-----Original Message-----
From: moon-bounces@moonbounce.info [mailto:moon-bounces@moonbounce.info] On Behalf Of Joe Taylor
Sent: Wednesday, November 24, 2010 3:12 AM
To: moon-net@list-serv.davidv.net; moon@moonbounce.info
Subject: Re: [Moon] [Moon-net] Libration Measurements


Hi Doug and all,

Vk3UM wrote:
> We are currently in a period of minimum Libration for specific times 
> of the day and the month. The actual time of zero Libration is quite 
> short and spans less than an hour. ...

Some readers of this reflector, especially those unable to attend the 
14th International EME Conference held in Dallas last August, may not 
know that calculation of libration rates has been included in the 
program WSJT for some time now.  They are also in the MoonSked program 
by David Anderson, GM4JJJ.

Work leading to the WSJT calculations was described in a paper presented 
at the EME conference.  The written version is posted on the WSJT web 
site: for the paper and the accompanying PowerPoint slides, go to 
http://www.physics.princeton.edu/pulsar/K1JT/refs.html
and click on references 14 and 15.

The paper describes the fundamental physics of EME propagation, with 
special emphasis on the effects of lunar librations.  It also presents 
the results of direct measurements of libration-induced Doppler spreads, 
in both self-echo and two-station situations, made with amateur EME 
equipment at frequencies ranging from 144 MHz to 10 GHz.  The 
measurements are in excellent agreement with theory -- see, for example, 
Figure 8 in the paper.  (This is hardly a surprise, since such results 
have existed in the professional "radar astronomy" literature for nearly 
half a century.)

It is possible to accurately predict not only the libration rate 
(degrees per minute of the lunar "wobble") but also the EME Doppler 
spread, in Hz, measured a specified number of dB down from an echo's 
peak.  This, of course, is the quantity we care about most for amateur 
EME communication.  It depends on the libration rate but also on the 
fraction of lunar surface contributing significantly to the observed 
signal.  This fraction grows rapidly from VHF through the microwave 
bands, as clearly shown by the measurements I described in Dallas.

Libration-induced Doppler spreads for self echoes and for the station 
you're working can be read directly from the "Astronomical Data" screen 
of WSJT 9.0.  The values labeled "Spread" are the maximum limb-to-limb 
broadening, in Hz.  Those labeled "w50" are the width (in Hz) that will 
contain about 50% of the echo power.

Similarly, MoonSked's "Sked Maker" screen can display the maximum 
limb-to-limb spread for any EME path.

I have not yet made detailed comparisons between the libration 
calculations displayed in WSJT and MoonSked, and those of the VK3UM 
Libration Calculator... but I assume they will agree closely.

Any one of these fine software tools can help you to understand and 
enjoy one of the more fascinating peculiarities of EME communication.

	-- 73, Joe, K1JT