EME communications technical details
As the albedo of the moon is very low (maximally 12% but usually closer to 7%), and the path loss over the 770,000 kilometre return distance is extreme (around 250 to 310 dB depending on VHF-UHF band used, modulation format and Doppler shift effects), high power (more than 100 watts) and high-gain antennas (more than 20 dB) must be used.
In practice, this limits the use of this technique to the spectrum at VHF and above.
The link equation used to determine EME Path Loss
- Determine moon distance
- Determine transmitter power
- Determine receive antenna power
Free space loss from an isotropic omnidirectional antenna is described by this formula. It calculates the surface area of an imaginary sphere of radius, d, that the radio wave illuminates uniformly:
- Loss = [ 4*pi*d/lambda]^2 where pi = 3.14, d = distance and lambda = wavelength, in meters
- Lambda = c/F F = Hz, c = 3*10^8 meters/sec.
- Lambda = 300/F when F is in MHz.
Substituting F into the free-space loss formula and converting to d into km:
- Loss = 4*pi*10^3*F*d/300 or
- Loss(dB) = 32.45 + 20Log(F) + 20Log(d)
Adding factors for reflection from the Moon results in
- Loss-eme(dB) = 32.45 + 20Log(F) + 20Log(2*d) + 50.21 - 10Log(.065)
The standard radar path-link formula as his basis for EME path-loss calculations
- Pr = Pt*Gt*Gr*Loss
- Loss = rho*lamba^2/(4*pi*)^3 *d^4
After including the factor for surface reflectivity it becomes
- Loss-eme(dB) = 100.4 + 20Log(F) + 40Log(d) - 10Log(rho)
- rho = 0.065*lunar diameter^2*pi/4
Since the diameter of the Moon is 3.5*10^6 km
- rho = 6.25 * 10^11 square-meters.
The formula becomes
- Loss-eme(dB) = 20Log(F) + 40LOG(d) - 17.49, F = MHz, d = km
For some reason not specified, Josef has increased the loss by 3-dB producing:
- Loss-eme(dB) = 103.4 + 20LOG(F) + 40LOG(d) - 10Log(rho) or
- Loss-eme(dB) = 20Log(F) + 40LOG(d) - 14.49
Note that the distance from the earth to the moon varies because the orbit of the moon is not perfectly circular. The moon's orbit is somewhat egg-shaped, that is to say it is not a pure oval. This means there is an Apogee (the largest distance) and a Perigee (the shortest distance).
Depending on the position of the moon with respect to the earth, Apogee can be as much as 406,700km, while Perigee can be as little as 356,400km.
- This translates to as much as 2.25dB difference in path loss from apogee to perigee.
- The mean distance from earth to moon is given as 384,400km.
- These calculations consider the fact that the moon is only 7% efficient as a reflector and, using the "radar equation" and the fact that the moon is a spherical reflector.
Current EME communications
Amateur radio (ham) operators utilize EME for two-way communications. EME presents significant challenges to amateur operators interested in working weak signal communications. Currently, EME provides the longest communications path any two stations on Earth can utilize for bi-directional communications.
Amateur operations use VHF, UHF and microwave frequencies. All amateur frequency bands from 50 MHz to 24 GHz have been used successfully, but most EME communications are on the 144, 432, or 1296 MHz bands. Common modulation modes utilized by amateurs are continuous wave with Morse Code, digital (JT65) and when the link budgets allow, voice.
Recent advances in digital signal processing have allowed EME contacts, admittedly with low data rate, to take place with powers in the order of 100 Watts and a single Yagi antenna.
Modulation types and frequencies optimal for EME
Other Factors influencing EME communications
Doppler effect - 300 Cycles at Moonrise/set
- At Moonrise, due to the Doppler effect between the Earth and Moon, Your echo's will appear 300 or so cycles higher in frequency at Moonrise.
- As the Moon traverses the sky to a point due south the Doppler approaches nil. As the Moon sets your echo's will appear lower in frequency till at Moonset they are now 300 cycles less.
- Doppler effects cause many problems when tuning into and locking signals from the moon.