# The Moon as reflector

The Moon as reflector is complicated. I’ll try to build an explanation here and on other pages.

Firstly, the Moon is about 390,000km away. The diameter of the Earth is only 12,500km. The result is that all stations ‘see’ (almost) the same Moon hemisphere wherever they are on the surface of the Earth.

## Scattered reflections

Secondly, the Moon is a rough sphere. Think deep craters and hills as well as boulders and plains. From scattering theory, the degree of roughness increases as the wavelength of the signal decreases. We can think about the scenario as the advance of a flat wavefront (toward the Moon). this is returned from a plurality of scatterers . The energy returned will describe a new wavefront, at each point on which the signal will have different amplitude and phase. This is caused by different scattering efficiencies and path lengths across the lunar surface.

The Moon’s movement and the signal scattering is shown graphically above.

The Moon orbits the Earth and rotates. Combined with the Earth’s orbit and rotation those movements cancel. As a result, the Moon presents approximately the same face to the Earth always.

The Moon does however have some irregular movement. Relative to someone observing on Earth, it nods (North-South), and it wobbles (East-West). And since it is on an elliptical orbit, it is moving at speed away from Earth and back again with a period of a month.

Considered locally, reflections are more effective near the centre of the Moon’s face. That’s logical since many of the reflections from the sides (towards the Moon’s outer edges or limbs) will be lost to space. This effect heightens with distance from the centre. Although this appears a steady state, the irregularity of the Moon’s movement means irregular reflections.

When viewed from a station on Earth, the received signal will be a vector sum of all arrivals from this reflection scenario. The receiver will experience fading, with a median value and discrete values in time distributed about that median. Hams at the centre of EME theory call this libration fading, caused by the libration movement.

Now, my experience is with mobile communications. The situation is like that when a terrestrial mobile travels at random in a city while sustaining a call with a cellular base station. The mobile experiences deep fading of over 30dB with a period of λ/2. In the terrestrial case the receiver is moving while the reflection environment is (relatively) static. In the EME case, the reflection environment is moving while the two stations are (relatively) static. And just like the terrestrial analogy, libration fading reduces to zero (no fading) from time to time and then reverts to the faded scenario between these lulls.

But unlike the terrestrial case, libration fading is predictable – metaphorically, the Moon is always driving down the same street.

I’ll add a note here for those statistically minded. The resultant signal power received from Moon reflection at a receiver on the surface of the Earth will be Rayleigh distributed during the multi-path fading periods. The distribution will likely revert to a Ricean distribution over months to describe a mixed fading picture and periods of reduced fading.

## The Moon as reflector

So, I’d suggest that libration fading can be avoided (by only transmitting during lulls), or it can be managed by ensuring higher signal by way of a fade margin. Practically, avoidance is the only option for all but large stations.  The path budget, and the idea of a fade margin is discussed in other pages.

The fast fading is countered by using digital modes like JT65. These are specifically designed with redundancy in the error correction code. Signal drop out is recognised and ignored.