X = (h2 + 2hR)1/2, where X is the distance to the horizon, R is lunar radius, and h is height of the observer/transmitter above ground. Horizon distances for the Moon are given in table 5.8, neglecting surface irregularities.
| Observer height h, m | Horizon distance X, km |
|---|---|
| 1.0 | 1.9 |
| 2.0 | 2.6 |
| 3.0 | 3.2 |
| 4.0 | 3.7 |
| 5.0 | 4.2 |
| 10.0 | 5.9 |
| 15.0 | 7.2 |
| 20.0 | 8.3 |
As the original facility grows the transponder network also must be expanded. At the very minimum, a mobile robot should remain in communication with at least three noncollinear beacons to accurately fix its location. (The problems of feature shadowing and unit downtime may require the use of four or five stations. The exact number and layout can only be determined after the specific landing site has been selected and mapped from orbit. One possible deployment geometry is a grid of equilateral triangles with sides roughly equal to the desired horizon distance, with transmitters at the vertices. For example, the triangle pattern edges should be roughly 2.6 km if 2-m high antennas are used. This ensures that the range circle of any mobile robot receiver always will encompass at least three transponder units, thus permitting high-accuracy triangulation. (See fig. 5.33.) Depending on the maximum size of the mature LMF and the maximum feasible height for transponder antennae, the number of transmitters necessary to support the growing seed may range from the tens up into the thousands.
In any case, the main seed computer may be presumed to carry lunar topographical maps of the landing locale, assembled prior to landing and accurate to l-m resolution, in hard memory. This knowledge, plus the accurate positional information provided by the transponder network, should help to eliminate surprises at the expanding LMF site and lessen the need for a highly sophisticated "intelligent" vision-based surface navigation capability.
5B.2 References
Kincaid, William et al.: Summer Study Background Briefing on Computer Vision, Fault-Tolerant Systems, Large Space Structures and Antennas. Lockheed Missiles & Space Company, 7 July 1980.
