# Calculators

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
- Drake

### Cylindrical Waveguide Feedhorn analysis

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 |

## Julian Date

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 T
_{0}. T_{0}=6.697374558+ (2400.051336*T)+(0.000025862*T^{2})+(UT*1.0027379093) - Reduce T
_{0}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

### d=1/p

**Notes:**

- 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^{2})/(16*d)

**Notes:**

- 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=10*log (k*(pi*D/W)^{2})

**Notes:**

- 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=W/D

**Notes:**

- 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.

### F_{d}=F_{o}*K*COS (LAT)*COS (DEC)*SIN (HA)

**Notes:**

- F
_{d}is the Doppler shift due to the earth's rotation - F
_{o}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
- K=pi*d/(c*t)

- d is the diameter of the earth (12756336 meters)
- c is the speed of light (3 x 10
^{8}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))

**Notes:**

- 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 +/-
90
^{o}declination

## Converting noise temperature to noise figure

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

**Notes:**

- F is in decibels
- T is in Kelvin
- Log is base 10

## Range at which a signal can be detected

### R=8x10^{-6}*(P_{e}*A/T)^{1/2}*
(t/B)^{1/4}

**Notes:**

- R is in light-years
- P
_{e}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 formula:

1/(LY*(4*pi*K)^{1/2})- LY is a light-year in meters (9.4608x10
^{15}) - K is Boltzman's constant (1.38x10
^{-23})

- LY is a light-year in meters (9.4608x10

## The Drake's Equation

### N=R*f_{s}*f_{p}*n_{e}*f_{l}*
f_{i}*f_{c}*L

**Notes:**

- R is the average rate of star formation in the galaxy
- f
_{s}is the fraction of stars that are suitable for planetary systems - f
_{p}is the number of suitable suns with planetary systems - n
_{e}is the mean number of planets that are located within the zone where water can exist as a liquid - f
_{l}is the fraction of such planets on which life actually originates - f
_{i}represents the fraction of such planets on which some form of intelligence arises - f
_{c}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