Re: Interstellar Propulsion idea using an Asteroid and a few comets!
From: Rob Dekker (rob_at_verific.com)
Date: 09/01/04
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Date: Wed, 01 Sep 2004 02:12:45 GMT
"AA Institute" <abdul.ahad@ntlworld.com> wrote in message news:adbf5bc1.0408311031.13cc4a3f@posting.google.com...
> "Alfred A. Aburto Jr." <aburto@sbcglobal.net> wrote in message news:<eVNYc.13630$Xg3.6189@newssvr27.news.prodigy.com>...
> <snip>
> > > >
> > > Good. Now we've established the two extreme limits of beam width
> > > versus range. I am sure there is an *optimum balance* between the two
> > > that will prove viable, given the ship's projected speeds being
> > > "slow". Add to this the potential to augment using radar, and factor
> > > in the un-quantifiable technology innovations to come for both lasers
> > > and echo detectors... we're there with a solution that cannot <yet> be
> > > quantified, but which can be "imagined"!
> >
> > Thinking of radar:
> > Using the Rayleigh Criterion as an estimate of the beamwidth of an Arecibo
> > like planetary radar (305m diameter) operating at 2.3GHz then the beamwidth
> > would be approximately BW = 1.22 * wavelength/dish_diameter, where
> > wavelength would be 0.13m for 2.3GHz and the dish_diameter would be 305m.
> > The beamwidth then is BW = 0.00052 radians. So to cover the whole sky at
> > once you would need to form N = 4*pi/BW beams = 24,166 beams. This is alot
> > of beams by todays standards of course! Suppose however we had the
> > capability to form 48 beams at once and we had the sensitivity to search out
> > to a range of 40AU (~ 6 light-hours) so we could ping twice a day with 48
> > beam coverage of the sky for each ping. In this scenario it would take about
> > ~250 days to cover the whole sky out to 40AU. The pings would not be sent
> > out at once, but spread out over a short time period (a few hours perhaps or
> > shorter). The difficult part to engineer would be to get the power to cover
> > out to 40AU in range (but not impossible). Well, I don't see it is a
> > hopeless situation by any means ...
> > Al
>
> Well, that's very reassuring. The fact that its *possible* to use
> radar is sufficient, since we are only exploring ideas. A dish
> 'approaching' the size of Arecibo's probably not hopelessly impossible
> to mount... (if the asteroid is large enough of course).
I hate to burst any bubbles here, but with an Arecebo-size dish at 2.3 GHz,
40AU radar depth is not achievable, I think. Not even for a single 'ping'.
Here is a "back-of-the-envelope" calculation :
Define :
ro is the radius of an object we want to detect (r=100m for an astroid?)
r is radius of the antenna we use for both sending and receiving (r=150m)
P is the LINE power used for the transmitter
kT is the system noise power in the receiver (about 10^-21 for a state-of-the-art receiver)
wl is the wavelength used (wl=0.13m at 2.3GHz)
R is the distance between the spaceship and the object (40AU = 6*10^12 m).
BW is bandwidth used in the transmission
pi is 3.14...
Then, assume that the object omnidirectionally reflects energy (it absorbs half, and reflects
the other half equally over a 180degree dome back to the transmitter).
I think this is reasonable to assume for a spherical shaped rugged object.
Then, using the seti@home FAQ page for transmitters and receivers, and a bit of formula
joggling, I obtain the following formula for the S/N ratio of this radar system :
S/N = P * (r/R)^4 * pi^2 * (ro/wl)^2 * 1/(4*kT) * 1/BW
If we want to get 1 'ping' across, then we need a single bit data transfer. This means BW*time==1.
So the formula for Energy (E = P*time) used in the ping then eliminates BW:
S/N = E * (r/R)^4 * pi^2 * (ro/wl)^2 * 1/(4*kT)
I thing this is actually a very general formula for radar (but I dont think I've seen it anywhere yet).
Fill in the numbers above, then to get a S/N ratio of 0db (we probably need 10 times more energy)
the energy in the ping must be at least 1.7*10^15 J.
So, if we use 100MW line-power transmitter (already bigger than anything we have on earth),
the ping (time) must be 1.7*10^7 sec (about half a year, in an absurtly narrow BW).
Of course, things become a bit easier for larger objects. For ro=100km objects, energy in the
ping becomes 1.7*10^9 J. The 100MW transmitter would need to be on for 17 sec, BW=1/17 Hz.
That's possible, but that is only 1 ping (in one beam). And 1.7GJoule is quite expensive to generate.
You cannot afford the electric bill, you can forget about scanning the entire sky in reasonable time,
and anything smaller than 100km across at 40AU away remains undetected.
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