Looks like just about everyone
except TruthSeeker1234 understood my point... as usual...
I can solve your orbit problems and at least some of your power problems. The giant fricking laser was placed at a Lagrange Point. This puts the laser far enough away to have good overhead aim and means that the machine would use almost no energy station-keeping.
True, we don't hve a launch vehicle capable of getting the thing to L1 but
the Russians might.
Yeah, we use the Lagrange points often for
current and
future orbiting observatories. Makes it easier to keep the hot Sun blocked from sensitive detectors. Hubble is lower only because it was designed for Shuttle to service it, mandating a far lower orbit.
For targeting deep sky objects L2 is good, but it suffers if you're targeting the ground. As has already been pointed out, targeting the WTC from LEO is already sub-minute of arc, and taking atmosphere into consideration, the beam is going to be diffraction-limited as it is. More distance -- in this case, about 15,000 times as much distance -- will diffuse the beam to uselessness.
For the "single WKBWD-sat" option, I had in mind a
Molniya orbit, an eccentric orbit allowing the killsat to "loiter" over NYC for a half-hour or so. This is, of course, academic, as the analysis clearly indicates two individual disposable spacecraft are the preferred solution.
You can make a weapon just as deadly at a much lower cost and weight. A simple kinetic energy weapon from orbit could be devastating. Imaging a 5 ton aerodynamic ceramic slug, with a sensor package and guidance fins, dropped (and thus accelerating) from a high orbit. A propulsion system to slow it down is all you need for it to fall.
GEO is around 42,000km. We'll assume a 5,000kg slug. Given our distance, we can calculate how long it would take for it to hit the ground (assuming no initial "push" downward and disregarding air resistence...which would only affect the very last 100km or so). The equation is t = SQRT(2*h/g), where h is the height and g is gravitic acceleration. With g=9.8m/s2 and h=42,000,000m, we can come up with about 20,200s (I rounded down).
Now, we can figure how fast it'd be going when it hits. Velocity = g*t, so we get 197,960 m/s. A pretty good clip.
We know that KE=1/2 mv2, so we can figure the energy here. We come up with 97,970,404,000,000 J...about 900 times the energy Mackey was working with for the laser beam.
Minor correction -- you can't assume constant gravity once distance becomes comparable to the radius of the Earth. You have to integrate Newton's Gravitational Equation. Or you can just look up the
delta V required to reach a certain orbit. In this case, the delta V is about 13.5 km / s.
Also your altitude for geosynchronous orbit seems to be radius from Earth's center, not above mean sea level. The altitude above MSL is roughly 35,700 km.
The correct impact figure for a 5 ton slug is about 4.6 x 10
11 Joules, or about 40 times that of the beam weapon. This figure is comparable to the collapse of the entire tower. So, your point is nonetheless entirely correct. Beams just aren't the way to go unless you need them for some reason, like instant time-on-target.
And yes, I've heard of
Project Thor.
My own shop recently did something quite similar, called
Deep Impact.
Lastly, user Mr. Skinny has given me more information on cutting-edge beam weapons, leading me to the
HELLADS programme. 150 kW sustained is pretty nice, though still about four orders of magnitude lower than the WWKBD needs. Also liquid cooling will work oddly in space. No gravity means no convection, so heat exchange is difficult. They're also reaching for 5 kg / kW, so the WWKBD laser would weigh 3,750 tons, assuming the technology scaled...
There are larger lasers in ground installations, of course, but they are
monstrous. Also generally too complex and too labor-intensive for flight. One could even consider
SLAC as a beam weapon of roughly 10 GW total power, but it would not be suitable for our application, and besides, it's
miles long.
