[amsat-bb] Arecibo on 432 MHz Moon Bounce (some calculations)

i8cvs domenico.i8cvs at tin.it
Sat Apr 10 19:20:04 PDT 2010

Hi All,

The specifications of the Arecibo Observatory Amateur Radio Club
for the 432 MHz Moon Bounce test on April 16-17 and 18 are as

Dish diameter: 1000 foot equivalent to 305 meters
Antenna gain: 60 dBi
Tx power: 400 W
Tx Frequency: 432.045 MHz

Since the given ERP is 243,902,443 Million Watts (see below)
and since 60 dB is equivalent to 1000000 (one Million) time in
power it comes out that the power reaching the feed of the dish is:

243902443 / 1000000 =  243 watt

The rest of the power 400-243 = 157 watt is lost in the feed line.

At 432 MHz a dish with a diameter of 305 meters has a -3dB points
main lobe angle equal to:

Theta = Lambda / Diameter = 0.69 / 305 = 0.00227 rad.

The above lobe of the dish at an average distance of 380000 km
light up a small circular surface S over the moon wich diameter is:

D = 380000 x 0.00227 = 865 km

The surface area S = (3.14 x 865^2) / 4 = 5.88 x 10^11 square meters

All the radiated power of 243 watt by the dish is now collected over
the above S area.

The reflectivity of the moon at 432 MHz is the 7% so that the power
scattered back isotropically by the moon is ( 243/100 ) x 7 = 17 watt

It is like to say that the power reflected back by the moon is 17 watt
feeding an isoptropic antenna or 17 watt EIRP or +12 dBW EIRP
radiated isotropically by the moon.

Since the surface of the moon lighed up by the dish is less then the whole
surface of the moon the usual calculation procedure for the EME link
considering the isotropic attenuation earth-moon-earth cannot be used
here because as seen by the Arecibo dish the diameter of the moon is
smaller than in reality and is large only 865 km in diameter not 3476 km
as is large in reality the moon.

With this is mind we must imagine the dish of Arecibo to be an isotropic
antenna with 17 watt applied to it and transmitting all around isotropically
from the moon.

My ground antenna has a gain G= 15 dBi and an antenna picked up noise
of 70 kelvin when looking at the cold sky

My receiving system  at 432 MHz has an overall Noise Figure of 0.7 dB
equivalent to 50 kelvin so that the noise floor KTB of my receiving system
in SSB with a bandwidth of 2400 Hz is

KTB=1,38 x 10^-23 x (50 + 70) x 2400=3.97x10^-18 watt= -174 dBW


Isotropic power reflected by the moon...+12 dBW
Isotropic attenuation for 380.000 Km.. - 197 dB
Power received on isotropic earth ant... - 185 dBW
Ground antenna gain...............................+  15 dBi
Power applied to ground receiver..........- 170 dBW
Noise floor of ground receiver..............-  174 dBW
Received Signal to Noise ratio S/N.......+ 4 dB

By the way when KP4AO will operate on CW I can switch on the 500 Hz
filter on my receiver and here I will gain in sensitivity 2400/500 = 4.8
time and  10 log  4.8 = 6.8 dB so that I gain 4 + 6.8 = 10.8 dB of overall
Signal to Noise ratio

If I can stake two 70 cm antennas with gain 15 dBi each I can gain about
another 3 dB and I can improve the S/N ratio to 10.8 + 3 = 13.8 dB

If I can stack four 70 cm antennas with gain 15 dBi each I can gain about
another  3 dB and I can improve the S/N ratio up to 13.8 + 3 = 16.8 dB
a real very strong signal on CW or 16.8 - 6.8 = 10 dB in SSB Signal to
Noise ratio wich is considered to be optimal for a comfortable reception
in SSB

By the way to work EME using a big dish having a lobe  with an aperture
angle "theta" smaller than the diameter subtended by the moon wich
is about 0.5 degrees i.e. 0.0087 radiants is useful only for the big dish to
hear better those stations using smaller dishes but the big dish to be
received better by the smaller one's "must" use more power and not increase
the diameter of the dish because as soon as the moon is completely resolved
the power scattered back isotropically do not increase increasing the
diameter of the dish.

In conclusion I believe that ground stations with an antenna gain of 15 dBi
and a receiving system with an overall Noise Figure of about 1 dB can easily
hear KP4AO on CW and barely in the noise on SSB

Stations with the same receiver overall Noise Figure and antenna gain from
18 to 21 dB can hear KP4AO on CW and SSB without problems.

Stations using 100 watt or more and the above antennas ranging from 15 dBi
to 21 dBi have chance to make QSO with KP4AO on CW

The above calculation shows that it is very difficult to hear KP4AO or be
heard using a small hand-held yagi pointed at the moon.

Have fun

73" de

i8CVS Domenico

----- Original Message -----
From: "MM" <ka1rrw at yahoo.com>
To: <amsat-bb at amsat.org>
Sent: Wednesday, April 07, 2010 3:06 PM
Subject: [amsat-bb] Arecibo on 432 MHz Moon Bounce

> Hi all:
> Here is a EME event you cant miss.
> Dust off your CW key, its time for Satellite, QRP EME.
> The 1,000 foot dish has 60 dBi on 432 mc and 400 watts.
> That comes out to be approximately 243,902,443 Million Watts ERP.
> enjoy
> wf1f
> www.marexgm.org
> (thanks to KB1MGI for passing on this data)
> Arecibo on 432 MHz Moon Bounce
> The Arecibo Observatory Amateur Radio Club will be putting the
> 1000-foot radio telescope on the air for 432 MHz EME from April 16-18.
> It can be heard with a small hand-held yagi pointed at the moon
> The scheduled times of operation are:
> April 16: 1645 - 1930 UTC
> April 17: 1740 - 2020 UTC
> April 18: 1840 - 2125 UTC
> Callsign: KP4AO
> Tx Frequency: 432.045 MHz
> Rx Frequency: 432.050 to 432.060+
> Tx power: 400 W
> Antenna gain: 60 dBi
> System noise temp: 120 K (cold sky)
> System noise temp: 330 K (when pointed at moon)
> KP4AO can be heard with a small hand-held yagi pointed at the moon and a
> good receiver. A 15 dBi antenna and 100 W will be enough to work us on
> CW.
> Operators at KP4AO will do their best to work as many stations as
> possible. Each session will start with a brief announcement and CQ in
> SSB. SSB QSOs may continue for 30 minutes to an hour, if the QSO rate
> remains high.
> The mode will be shifted to CW as soon as it is judged that higher QSO
> rates would result.
> We will listen for calls at frequencies 5-15 kHz higher than our own,
> and even higher if QRM warrants. Callers who s-p-r-e-a-d o-u-t are more
> likely to be copied.
> If you've already worked us in any mode, please do not call again --
> give others a chance.
> If we call "CQ QRP", we will listen for stations running 100 W or less
> to a single yagi. Please do not answer such a CQ if you are running more
> power or have a larger antenna.
> On April 18, if we reach a condition where most calling stations have
> been worked, and we judge that operating in the digital mode JT65B would
> produce a higher QSO rate, we will switch to JT65B.
> Note that any of these planned operating strategies may be changed as
> circumstances dictate.
> We are extremely fortunate to have been granted access to the world's
> largest radio telescope for this amateur radio good-will event. We look
> forward to working as many stations as possible in the alloted time!
> >From QRZ.COM
> Moon-Net Email reflector
> http://list- serv.davidv. net/mailman/ ...erv.davidv. net
> Moon Bounce information
> http://www.vhfdx. info/eme. html
> UK Ham makes EME contact with just 25 watts
> http://www.southgat earc.org/ news/jan. ..me_contact. htm
> Earth-Moon-Earth with 20 Watts
> http://www.southgat earc.org/ news/jan. ..h_20_watts. htm
> WSJT Software for EME
> http://www.physics. princeton. edu/pulsar/ K1JT/
> _______________________________________________
> Sent via AMSAT-BB at amsat.org. Opinions expressed are those of the author.
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