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*To*: T.L.G.vanderLinden@student.utwente.nl (Timothy van der Linden)*Subject*: Re: starship-design: Required microwave-antenna size. 100-light-year trip.*From*: kgstar@most.fw.hac.com (Kelly Starks x7066 MS 10-39)*Date*: Mon, 28 Oct 1996 08:37:21 -0500*Cc*: starship-design@lists.uoregon.edu*Reply-To*: kgstar@most.fw.hac.com (Kelly Starks x7066 MS 10-39)*Sender*: owner-starship-design

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- >>length. >> >>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 >Then > 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... > >Timothy 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 ---------------------------------------------------------------------- Kelly Starks Phone: (219) 429-7066 Fax: (219) 429-6859 Sr. Systems Engineer Mail Stop: 10-39 Hughes defense Communications 1010 Production Road, Fort Wayne, IN 46808-4106 Email: kgstar@most.fw.hac.com ----------------------------------------------------------------------

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