Last Updated on January 18, 2025 by John Berry
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 so the path loss to the Moon and back is large. The diameter of the Moon is about 3,500km. Radio waves from antennas on the Earth pointed at the Moon will be reflected or scattered by the Moon’s surface. Since the Moon’s diameter is huge, it is a relatively good reflector or scatterer simply because it is so big. It’s like a huge billboard.
Scattered reflections
Secondly, the Moon is a somewhat 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 from each point on 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 loss heightens with distance from the centre. And although this appears a steady state, the irregularity of the Moon’s movement means irregular reflections and libration fading.
Reflection coefficient
The effectiveness of a reflecting surface is characterised by its reflection coefficient. If the energy incident on the reflector is all returned, the reflection coefficient is 1. Whilst the Moon is big (and hence there’s reflection and scattering happening over a large area), much of the energy is absorbed. Attempts at measurement of the reflection coefficient put the figure at between 6.5% and 11%. So just a few percent of the energy is returned. But there’s no definitive value, and little understanding about how reflections and scattering vary with frequency.
The Moon as reflector
In summary:
- Waves arriving at the Moon’ surface will be reflected and scattered.
- The signal received back on Earth is the aggregate of all refections and scatters.
- Doppler shift and Doppler distortion of the resultant signal will be experienced.
- Only the centre of the Moon’s surface is effective in reflection and scattering.
- The Moon’s reflection coefficient is between 6.5% and 11%.
The path budget using these effects, and the idea of a fade margin as a measure of ability to communicate, is discussed in other pages.