e^2 * sin(2*M)
                             + 13/12 * e^3 * sin(3*M)........ n terms ]

         v is true anomaly
         M is mean anomaly
         e is eccentricity
         pi is 3.14159...

         e^3 means the third power of e. Note how  the third
         power is involved the first term as well as the last.


A  more expanded series can give a better result so this is what i have used 
in  my code :


 v = m + (2 * e - 0.25 *pow(e,3) + 5/96 * pow(e,5)) * sin(m)  +
 (1.25 * pow(e,2) - 11/24 * pow(e,4)) * sin(2*m) + 
(13/12 * pow(e,3) -  43/64 * pow(e,5)) * sin(3*m) + 
103/96 * pow(e,4) * sin(4*m) + 1097/960 * pow(e,5)  * sin(5*m);

Code snippet #15

text

1 
2    X = r * [cos(o) * cos(v + p - o) - sin(o) * sin(v + p - o) *
3     cos(i)]
4    Y = r * [sin(o) * cos(v + p - o) + cos(o) * sin(v + p - o) *
5     cos(i)]
6    Z = r * [sin(v + p - o) * sin(i)]
7
8    r is radius vector
9     v is true anomaly
10    o is longitude of ascending node
11    p is longitude   of perihelion
12    i is inclination of plane of orbit
13
14    the quantity   v + p - o is the angle of the planet measured
15    in the plane of the orbit from   the ascending node
16

 
    X = r * [cos(o) * cos(v + p - o) - sin(o) * sin(v + p - o) *
     cos(i)]
    Y = r * [sin(o) * cos(v + p - o) + cos(o) * sin(v + p - o) *
     cos(i)]
    Z = r * [sin(v + p - o) * sin(i)]

    r is radius vector
     v is true anomaly
    o is longitude of ascending node
    p is longitude   of perihelion
    i is inclination of plane of orbit

    the quantity   v + p - o is the angle of the planet measured
    in the plane of the orbit from   the ascending node

Code snippet #23

text

1    alpha = arctan(Yq/Xq)
2     
3    If Xq is negative then add 180  degrees to alpha  
4    If Xq is positive and Yq is negative then add 360 degrees  to
5    alpha
6
7    alpha is usually expressed in hours, so divide by 15
8
9    delta = arctan( Zq / SQRT(Xq^2 + Yq^2)) 
10
11    distance = SQRT( Xq^2 +  Yq^2 + Zq^2)          
12

    alpha = arctan(Yq/Xq)
     
    If Xq is negative then add 180  degrees to alpha  
    If Xq is positive and Yq is negative then add 360 degrees  to
    alpha

    alpha is usually expressed in hours, so divide by 15

    delta = arctan( Zq / SQRT(Xq^2 + Yq^2)) 

    distance = SQRT( Xq^2 +  Yq^2 + Zq^2)

Code snippet #12

text

1    M = 232.910644 degrees or 4.065057601 radians
2    e = 0.093346
3Therefore,
4     v = 224.9688989 degrees  or 3.926448  radians
5
6Note: In my code I have   done all the calculations in  Radians

    M = 232.910644 degrees or 4.065057601 radians
    e = 0.093346
Therefore,
     v = 224.9688989 degrees  or 3.926448  radians

Note: In my code I have   done all the calculations in  Radians

Code snippet #14

text

1a = 1.523762
2e = 0.093346
3v =224.9688989
4
5r = 1.523762 * (1   - 0.093346^2) / [ 1 + 0.093346 * cos (224.9688989) ]
6  = 1.617293 a.u

a = 1.523762
e = 0.093346
v =224.9688989

r = 1.523762 * (1   - 0.093346^2) / [ 1 + 0.093346 * cos (224.9688989) ]
  = 1.617293 a.u

Code snippet #10

text

1        n = 0.523998
2        d = 928
3        L = 82.9625
4        p  = 336.322
5
6        M = 0.523998 * 928 + 82.9625 - 336.322
7          = 232.910644
8

        n = 0.523998
        d = 928
        L = 82.9625
        p  = 336.322

        M = 0.523998 * 928 + 82.9625 - 336.322
          = 232.910644

Code snippet #13

text

1      r = a * (1 - e^2) / [1 + e * cos(v)]
2  
3          a is the  semi-major axis
4          e is the eccentricity
5          v is the true anomaly
6
7          the radius vector r will be in the same units as a
8          a.u. in  this case.
9

      r = a * (1 - e^2) / [1 + e * cos(v)]
  
          a is the  semi-major axis
          e is the eccentricity
          v is the true anomaly

          the radius vector r will be in the same units as a
          a.u. in  this case.

Code snippet #16

text

1    r = 1.617293
2    v = 224.9688989
3    o = 49.668
4    p = 336.322
5    i = 1.8496
6    v + p - o = 511.6228989 - 360 = 151.6228989
7 
8    and  I get the following rectangular coordinates;
9
10    X  = -1.506606
11    Y  = -0.587503
12    Z  =  0.024809
13
14    SQRT(X^2 + Y^2 + Z^2) should be same  as r
15

    r = 1.617293
    v = 224.9688989
    o = 49.668
    p = 336.322
    i = 1.8496
    v + p - o = 511.6228989 - 360 = 151.6228989
 
    and  I get the following rectangular coordinates;

    X  = -1.506606
    Y  = -0.587503
    Z  =  0.024809

    SQRT(X^2 + Y^2 + Z^2) should be same  as r

Code snippet #4

text

1        Days to beginning of month
2
3        Month   Normal year     Leap year
4        Jan         0             0
5        Feb        31            31
6         Mar        59            60
7        Apr        90            91
8        May        120           121
9        Jun       151           152
10        Jul       181            182
11        Aug       212           213
12        Sep       243           244
13         Oct       273           274
14        Nov       304           305
15        Dec        334           335
16
17        Days since J2000 to beginning of each year
18
19                   Days
20        1999     -366.5
21        2000       -1.5
22         2001      364.5
23        2002      729.5
24        2003     1094.5
25         2004     1459.5
26        2005     1825.5
27Similarly,
28        2013      4747.5
29        2016     5842.5

        Days to beginning of month

        Month   Normal year     Leap year
        Jan         0             0
        Feb        31            31
         Mar        59            60
        Apr        90            91
        May        120           121
        Jun       151           152
        Jul       181            182
        Aug       212           213
        Sep       243           244
         Oct       273           274
        Nov       304           305
        Dec        334           335

        Days since J2000 to beginning of each year

                   Days
        1999     -366.5
        2000       -1.5
         2001      364.5
        2002      729.5
        2003     1094.5
         2004     1459.5
        2005     1825.5
Similarly,
        2013      4747.5
        2016     5842.5

Code snippet #9

text

1        M = n * d + L - p 
2
3        n is daily motion
4        d  is the number of days since the date of the elements
5        L is the mean longitude
6        p is the longitude of perihelion 
7
8        M should be in range 0  to 360 degrees, add or subtract
9          multiples of 360 to bring M into this  range.
10

        M = n * d + L - p 

        n is daily motion
        d  is the number of days since the date of the elements
        L is the mean longitude
        p is the longitude of perihelion 

        M should be in range 0  to 360 degrees, add or subtract
          multiples of 360 to bring M into this  range.

Alitude-Azimuth Calculator

It is a cpp code that calculates Ra and Declination of all the nine planets with proper data and time as an input and with the Location input it give azimuth and altitude.

no description/ Read More

Latest commit to the master branch on Invalid date

Download as a zip

Code snippet #1

text

1JD = 2450680.5
2Equinox and mean ecliptic of J2000.0
3
4       Earth           Mars
5
6i     0.0       1.8496   
7o     0.0       49.668
8p     103.147    336.322
9a     1.0000    1.523762
10n     0.985611  0.523998
11e     0.016679   0.093346
12L     324.5489  82.9625
13
14The values for the other planets can   be found in
15the C program below.
16

JD = 2450680.5
Equinox and mean ecliptic of J2000.0

       Earth           Mars

i     0.0       1.8496   
o     0.0       49.668
p     103.147    336.322
a     1.0000    1.523762
n     0.985611  0.523998
e     0.016679   0.093346
L     324.5489  82.9625

The values for the other planets can   be found in
the C program below.

Code snippet #17

text

1   Xe = r * cos(v + p)
2   Ye = r * sin(v + p)
3   Ze = 0
4
5    r is radius vector of Earth
6   v is true anomaly for Earth
7   p is longitude   of perihelion for Earth
8

   Xe = r * cos(v + p)
   Ye = r * sin(v + p)
   Ze = 0

    r is radius vector of Earth
   v is true anomaly for Earth
   p is longitude   of perihelion for Earth

Code snippet #2

text

1Elements
2
3i - inclination
4o - longitude of ascending node at  date of elements 
5p - longitude of perihelion at date of elements 
6a - mean  distance (au)
7n - daily motion 
8e - eccentricity of orbit
9l - mean longitude  at date of elements
10
11Calculated quantities
12
13M - mean anomaly (degrees)
14V  - True anomaly (degrees)
15r - radius vector (au) referred to current coordinate  origin
16X - recangular coordinate (au)
17Y - recangular coordinate (au)
18Z  - recangular coordinate (au)
19alpha - right ascension (hours or decimal degrees  according to
20context)
21delta - declination (decimal degrees)
22

Elements

i - inclination
o - longitude of ascending node at  date of elements 
p - longitude of perihelion at date of elements 
a - mean  distance (au)
n - daily motion 
e - eccentricity of orbit
l - mean longitude  at date of elements

Calculated quantities

M - mean anomaly (degrees)
V  - True anomaly (degrees)
r - radius vector (au) referred to current coordinate  origin
X - recangular coordinate (au)
Y - recangular coordinate (au)
Z  - recangular coordinate (au)
alpha - right ascension (hours or decimal degrees  according to
context)
delta - declination (decimal degrees)

Code snippet #24

text

1  (right ascension) alpha = 15.440000 hrs
2          
3  (declination)  delta = -18.250000 degs
4         
5   distance = 1.077971278 a.u.      
6

  (right ascension) alpha = 15.440000 hrs
          
  (declination)  delta = -18.250000 degs
         
   distance = 1.077971278 a.u.

Code snippet #24

text

1  (right ascension) alpha = 15.440000 hrs
2          
3  (declination)
4  delta = -18.250000 degs
5         
6   distance = 1.077971278 a.u.      
7

  (right ascension) alpha = 15.440000 hrs
          
  (declination)
  delta = -18.250000 degs
         
   distance = 1.077971278 a.u.

Code snippet #13

text

1      r = a * (1 - e^2) / [1 + e * cos(v)]
2  
3          a is the
4  semi-major axis
5          e is the eccentricity
6          v is the true anomaly
7
8
9          the radius vector r will be in the same units as a
10          a.u. in
11  this case.
12

      r = a * (1 - e^2) / [1 + e * cos(v)]
  
          a is the
  semi-major axis
          e is the eccentricity
          v is the true anomaly


          the radius vector r will be in the same units as a
          a.u. in
  this case.

Code snippet #12

text

1    M = 232.910644 degrees or 4.065057601 radians
2    e = 0.093346
3Therefore,
4    v = 224.9688989 degrees  or 3.926448  radians
5
6Note: In my code I have  done all the calculations in  Radians

    M = 232.910644 degrees or 4.065057601 radians
    e = 0.093346
Therefore,
    v = 224.9688989 degrees  or 3.926448  radians

Note: In my code I have  done all the calculations in  Radians

Code snippet #14

text

1a = 1.523762
2e = 0.093346
3v =224.9688989
4
5r = 1.523762 * (1  - 0.093346^2) / [ 1 + 0.093346 * cos (224.9688989) ]
6  = 1.617293 a.u

a = 1.523762
e = 0.093346
v =224.9688989

r = 1.523762 * (1  - 0.093346^2) / [ 1 + 0.093346 * cos (224.9688989) ]
  = 1.617293 a.u

Alitude-Azimuth Calculator

It is a cpp code that calculates Ra and Declination of all the nine planets with proper data and time as an input and with the Location input it give azimuth and altitude.

no description/ Read More

Latest commit to the master branch on Invalid date

Download as a zip

Code snippet #17

text

1   Xe = r * cos(v + p)
2   Ye = r * sin(v + p)
3   Ze = 0
4
5   r is radius vector of Earth
6   v is true anomaly for Earth
7   p is longitude  of perihelion for Earth
8

   Xe = r * cos(v + p)
   Ye = r * sin(v + p)
   Ze = 0

   r is radius vector of Earth
   v is true anomaly for Earth
   p is longitude  of perihelion for Earth

Code snippet #1

text

1JD = 2450680.5
2Equinox and mean ecliptic of J2000.0
3
4       Earth          Mars
5
6i     0.0       1.8496   
7o     0.0       49.668
8p     103.147   336.322
9a     1.0000    1.523762
10n     0.985611  0.523998
11e     0.016679  0.093346
12L     324.5489  82.9625
13
14The values for the other planets can  be found in
15the C program below.
16

JD = 2450680.5
Equinox and mean ecliptic of J2000.0

       Earth          Mars

i     0.0       1.8496   
o     0.0       49.668
p     103.147   336.322
a     1.0000    1.523762
n     0.985611  0.523998
e     0.016679  0.093346
L     324.5489  82.9625

The values for the other planets can  be found in
the C program below.

Code snippet #21

text

1    Xq = X'
2    Yq = Y' * cos(ec) - Z' * sin(ec)
3    Zq = Y' * sin(ec)
4  + Z' * cos(ec)
5
6    Xq are the equatorial coordinates
7    X' are the geocentric
8  ecliptic coordinates      
9    ec is the obliquity of the ecliptic 
10

    Xq = X'
    Yq = Y' * cos(ec) - Z' * sin(ec)
    Zq = Y' * sin(ec)
  + Z' * cos(ec)

    Xq are the equatorial coordinates
    X' are the geocentric
  ecliptic coordinates      
    ec is the obliquity of the ecliptic

Code snippet #23

text

1    alpha = arctan(Yq/Xq)
2     
3    If Xq is negative then add 180
4  degrees to alpha  
5    If Xq is positive and Yq is negative then add 360 degrees
6  to
7    alpha
8
9    alpha is usually expressed in hours, so divide by 15
10
11
12    delta = arctan( Zq / SQRT(Xq^2 + Yq^2)) 
13
14    distance = SQRT( Xq^2 +
15  Yq^2 + Zq^2)          
16

    alpha = arctan(Yq/Xq)
     
    If Xq is negative then add 180
  degrees to alpha  
    If Xq is positive and Yq is negative then add 360 degrees
  to
    alpha

    alpha is usually expressed in hours, so divide by 15


    delta = arctan( Zq / SQRT(Xq^2 + Yq^2)) 

    distance = SQRT( Xq^2 +
  Yq^2 + Zq^2)

Code snippet #15

text

1 
2    X = r * [cos(o) * cos(v + p - o) - sin(o) * sin(v + p - o) *
3    cos(i)]
4    Y = r * [sin(o) * cos(v + p - o) + cos(o) * sin(v + p - o) *
5    cos(i)]
6    Z = r * [sin(v + p - o) * sin(i)]
7
8    r is radius vector
9    v is true anomaly
10    o is longitude of ascending node
11    p is longitude  of perihelion
12    i is inclination of plane of orbit
13
14    the quantity  v + p - o is the angle of the planet measured
15    in the plane of the orbit from  the ascending node
16

 
    X = r * [cos(o) * cos(v + p - o) - sin(o) * sin(v + p - o) *
    cos(i)]
    Y = r * [sin(o) * cos(v + p - o) + cos(o) * sin(v + p - o) *
    cos(i)]
    Z = r * [sin(v + p - o) * sin(i)]

    r is radius vector
    v is true anomaly
    o is longitude of ascending node
    p is longitude  of perihelion
    i is inclination of plane of orbit

    the quantity  v + p - o is the angle of the planet measured
    in the plane of the orbit from  the ascending node

Code snippet #9

text

1        M = n * d + L - p 
2
3        n is daily motion
4        d
5  is the number of days since the date of the elements
6        L is the mean longitude
7
8        p is the longitude of perihelion 
9
10        M should be in range 0
11  to 360 degrees, add or subtract
12          multiples of 360 to bring M into this
13  range.
14

        M = n * d + L - p 

        n is daily motion
        d
  is the number of days since the date of the elements
        L is the mean longitude

        p is the longitude of perihelion 

        M should be in range 0
  to 360 degrees, add or subtract
          multiples of 360 to bring M into this
  range.

Code snippet #16

text

1    r = 1.617293
2    v = 224.9688989
3    o = 49.668
4    p = 336.322
5
6    i = 1.8496
7    v + p - o = 511.6228989 - 360 = 151.6228989
8 
9    and
10  I get the following rectangular coordinates;
11
12    X  = -1.506606
13    Y
14  = -0.587503
15    Z  =  0.024809
16
17    SQRT(X^2 + Y^2 + Z^2) should be same
18  as r
19

    r = 1.617293
    v = 224.9688989
    o = 49.668
    p = 336.322

    i = 1.8496
    v + p - o = 511.6228989 - 360 = 151.6228989
 
    and
  I get the following rectangular coordinates;

    X  = -1.506606
    Y
  = -0.587503
    Z  =  0.024809

    SQRT(X^2 + Y^2 + Z^2) should be same
  as r

Code snippet #10

text

1        n = 0.523998
2        d = 928
3        L = 82.9625
4        p
5  = 336.322
6
7        M = 0.523998 * 928 + 82.9625 - 336.322
8          = 232.910644
9

        n = 0.523998
        d = 928
        L = 82.9625
        p
  = 336.322

        M = 0.523998 * 928 + 82.9625 - 336.322
          = 232.910644

Code snippet #2

text

1Elements
2
3i - inclination
4o - longitude of ascending node at
5  date of elements 
6p - longitude of perihelion at date of elements 
7a - mean
8  distance (au)
9n - daily motion 
10e - eccentricity of orbit
11l - mean longitude
12  at date of elements
13
14Calculated quantities
15
16M - mean anomaly (degrees)
17V
18  - True anomaly (degrees)
19r - radius vector (au) referred to current coordinate
20  origin
21X - recangular coordinate (au)
22Y - recangular coordinate (au)
23Z
24  - recangular coordinate (au)
25alpha - right ascension (hours or decimal degrees
26  according to
27context)
28delta - declination (decimal degrees)
29

Elements

i - inclination
o - longitude of ascending node at
  date of elements 
p - longitude of perihelion at date of elements 
a - mean
  distance (au)
n - daily motion 
e - eccentricity of orbit
l - mean longitude
  at date of elements

Calculated quantities

M - mean anomaly (degrees)
V
  - True anomaly (degrees)
r - radius vector (au) referred to current coordinate
  origin
X - recangular coordinate (au)
Y - recangular coordinate (au)
Z
  - recangular coordinate (au)
alpha - right ascension (hours or decimal degrees
  according to
context)
delta - declination (decimal degrees)

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