Spring 2008 Issue

Lunar Link Analysis

By Dr. H. Paul Shuch, N6TX

In the previous Orbital Classroom column in the Winter 2008 issue of CQ VHF, we introduced the European and American Student Moon Orbiter initiatives (ESMO and ASMO, respectively), and mentioned that AMSAT may well have a role to play in their comm link and Earth station design. This time we will create a straw-man system specification for a reliable digital link to cover lunar distances, and discuss the antenna requirements for a capable command station. It should be noted that this column does not constitute an actual design proposal. Rather, it is my intent to show, by hypothetical example, the kinds of considerations that the ESMO and ASMO student designers (and their faculty advisors) will need to address in developing their own proposals.

The primary driver for any space communications link design is the power budget on the spacecraft itself. We consider the downlink to be limiting, in that the spacecraft’s power budget is finite. (We can assume that the power available on Earth for uplink transmissions is virtually unlimited.) For solar-powered spacecraft, the power budget is, in turn, limited primarily by the spacecraft’s mass and physical dimensions. For the present study, we will make the conservative assumption that the power budget will be no greater than that available on a standard university CubeSat.1 The typical 10-cm cube of 1-kg mass, with high efficiency photocells covering six sides of the cube, readily produces (when in sunlight) at least 1 watt (+30 dBi) of continuous-wave RF output in any one of the popular 145-, 435-, or 2400-MHz downlink frequencies common in the Amateur Satellite Service.

For the sake of this analysis, let’s assume our downlink will operate at UHF, in the 435-MHz band. We will further stipulate that the spacecraft lacks attitude control; hence we will require an omnidirectional downlink antenna. Because it would be easy to stow and deploy, it is common practice to equip CubeSats with a Vee dipole for UHF uplink or downlink. Such an antenna can be assumed to exhibit a gain on the order of +2.2 dBi, yielding an Effective Isotropic Radiated Power (EIRP) of +32.2 dBm.

Let’s approximate the mean distance between the Earth and the Moon as 400,000 km. Over this distance, isotropic free-space path loss at a wavelength of 70 cm is on the order of 197.3 dB. Subtracting this loss from the spacecraft’s downlink EIRP, we see that the isotropic power incident upon the Earth will be on the order of –165 dBm. This is a weak signal to be sure, which will require substantial antenna gain to pull out of the noise.
Figure our ground station is going to be built around a large, fully steerable parabolic dish. Obviously, the larger the dish, the more gain the antenna exhibits, and the more downlink signal is recovered at Earth. However, bigger is not necessarily better. The higher the gain of any antenna, the narrower its beamwidth will be and the harder it will be to aim and track. Remember that the spacecraft is going to be orbiting the Moon and is a vanishingly small target. A ground-station antenna with beamwidth sufficient to cover the entire lunar neighborhood will certainly simplify matters by lessening demands on the dish’s tracking hardware and software. Also, a little extra beamwidth will allow us a little slop in ground-station operations, albeit at the cost of a bit of gain. Viewed from Earth, the Moon subtends 1/2 degree in the sky. Let’s say we’re going to make our antenna beamwidth 2 degrees so that when we point it at the moon, given even a 1-degree pointing error, the satellite’s signals will still be captured.

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