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"Well, as you heard in the courtroom, Alpha Centauri isn’t really one star — it’s actually three stars very close together. We call the three parts Alpha Centauri A, B, and C, in descending order of brightness. The Tosoks claim they come from a planet orbiting Alpha Centauri A, and I’m inclined to believe that. If they came from B, the principal lighting aboard their mothership would be orange instead of yellow."

"Okay."

"Well, Centauri A is a almost a twin for our sun. It’s what we call a G2V star, precisely the same spectral class as Sol, and—"

"Sol?"

Frank smiled. "Sorry. The word ‘sun’ is actually a generic term. Any star that has planets is a sun. Our sun’s proper name is Sol, after the Roman god of the sun."

Dale nodded.

"So, as I was saying," continued Frank, "Alpha Centauri A is actually damn near a twin for our own sun, Sol. It’s the same color, the same temperature, and so on. And it’s about the same age — actually, a little older. But there’s one significant way in which Centauri A differs from Sol."

"And what’s that?"

"Its brightness. Centauri A is an inherently brighter star — fifty-four percent brighter than our sun."

"So?"

"So even on cloudy days here, all the Tosoks wear those pop-in sunglasses. If they’re from a world of a brighter star, our dimmer sun shouldn’t bother them."

"Maybe they have a different atmosphere from us; maybe it’s not transparent like ours is."

Frank nodded, impressed. "That would be an excellent explanation, except for one thing: the Tosoks breathe our air without any difficulty, and when Clete went aboard their mothership, he breathed their air without trouble, too — and you saw in those videotapes that it was crystal clear."

"Well, then, maybe they orbit their sun farther out than we orbit ours."

They had come to a park bench. Dale motioned for them to sit down.

"Exactly," said Frank, lowering himself to the bench. "In fact, when I was talking to Kelkad about how long it would take to build replacement parts for the mothership, he got upset when I said two years — but he calmed down when Hask explained I meant two Earth years. The Tosok year is obviously much longer, and since Alpha Centauri A is about the same mass and size as Sol, to have a substantially longer year, the Tosok home world must orbit much farther out from it than we do from our sun."

"I don’t know anything about astronomy," said Dale, "but that sounds reasonable."

"Well, it is — sort of. Remember, Centauri A is the same size, but 1.54 times as bright as our sun. A planet orbiting the same distance from Centauri A as Earth is from Sol would therefore get 1.54 times as much light from it."

"Okay."

"But if you double the distance, you only get one quarter of the sunlight. So, a planet orbiting Centauri A at a distance of two AUs — two times the distance between Earth and Sol — would get one quarter of 1.54 times Sol’s light as seen from Earth. That works out to — let me think — something like forty percent of what we get."

"Well, that would explain why they always need sunglasses, even on cloudy days. But wouldn’t that also make their world much cooler than ours?"

Frank smiled. "For someone who doesn’t know anything about astronomy, you ask all the right questions. Certainly, Clete said the mothership’s air temperature, even outside the hibernation room, was only about fifty degrees Fahrenheit. But how far away from a G2V star can a planet be and still have a fifty-degree surface temperature? Well, the answer depends on how much carbon dioxide, water vapor, and methane there is in the atmosphere of the Tosok home world. See, those gases trap heat. You’ve heard of the greenhouse effect? It’s caused by excess amounts of them, all of which are clear, colorless gases. They’re the wild card in planetary positions. If you’ve got enough of a greenhouse effect, you could be much farther from our sun and still have surface temperatures comparable to those on Earth — in theory, there could be an Earth-like planet out in the orbit of Jupiter as long as it had enough greenhouse gases to trap sufficient heat."

"So there’s your answer," said Dale. "The Tosoks come from a planet that orbits much farther from its star than we do from ours."

"Ah, but you’re forgetting something when you say ‘its star,’ singular. Alpha Centauri is a multiple-star system. When Centauri A and B are at their closest to each other, they’re only eleven AUs apart — just about one billion miles."

Dale frowned. "So you’re saying the light from Centauri B would make things bright, even if the Tosok world orbited a long way from Centauri A?"

"No, no. Even at its closest approach, Centauri B would only appear about one percent as bright as our sun. That’s still thousands of times brighter than our full moon — meaning nights on the Tosok home world when A has set but B is still up are probably reasonably bright, but surely no brighter than our streetlights make our streets."

"Oh."

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