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Re: starship-design: Required microwave-antenna size. 100-light-year trip.

At 12:16 PM 10/28/96, Timothy van der Linden wrote:
>Rex wrote:
>>1. ANTENNA SIZE REQUIREMENT (A tutorial; read at your own risk.)
><Tutorial removed>
>>If we set the Fraunhofer-diffraction angular width equal to the
>>angle subtended by the sail diameter (Ds) at the range R, we can
>>get an expression for the diameter of the emitting antenna (De)
>>that is required to put "84 percent" of the emitted power within
>>the area of the sail:
>>     De = 2.44 * lambda * R/Ds   .
>>For microwaves with lambda = 1 cm and a sail diameter of 100 km,
>>say, the required diameter of the emitting antenna grows 2.31
>>million km for each light-year of distance to the sail, to keep
>>the main lobe just within the sail diameter.  This is for an
>>antenna whose figure (shape) is correct to a fraction of a wave-
>>For an emitting-antenna diameter of 2.31 million km (and wave-
>>length of 1 cm) for a 1-lt-yr distance to the sail, the boundary
>>between near and far fields is at a range of about 23 thousand
>>lt-yr, far enough away to say we're operating in the near field.
>>[Note: at 1 lt-yr distance, the spot size is
>>(1 lt-yr/23,000 lt-yr) * 2.31 x 10^6 km = 100 km, the diameter of
>>the sail, as desired.]
>>Are we prepared to build an expanding antenna this large?  It
>>looks as if the M(aser)ARS should be a L(aser)ARS.  For any wave-
>>length, however, figure control is going to remain a headache.
>What if
> lambda = 500 nm = 5E-7 m, (Blueish green)
> R = 10 ly = 9.46E16 m
> Ds = 300 km = 3E5 m
> De = 2.44 * lambda * R/Ds = 2.44 * 5E-7 * 9.46E16 / 3E5 = 3.85E5 m = 385 km
>range > De^2/(2.44 lambda)  ---> 9.46E16<1.215E17
>So we are just around the border between the near and far field.
>300 and 385 kilometer diameters don't seem like a headache...

A 300-400 kilometer laser array?  Again it would be a bit hard to fit on
our moon.  Harder to sycronize since the frequencies are shorter.  Also the
sail has now gone from a wire mesh to a reflective sheet.


Kelly Starks                    Phone: (219) 429-7066    Fax: (219) 429-6859
Sr. Systems Engineer                                     Mail Stop: 10-39
Hughes defense Communications
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Email:  kgstar@most.fw.hac.com