Calculators

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
• 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
• Drake

						Measured
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

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

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.

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.

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.

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.

d=1/p

Notes:

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

f=(D²)/(16*d)

Notes:

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

G=10*log (k*(pi*D/W)²)

Notes:

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

BW=W/D

Notes:

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

F_d=F_o*K*COS (LAT)*COS (DEC)*SIN (HA)

Notes:

1. F_d is the Doppler shift due to the earth's rotation
2. F_o 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

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

Notes:

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 +/- 90^o declination

F=10*Log((T+290)/290)

Notes:

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

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

Notes:

1. R is in light-years
2. P_e 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*(4*pi*K)^1/2)
   1. LY is a light-year in meters (9.4608x10¹⁵)
   2. K is Boltzman's constant (1.38x10^-23)

N=R*f_s*f_p*n_e*f_l* f_i*f_c*L

Notes:

1. R is the average rate of star formation in the galaxy
2. f_s is the fraction of stars that are suitable for planetary systems
3. f_p is the number of suitable suns with planetary systems
4. n_e is the mean number of planets that are located within the zone where water can exist as a liquid
5. f_l is the fraction of such planets on which life actually originates
6. f_i represents the fraction of such planets on which some form of intelligence arises
7. f_c 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