Radar

The Launch Loop and the Space Elevator are both long and skinny, and need to move out of the way of large space debris. The space elevator moves radially, and the launch loop moves up and down. In both cases, it does not matter where along the line of the system that an impact might occur; we are moving the whole line, the less the better. So, we need high radial accuracy for impactor trajectories, and little axial accuracy. That suggests an asymmetrical radar emitter and receiver, very wide and not so tall for the space elevator, tall and not so wide for the launch loop.

Launch Loop

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Space Elevator

The space elevator will have an array of radars in a circle around the space elevator ribbon on the top of the 50km platform. We are not concerned with material that is going to miss - that will have a large horizontal angular velocity when viewed from the radar. We are much more concerned with small material which is likely to hit the ribbon - it will not change incoming angle much.

From the high platform, we can see debris coming from thousands of kilometers away. Assume that we are using Ka band radar at 34GHz / 8.8mm (the police radar band, not many police in the mid Pacific!) and a 40 meter wide, 0.5 meter high dish, with a vertical line of appropriately phased emitters and receivers - done properly, we get a beam about 220 microradians wide, and wrapping from the horizon to overhead. At 3000 km distance, the beam is 660 meters wide. Assume we are looking for objects in circular orbits; while many actual orbits will be elliptical, they tend to decay towards circular. The analysis does not change much for elliptical tracks.

Space debris and radar assumptions

Assume 1 million debris objects are between shells at 700km and 1700km altitude, a total volume of 7.2E11 km, for a density of 1.38E-6 objects/km³. If we are looking at a slab 600 meters wide, one antenna will be looking at about 10 million cubic kilometers, or about 14 objects, thoughout the horizon-to-90-degree zone.

Most of these objects will have the wrong velocity towards the antenna, and thus the wrong doppler frequency. If we integrate over a 10 second period, we can look at a very narrow band of (shifting) frequency results at the IF receiver - 0.1 Hz. That means our radar can be very sensitive and selective.

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Assume a range of 5000 km ( round trip 33ms ) and that we can digitally integrate over multiple returns. We do not need to actually locate particles, we just need to assign them to "slabs" and move the elevator to the slabs with the least radar return energy. A "slab" defined here is a 50 meter wide section through the shell, out to the radar horizon, looking approximately like a stone arch.

• a2.c . . . a2.gp

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• http://www.esa.int/esapub/bulletin/bullet109/chapter16_bul109.pdf

• http://www.fhr.fgan.de/fhr/fhr_c589_en.html

• http://orbitaldebris.jsc.nasa.gov/measure/optical.html