Useful Formulas for Amateur SETI

Questions - Comments eMail Me I will respond..

Critical measurements of horn and waveguide for this Argus station. From the feedhorn.xls spreadsheet available on the SETI League web site:

Cylindrical Waveguide Feedhorn analysis

Freq = 1.42 GHz 21.1 cm   5.9 In
Waveguide Dia. = 6 in  15.2 cm    
Lower Cutoff = 1.14 GHz  26.4 cm    
Upper Cutoff = 1.49 GHz  20.1 cm    
Guide Wavelength = 13.87 in  35.2 cm    
Probe placement = 3.47 in  8.8 cm   3.562
Feedhorn Length = 10.41 in 26.4 cm    
Zo = 629 ohms 1.67 vswr    
Choke Ring Depth = 4.16 in 10.6 cm    
Choke Ring Diameter = 14.32 in 36.4 cm    
Dish F/D Ratio = 0.4         (Valid range: 0.25 to 0.50)
Feedhorn Placement:           focal point of reflector falls inside lip of feedhorn by:
    1.46 in  3.7 cm  
Choke Ring Placement:            
            Distance from front of feed horn to back of choke ring, for:
Max. Gain (10 dB taper) 4.59 in 11.7 cm   4.5in
Min. Noise (15 dB taper) 4.10 in  10.4 cm    

Julian Date

The Julian date is the number of days since Greenwich mean noon on the first of January, 4713 B.C.

To compute the Julian Date:

  1. Convert local time to Greenwich Mean Time
  2. Let Y equal the year, M equal the month, D equal the day in decimal form.
  3. If M equals 1 or 2 then subtract 1 from Y. and add 12 to M.
  4. Compute A. A=INT(Y/100)
  5. Compute B. B=2-A+INT(A/4). However, if the date is earlier than October 15, 1582 then B=0.
  6. Calculate C. C=INT(365.25*Y). If Y is negative then C=INT((365.25*Y)-.75).
  7. Calculate E. E=INT(30.6001*(M+1))
  8. Calculate JD (Julian Date). JD=B+C+D+E+1720994.5

Greenwich Sidereal Time (GST)

  1. Calculate JD (Julian Date) corresponding to 0 hours GMT for this date. (This value should end in .5)
  2. Calculate UT. This is the GMT in decimal hours.
  3. Calculate T. T=(JD-2451545.0)/36525.0
  4. Calculate T0. T0=6.697374558+ (2400.051336*T)+(0.000025862*T2)+(UT*1.0027379093)
  5. Reduce T0 to a value between 0 and 24 by adding or subtracting multiples of 24. This is the GST in decimal hours.

Local Sidereal Time (LST)

  1. Convert the GST to decimal hours and the longitude) to decimal degrees. If longitude is west then L is negative.
  2. Calculate LST. LST=GST+(L/15)
  3. Reduce LST to a value between 0 and 24 by adding or subtracting multiples of 24. This is the LST in decimal hours.

Hour Angle (HA) and Declination (DE) given the Altitude (AL) and Azimuth (AZ) of a star and the observers Latitude (LA) and Longitude (LO)

  1. Convert Azimuth (AZ) and Altitude (AL) to decimal degrees.
  2. Compute sin(DE)=(sin (AL)*sin (LA))+(cos(AL)*cos (LA)*cos (AZ)).
  3. Take the inverse sine of sin(DE) to get the declination.
  4. Compute cos (HA)=(sin (AL)-(sin (LA)*sin(DE)))/(cos (LA)*cos (DE)).
  5. Take the inverse cosine of cos (HA).
  6. Take the sine of AZ. If it is positive then HA=360-HA.
  7. Divide HA by 15. This is the Hour Angle in decimal Hours.

Hour Angle to Right Ascension

  1. Convert Local Sidereal Time and Hour Angle into decimal hours.
  2. Subtract Hour Angle from Local Sidereal Time.
  3. If result is negative add 24.
  4. This is the Right Ascension in decimal hours.

Parallax (p) to Distance (d) Conversion


  1. Parallax is in arcseconds.
  2. Distance is in parsecs.
  3. 1 parsec equals 3.2616 light years.

Relationship between the focal point (f), diameter (D) and depth (d) of a parabolic reflector


  1. f, D, and d are all in the same units.
  2. The focal point is measured from the bottom of the reflector.

Gain of a parabolic reflector given the diameter (D), wavelength (W) and efficiency factor (k)

G=10*log (k*(pi*D/W)2)

  1. G is the gain over an isotropic radiator.
  2. k is usually about .55
  3. D and W are in the same units.

An approximation for Beam Width (BW) given diameter (D) and wavelength (W)


  1. BW is in radians (multiply by 57 to convert to degrees)
  2. D and W are in the same units.

Doppler shift due to the earth's rotation.


  1. Fd is the Doppler shift due to the earth's rotation
  2. Fo is the frequency of observation
  3. LAT is the latitude of the antenna
  4. DEC is the declination of observation
  5. HA is the hour angle of observation in degrees
  6. K=pi*d/(c*t)
    • d is the diameter of the earth (12756336 meters)
    • c is the speed of light (3 x 108 meters/seconds)
    • t is the number of seconds in a sidereal day (86197 seconds)
    • K is 1.546111 x 10-6

A good artical on this subject by Marko Cebokli (S57UUU) is available on the SETI League web site here

Length of time a star remains in the beam of an antenna

T=13751*W/(D*COS (DEC))

  1. W is the wavelength
  2. D is the diameter of the dish
  3. DEC is the declination of the star
  4. W and D are in the same units
  5. T is in seconds
  6. This is an approximation which breaks down if the dish is pointed near +/- 90o declination

Converting noise temperature to noise figure


  1. F is in decibels
  2. T is in Kelvin
  3. Log is base 10

Range at which a signal can be detected

R=8x10-6*(Pe*A/T)1/2* (t/B)1/4

  1. R is in light-years
  2. Pe is the effective radiated power of the transmitter in watts
  3. A is the effective area of the receiving antenna in square meters
  4. T is the excess receiver noise temperature in Kelvin
  5. t is the averaging time of the receiver in seconds
  6. B is the bandwidth of the signal in Hertz
  7. 8x10-6 is a constant and calculated using the formula:
    1. LY is a light-year in meters (9.4608x1015)
    2. K is Boltzman's constant (1.38x10-23)

The Drake's Equation

N=R*fs*fp*ne*fl* fi*fc*L

  1. R is the average rate of star formation in the galaxy
  2. fs is the fraction of stars that are suitable for planetary systems
  3. fp is the number of suitable suns with planetary systems
  4. ne is the mean number of planets that are located within the zone where water can exist as a liquid
  5. fl is the fraction of such planets on which life actually originates
  6. fi represents the fraction of such planets on which some form of intelligence arises
  7. fc is the fraction of such intelligent species that develop the ability and desire to communicate with other civilizations
  8. L is the mean lifetime (in years) of a communicative civilization