Pretty much. A telescope 1000x the diameter is going to image a source only 1 millionth as bright. But you can't put as many big telescopes up there as you can small ones. They're more expensive, and bigger telescopes cannot track as fast. Also, a larger telescope does not mean you can get a greater FOV. That depends on many things. In general, imaging a larger patch of the sky means that your angular resolution suffers for a given imaging technology.Junghalli wrote:Hmm, doing some quick calculations based on the area of a circle, I got a 200.88 meter diameter aperture to be able to image a 206 megawatt light at a distance of 1 AU. Obviously, this would have to take the form of an array of linked telescopes, rather than a single giant scope. The inverse square law would then suggest that being able to detect at longer ranges would be a matter of multiplying the effective radius of the scope by 2 (and hence the effective area by 4) if you want to double the range. So monitoring the entire solar system up to around Pluto orbit would require an effective aperture around 6 km across (or, rather, a truly massive array of smaller telescopes). You'll probably want a rosette of such arrays, of course, so you can monitor the entire solar system.
That sound about right?
So you now have to spend more resources to keep yourself safe. Eventually, you're going to run out of them.
Then your accuracy suffers. With a long baseline, you can use paralax efficiently by matching starfields except for the point you're interested in. The longer your baseline, the less accurate your angular resolution. Shorten up the baseline, the less paralax you can observe, and the less accurate your distance measurements. It also means you have to keep track of your partner; the accuracy of the paralax measurement is limited to how well you know that baseline.Junghalli wrote:If the problem is light lag the solution seems relatively simple. You just have two redundant posts within a short distance of each other (say, a few thousand or tens of thousands of kilometers).
And, again, I've forced you to spend more resources to keep yourself safe. That's a win for me, not you.
Half-order of magnitude. Of course, "if they so choose" indicates that they might have imaged their own interesting object and sent out similar signals. In which case, the airwaves are going to be clogged with chatter. The three way chat seemed to be the minimum negotiation handshake. Of course, I glossed over a lot of detail here.On the same issue, Darth Holbytlan wrote:Why is a three-step process necessary? Instead, just send a request for help along with any location information in the first message. The second site can act on it immediately if they so choose. Of course, that's only half an order of magnitude improvement in speed or baseline size, so it's still SOL time.
You seem to miss the fact in my preceeding section that the solution is genuinely unidentified. Determining the thrust takes three equations:Junghalli wrote:How short is short? A low thrust drive system would need a burn lasting hours or days at least to get any significant velocity. I'd think that would leave you plenty of times to do stuff like, say, track the changing distance between the ship and several of your own platforms with parallax and use that to calculate the probable trajectory.
The enemy can do a long series of tiny burns, of course, but that still leaves the necessity for many thousands of tiny flashes. A few hundred or thousand such flashes in close proximity to a known enemy base could be marked as suspicious, and from there observation could begin, with an eye toward putting together a cumulative profile from thousands of events rather than trying to determine everything from just one sighting.
F_x = Dm u_x
F_y = Dm u_y
F_z = Dm u_z
You know the mass flow, Dm, but only one component of the exhaust velocity, u (assuming you're able to get either, see below), and therefore only one component of the force. The pixel resolution of 369.5 km means you can move 184.7 km and not worry about moving into a new pixel. If the Daedalus-type rocket, with a burn of 38 seconds (not long enough at 1 AU for the ship to move out of a pixel), this would result in an uncertainty of its proper motion of up to 2 km/s in any direction (or more, depending on the mass — remember that Daedalus was intended to go interstellar; in-system doesn't need nearly as much mass). You do not know where to look.
And even if you are somehow able to perform this trick, the enemy facility can simply turn on a big ol' flashlight and blast you in the face with light sufficient to drown out any schanannigans. If it did this regularly, you'd never be able to tell when that ship lifted off.
Finally, barring that, the ship could simply use an orbital facility to its advantage and simply slingshot itself away from the station, using the much more massive station itself as its reaction mass. There'd be no exhuast to observe, and no outward sign that anything had launched.
There's a big difference between imaging Pluto and an incoming enemy ship: we know where Pluto is. We can take a snapshot anytime we want and be almost certain that it is, in fact, Pluto. Not so with an incoming ship that might be confused for a fleck of nearby dust. We don't know where the enemy ship is, or even that it's out there to be found, until we find it.aimless wrote:Why are we assuming we need 100 pJ in 1 second? Which figures are correct, yours or GMTs? To quickly requote the pertinent entry:
Basically saying that you can have detection several orders of magnitude less than the 100 pJ you're asking for.