Useful Formulas for Amateur SETI
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
- Julian Date
- Greenwich Sidereal Time
- Local Sidereal Time
- Hour Angle and Dec
- Hour Angle to Ra
- Parallax to Distance
- Focal Point of a parabolic reflector
- Gain of a parabolic reflector
- Beam Width
- Doppler Shift from Earth's Rotation
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|
|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:|
|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|
To compute the Julian Date:
- Convert local time to Greenwich Mean Time
- Let Y equal the year, M equal the month, D equal the day in decimal form.
- If M equals 1 or 2 then subtract 1 from Y. and add 12 to M.
- Compute A. A=INT(Y/100)
- Compute B. B=2-A+INT(A/4). However, if the date is earlier than October 15, 1582 then B=0.
- Calculate C. C=INT(365.25*Y). If Y is negative then C=INT((365.25*Y)-.75).
- Calculate E. E=INT(30.6001*(M+1))
- Calculate JD (Julian Date). JD=B+C+D+E+1720994.5
Greenwich Sidereal Time (GST)
- Calculate JD (Julian Date) corresponding to 0 hours GMT for this date. (This value should end in .5)
- Calculate UT. This is the GMT in decimal hours.
- Calculate T. T=(JD-2451545.0)/36525.0
- Calculate T0. T0=6.697374558+ (2400.051336*T)+(0.000025862*T2)+(UT*1.0027379093)
- 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)
- Convert the GST to decimal hours and the longitude) to decimal degrees. If longitude is west then L is negative.
- Calculate LST. LST=GST+(L/15)
- 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)
- Convert Azimuth (AZ) and Altitude (AL) to decimal degrees.
- Compute sin(DE)=(sin (AL)*sin (LA))+(cos(AL)*cos (LA)*cos (AZ)).
- Take the inverse sine of sin(DE) to get the declination.
- Compute cos (HA)=(sin (AL)-(sin (LA)*sin(DE)))/(cos (LA)*cos (DE)).
- Take the inverse cosine of cos (HA).
- Take the sine of AZ. If it is positive then HA=360-HA.
- Divide HA by 15. This is the Hour Angle in decimal Hours.
Hour Angle to Right Ascension
- Convert Local Sidereal Time and Hour Angle into decimal hours.
- Subtract Hour Angle from Local Sidereal Time.
- If result is negative add 24.
- This is the Right Ascension in decimal hours.
Parallax (p) to Distance (d) Conversion
- Parallax is in arcseconds.
- Distance is in parsecs.
- 1 parsec equals 3.2616 light years.
Relationship between the focal point (f), diameter (D) and depth (d) of a parabolic reflector
- f, D, and d are all in the same units.
- 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 is the gain over an isotropic radiator.
- k is usually about .55
- D and W are in the same units.
An approximation for Beam Width (BW) given diameter (D) and wavelength (W)
- BW is in radians (multiply by 57 to convert to degrees)
- D and W are in the same units.
Doppler shift due to the earth's rotation.
Fd=Fo*K*COS (LAT)*COS (DEC)*SIN (HA)Notes:
- Fd is the Doppler shift due to the earth's rotation
- Fo is the frequency of observation
- LAT is the latitude of the antenna
- DEC is the declination of observation
- HA is the hour angle of observation in degrees
- 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
- W is the wavelength
- D is the diameter of the dish
- DEC is the declination of the star
- W and D are in the same units
- T is in seconds
- This is an approximation which breaks down if the dish is pointed near +/- 90o declination
Converting noise temperature to noise figure
- F is in decibels
- T is in Kelvin
- Log is base 10
Range at which a signal can be detected
- R is in light-years
- Pe is the effective radiated power of the transmitter in watts
- A is the effective area of the receiving antenna in square meters
- T is the excess receiver noise temperature in Kelvin
- t is the averaging time of the receiver in seconds
- B is the bandwidth of the signal in Hertz
- 8x10-6 is a constant and calculated using the
- LY is a light-year in meters (9.4608x1015)
- K is Boltzman's constant (1.38x10-23)
The Drake's Equation
- R is the average rate of star formation in the galaxy
- fs is the fraction of stars that are suitable for planetary systems
- fp is the number of suitable suns with planetary systems
- ne is the mean number of planets that are located within the zone where water can exist as a liquid
- fl is the fraction of such planets on which life actually originates
- fi represents the fraction of such planets on which some form of intelligence arises
- fc is the fraction of such intelligent species that develop the ability and desire to communicate with other civilizations
- L is the mean lifetime (in years) of a communicative civilization