## 7 Effects of Planetary Rotation or Planetary Orbits
Laser terminals in polar orbits about both planets, combined with conventional wide-band microwave relays to Earth, would eliminate atmospheric transmission and scattering losses and potentially provide quasi-continuous wideband communication except for brief periods twice per Earth year, i.e., when the outer planets are at or near the minimum and maximum interplanetary distance (\(\theta_{PQ}\) = 0 or 180 degrees) when the Sun would either blind the planetary terminal or block the beams entirely. In addition, the initial angular area of uncertainty for the location of the planetary orbiter would be constrained to a narrow circular rim defined by the orbital altitude above the planet's surface, i.e., \(A_{O}=\pi Dh\) where \(D\) is the angular diameter of the planet as viewed by the opposite terminal and \(h<<D\) is the maximum altitude of the satellite. A land-based terminal, on the other hand, could be located anywhere within the angular disk, i.e., \(A_{L}=\pi D^{2}/4\), as listed in Columns 8 and 9 of Table 1, a factor \(D/4h\) larger. The look-ahead angle for a satellite in polar orbit about a planet of angular diameter \(D\) is roughly equal to \(\pi D/\tau_{orb}\) and is plotted in Figure 7 for the various planets as a function of the orbital period. The shape of the transmitted beams is not Gaussian as is often assumed by some authors. On the contrary, the antenna pattern of the optimized transmit telescope consists of a strong central lobe surrounded by increasingly weaker circular rings [17]. The rings result from the truncation of the Gaussian beam profile by the finite diameter of the telescope and are further modified by the presence of a secondary mirror, if any. In fact, the presence of a secondary mirror slightly reduces the intensity of the central lobe while simultaneously increasing the amplitudes of the outer rings [17]. Within the central lobe, the signal strength drops to roughly 10% of the peak value for pointing errors equal to \(\lambda/D\). Thus, for the 1 GHz OOK system discussed earlier, the desired 21 received photons per bit would be reduced to about 2 photons per bit due to this pointing error, thereby resulting in an unacceptable bit error rate. It is also worth noting that the Earth terminal telescope diameter, \(D_{E}\), is highly likely to be much larger than the planetary telescope diameter, \(D_{P}\), requiring the Earth terminal pointing to be much more accurate in transmission mode for a two-way communications link. It is therefore extremely important to either maintain a very tight coalignment of the transmit and receive telescope optical axes or increase the laser power to compensate for the optical loss. We will now discuss a possible solution. To expedite the acquisition and coalignment of the planetary and Earth terminals, one can include a defocusing element in each telescope and a partitioned single-photon sensitive detector array in each receiver focal plane. The defocusing element would temporarily merge the central lobe and the surrounding diffraction rings into a much broader (and therefore lower intensity) far field pattern with a mild degree of spatial modulation [17]. As mentioned briefly in Section 5, the amount of beam broadening is determined by the parameter \(\beta^{\prime}=\beta/2\pi=D^{2}/\beta(\lambda R)\) where \(D\) is the diameter of the telescope primary mirror and \(\lambda R\) is again the product of the laser wavelength and the range to the opposite terminal. Figure 5 in [17] suggests that choosing the value \(\beta^{\prime}=2.4\) would increase the planetary beam spread in the far field by a factor of 7 relative to the original central lobe. This would increase the transmitted beam area for acquisition by a factor of 49, thereby greatly accelerating acquisition of the opposite terminal. However, the mean reduction in signal strength due to defocusing would be about 2 orders of magnitude.