Stephenson doesn't really understand orbital dynamics, alas. His description of the appearance of satellite orbits as seen from the ground is just plain WRONG... an observer not at the pole will not see the simple radial pattern, but instead a series of arcs that do not cross the pole star. He also ignores the planet's shadow- most nighttime passes are invisible because the satellite is not illuminated.
Also "polar" orbits are typically not at inclination 90, but at something like 97 degrees to allow the equatorial bulge to precess the plane to stay sun synchronous. This makes interpreting the results of an all-sky survey even harder.
The black mirrors might hide the objects at either end, but the tether itself would be very obvious, lit up in sunlight... an electrodynamic tether wouldn't be able to do the apogee velocity matching needed in the short time available... proximity operations, like the postlaunch roundup, don't need to use explicit orbital element changes, you just do straight line maneuvers with a little extra thrust perpendicular to make up for the tides... the transfer orbit to the target would have taken only hours, not days... arrgh.
Stephenson tried, he really did- but I wish he had played with Orbiter before writing the spaceflight scenes.