Really Long Baseline Interferometry

[Kragen Sitaker]

In http://www.cap-lore.com/MathPhys/RLBI.html, Norm Hardy writes:
   Just now I have realized an error of several orders of magnitude. The
   bandwidth to earth, measured in GHz, does not suffice to carry
   the information that the resolution of the very long base line
   interferometry of the configuration suggests. Except for that the
   arithmetic suggests a picture of a distant galaxy with seveal million
   pixels in both directions.

Surely this is a solvable problem.  For example:
- each satellite could record data for a short time and transmit it for
  a long time
- the satellites could communicate with Earth (or one another) by
  non-radio means; 
  - for example, by laser.  You should be able to use all the WDM tricks
    telcos use over glass fiber through free space, and you don't need
    solitons to prevent wavelength dispersion, because it doesn't happen
    in free space; and you may also have available spatial multiplexing
    tricks not available through glass fiber; apart than the obvious one
    of pointing the transmitting optics at the receiver, the receiver
    may be able to distinguish spatially separated sources as well
  - or, at additional expense, you could send the data by courier.  A
    continuous stream of small courier satellites traveling between the
    two radio-telescope satellites could carry an arbitrarily high
    bandwidth, and as long as your timestamps have enough bits in them,
    the latency wouldn't matter.  Never underestimate the bandwidth of a
    station wagon full of hard disks.  (It should be possible at this
    point for cubic-meter couriers to contain several terabytes of
    disk, which should hold several hours of observations.)

The prospect of a radio telescope able to image nearby solar systems in
subplanetary detail excites me immensely.

The arithmetic of such things, in my limited understanding, is that you
can resolve features of size on the order of lambda d/D, where d is the
distance to the feature, lambda is the wavelength, and D is the
baseline.  Here our wavelength is perhaps 5cm and our baseline (between
the L4 and L5 Lagrange points of the Earth-Sun system) is about
2.6e13 cm, and I think the nearest solar systems are on the order of 1e19
cm away, so lambda d/D is about 2e6 cm, or 20 km.  The Earth's radius
is about 6400 km, so an image of the Earth at this resolution would be
about 640x640 pixels.  You'd be able to see not just mountains, oceans,
and valleys, but also cities and possibly even roadways.

All of this is assuming enough power would be reflected or transmitted
by such a planet to be detectable over the background noise.

(L4 and L5 tend to be kind of dirty, so it might be better to avoid
them and use something else.)