More Useful Formulas for Amateur SETI

The following is derived from a number of sources including:

Location of the Sun on the Ecliptic

  1. Subtract 2447892.5 from the Julian Date to get D
  2. Multiply D by 0.017202792 to get N
  3. Add N to 0.535575323 to get M
  4. Add or subtract 6.2831853 to M to get a value between 0 and 6.2831853
  5. Solve E-0.016713*sin(E)=M for E
  6. Solve tan(V/2)=1.016855*tan(E/2) for V
  7. Multiply V by 57.295779 and add 282.768422 to get W
  8. Add or subtract 360 to get a value between 0 and 360
  9. This is the Ecliptic Longitude. The Ecliptic Latitude is 0.

Ecliptic Coordinates given Right Ascension(RA) and Declination(DE)

  1. Convert Declination(DE) to degrees
  2. Convert Right Ascension(RA) to Hours then multiply by 15 to convert to degrees.
  3. Compute sin(LA)=0.917464*sin(DE)-0.397819*sin(RA)*cos(DE).
  4. Take the inverse sine of sin(LA).
  5. This is the Ecliptic Latitude.
  6. Compute y=0.917464*sin(RA)+0.397819*tan(DE).
  7. Compute x=cos(RA).
  8. take the inverse tan of (y/x) and call it LO.
  9. If LO is negative add 180 degrees.
  10. If x or y is negative add 180 degrees to LO.
  11. LO is the Ecliptic Longitude.

Doppler Shift do to Earth's orbit around the Sun relative to a given Ecliptic Latitude(LAE) and Longitude(LOE).

Fd=K*Fo*cos(LAE)*sin(LOS-LOE)

Notes:
  1. Fd is the doppler due to the earth's orbit of the sun.
  2. Fo is the frequency of interest.
  3. LOS is the Ecliptic Longitude of the Sun.
  4. LOE is the given Ecliptic Longitude.
  5. LAE is the given Ecliptic Latitude.
  6. K=v/c

    7.  
  7. c is the speed of light (3 x 108 meters/second)
  8. v is the speed the earth orbits the sun (29800 meters/second)
  9. K is 9.9333 x 10-5

    10.  

Doppler Equation

Fd=Fo*(1-v/c)

Notes:
  1. Fd is the doppler shifted frequency.
  2. Fo is the frequency transmitted by the source.
  3. v is the relative velocity in meters per second.
  4. v is positive moving away the source.
  5. c is the speed of light (3 x 108 meters/second)

Relativistic Doppler Equation

Fd=Fo*(1-(v/c)2)1/2/ (1-((v/c)*cos(A)))

  1. Fd is the doppler shifted frequency.
  2. Fo is the frequency transmitted by the source.
  3. v is the relative velocity in meters per second.
  4. A is the angle the observer is moving at relative to the source.
  5. A is 0 moving toward the source and 180 moving away.
  6. c is the speed of light (3 x 108 meters/second)