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Re: problems with beaming

To Lee

A laser beam conforms with the inverse-square law because the
area through which it passes, at constant angular width, in-
creases as the square of the distance.  The attenuation in
interstellar space due to absorption by matter in the beam
and scattering out of the beam by that same matter is a small
effect compared with the inverse-square-law dissipation of the
beam power per unit target area.

A laser beam of yellow light (lambda about 0.6E-6 m) from an
objective mirror with a diameter D of 400 km (your number)
would have a diffraction-limited angular divergence
(1.22 lambda/D) of about 1.8E-12 radian.  (We ignore here
problems with maintaining the figure of a 400-km-diameter
mirror to within a fraction of the wavelength of the laser
light.)  At a distance of ten light-years (9.46E13 km), say,
the linear width of this laser beam would be about 170 km.
For a mirror diameter of 40 km, the beam width at ten light-
years would be 1700 km; for 4 km, 17,000 km.  In the middle
case, a sail with a diameter of 100 km, say, would capture
(100/1700)^2, or about 1/300th, of the beam power (assuming,
for simplicity, a constant power per unit area across the
beam), or about 1/3rd of the beam power at one light-year
distance.  The plausibility of a laser-propelled-sail pro-
ulsion system therefore seems to hinge on the feasibility of
making a many-km-diameter laser objective mirror with a sur-
face precision of a fraction of the wavelength of light
and/or making a laser with a power orders of magnitude
greater than the sail would use.

Regards, Rex