Let's examine the problem of minimum detectability. A starship will probably have two basic long-range sensory systems:
A) Radio antennae: A hostile starship will be a significant source of radio and microwaves (if active,) and large radio receiver surfaces are much easier to build and deploy than large receiver surfaces for lower portions of the EM spectrum.
B) IR/optical telescopes: A hostile starship will tend to glow brightly in the IR portion of the spectrum, and will also reflect ambient light. If it's got a large, powerful engine, and that engine is active, we can expect to see the drive plume as well.
You could speculate that a starship might also carry an X-ray/gamma ray telescope, since matter/antimatter annihilation produces well-characterized gamma rays. A large enough starship could carry a neutrino detector, since just about any conceivable high-density energy generation scheme will produce copious neutrinos as a byproduct. However, the highly penetrative nature of neutrinos, and the fact that the cosmos is loaded with neutrino sources would suggest that the signal-to-noise ratio of a neutrino telescope is going to be abysmally low. Gravity wave detectors are also out for much the same reasons, although both of these instruments may make a certain amount of sense aboard fixed early-warning platforms.
So let's examine the optical telescope. Our starship's optical telescopes aren't going to be very big, since huge mirrors with the fast focal-ratios needed for wide-field imaging are difficult to accurately figure, large telescopes require large housings, and tend not to be very easy to swing around. And we want the widest field possible.
Fortunately, NASA's provided us with an ideal example of a long-range, wide-field imaging telescope. The Kepler Mission features a wide-field telescope with about 1 meter of effective aperture. It feeds photons to a 95 megapixel camera watching a ten degree wide swath of the sky. For an optical telescope, this is a stupendously wide field of view. It works out to be 105 deg2
. However, the area it must cover is 20,626.48
. A 'mere' 196 images. Depending on how long your exposure time is, and the time required to slew the telescope over to the next patch, this might take a while.
An extremely sensitive sensor, such as the one used on the New Horizons spacecraft's LORRI imager picked up Pluto in a 1 second exposure. Pluto can be modeled as a 4.2 TW light source (Average albedo of 0.575, radius of 1151 km,) for an irradiance of just 1.89x10-8
at the 4.2 billion kilometer distance that New Horizons was at when it first imaged Pluto. The New Horizons imager has an aperture of a mere 0.2 meters. Meaning Pluto illuminated one pixel of the detector with 2.38x10-15
W of power. Our starship-mounted telescope has about 25x the light gathering area, so it could match this feat at roughly five times the distance.
So, we could take 1 second exposures and be golden, right? Well, not exactly. We want to reduce the noise we get in our images. Some we reduce by circulating coolant through our telescope. Much of it we'll reduce by stacking
multiple exposures, so we can mathematically eliminate the noise. So we'll take 15 exposures, then bump the telescope to the next patch of sky and wait however long it takes for the vibrations to damp out. We'll assume this takes another 15 seconds. It'd probably take much less, but this gives us 30 seconds of time spent on each patch of the sky. So our single telescope will take 98 minutes to scan a hemisphere's worth of sky. Put four on the top side of the hull, and we could be done in 25 minutes. Bear in mind that the sensor we're talking about is tuned to a very low-light environment. Less-sensitive sensors will require longer exposure times. If we took a modern off-the-shelf astronomical imaging CCD which requires around 450 seconds of total exposure time (30 seconds per raw frame x 15 exposures to stack) to image similarly dim objects with similarly fast optical systems, it would take over a day for our one telescope to do this "all-sky" scan.
So this tells us we could spot every object the size of Pluto within a 21 billion kilometer radius, and could do it in under 100 minutes if our starship had an especially cheap sensor suite. How about something smaller, like a Star Destroyer? Take two admirals, Jamie and Adam. Jamie would like to find Adam's ISD before Adam can get close enough to mess Jamie's shit up. (I've picked the ISD because it can be modeled as a white-painted triangle with an area of 0.812 km2
. Conveniently, the albedo of white paint is 0.5 to 0.9, and Star Destroyer white is on the lower end of this . . . so we'll arbitrarily give it the same albedo as Pluto.)
So, if we start Adam out at the orbit of Pluto, his ISD looks like a 409 kilowatt light-bulb. Plug in the minimum irradiance derived above, and he's detectable at a mere 6.56 million kilometers away.
Since there's nothing of merit out at Pluto, let's start him somewhere closer, say the orbit of Mars. Now Adam's ISD looks like a 286 megawatt light-bulb, and could be seen by our sensor at 173.5 million kilometers away. However
, his apparent size at that distance is 0.0019 arc-seconds. The optics of a 1 meter telescope won't resolve a point-source of light to any better than 0.25 arc-seconds. We'll see him, but as a dim point of light.
Now let's add in his thermal emissions. Let's assume that Adam is trying to be clever and is trying to slip in with engines and reactors cold. However, because his crew likes living, he's got a base temperature of 273.15K for a black body irradiance of 315.64 W/m2
. In the far infrared, his ISD looks like a 256 megawatt bulb, assuming the side facing Jamie happens to be all radiator. The distance he becomes detectable in the far-IR is actually a bit closer than the distance he becomes detectable in visible. Useless at Mars, but out at Pluto, he'll be detectable over 130 million kilometers further away in far-IR than he is in visible. If he's got some freaky cooling and insulation, along with magic stealth that gets him down to Darth Wong's postulated 7 W/m2
, he still looks like a 5.7 megawatt bulb in far-IR, and our telescope sensor will spot him at 24.5 million kilometers off.
Astronomically speaking, these are pretty short distances. If Adam drops out of hyperspace around Pluto and accelerates towards Jamie at Mars, he's going to have enough burn time to be going fast enough to force an engagement by the time Jamie can pick him up. And remember, at these distances, Adam's ship is going to appear to be a star-like point in our survey telescope. If he's coming head-on to Jamie, we'll have to filter him out from all the other dim star-like points out there. So we may not actually catch Adam until a few iterations of the scan after we might've first spotted him, at which point, his growing brightness will make him stand out.