Of a fleet (of worlds) passing in the night

A recurring theme in reader emails and some reviews of Fleet of Worlds series books is, "Why don't the [your choice of crafty Known Space species] notice the Fleet as it barrels through space? Even today, astronomers see stars across great distances, and the worlds of the Fleet (with one exception, discussed below) are lit by artificial suns.

The traditional answer (found in Ringworld, long before my entry into Known Space) is that no one thought to look between the stars. People (and Kzinti, and ...) hunted for Puppeteers on some as-yet undiscovered conventional world orbiting a sunlike star.

What about before the Fleet set "sail" (not that, pre-Ringworld, anyone in Known Space suspected world-moving technology could exist)? Puppeteers had long ago relocated their planets to new orbits far from their sun -- which had undergone late-in-life expansion into a red giant. Any artificial suns close to planets would be very hard to spot from a great distance against the backdrop luminosity of a red giant!

In short: the Fleet went undetected because everyone looked in the wrong places.

But there's a second, more quantitative answer. I'm not sure it needs to be spelled (numbered?) out in the context of storytelling, but I think it's worth relating somewhere. So here goes.

The short answer is: the artificial suns are small.

Life on Earth depends on sunlight -- but Earth does not receive much of the sun's light! The two relevant parameters:

• Earth's average orbital radius (149.6 million kilometers, in scientific notation, 1.496 E8 km)
• Earth's radius (6,378 kilometers, aka 6.378 E3 km)

A sphere sized with Earth's orbital radius has a surface area of 2.812 E17 km sq. Earth's cross section (defined by the intersection of a plane with Earth's equator) is a mere 1.278 E8 km sq.

The ratio is (1.278 E8) / (2.812 E 17) = 4.5 E -10 (and note the negative exponent!)

Earth intercepts about 1/20th of a billionth of the energy emitted by the sun.

The worlds of the Fleet of Worlds are Earth-like. To a first approximation then, the Puppeteers need to supply each world with as much energy as the solar energy Earth gets. If the artificial suns orbit close to the worlds they warm, then about half of the energy they put out will reach the world below. So, (in round numbers), the artificial suns that warm and light one world will together emit 1/10th of a billionth of the energy emitted by our sun. Four such artificially maintained worlds will emit 4/10s of a billionth of the energy emitted by the sun.

The fifth world, the Puppeteer home world [Hearth], is heated solely by its own industrial waste heat (derived from fusion using heavy hydrogen in Hearth's oceans). To a first approximation, that involves as much energy as is used to light and heat the Fleet's farm worlds. So: we're up to 5/10s of a billionth of solar output: 5.0E-10 of solar output.

For comparison, the smallest, coolest red dwarf stars emit only about 1 / 10,000 the energy of what our sun emits. The energy emitted by all five worlds of the Fleet is but 5 millionths as energetic as the dimmest red dwarf!

So there you have it: another reason not to notice the Fleet of Worlds, unless the (insert here: name of preferred high-tech species) is very close and very observant.

All that said, what if you happened to get close? (The Fleet is far from Earth, far from the boundaries of what humans arrogantly call Known Space). Would you -- especially with far-future advanced instruments -- see the worlds of the Fleet? Identify them as something very special?

Hell, yes.

• Relative to the galaxy as a whole, they're zipping along at relativistic speeds. 
• The light they emit varies very quickly (because the artificial suns orbit close to the worlds, the worlds orbit around each other, and the emissions of the suns vary to mimic day/night and annual cycles). 
• One world, lacking suns, puts out as much energy as any of the others, but mostly in infrared (the waste heat). 

No way would the discoverers not be very curious.

And no wonder the Puppeteers got more terrified than usual once they abandoned their traditional hiding place ...