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About a decade ago, I attended a conference inaugurating the campus of New York University in Abu Dhabi along with a colleague from Princeton University, Ed Turner. The conference included a tour through the neighborhood, during which the local guide bragged that their city lights can be seen all the way from the moon. Ed and I looked at each other and wondered: from how far away could the Hubble Space Telescope (HST) detect city lights?

During the following day, we calculated that the Hubble Deep Field could notice a city like Tokyo on objects in the Kuiper belt at 30–50 times the Earth-sun separation. But can we distinguish artificial lights from natural reflection of sunlight if they have a similar color?

In answering this question, Ed and I stumbled across a key insight concerning the dependence of the observed flux on the distance of the light source. The flux of reflected sunlight declines inversely with the square of the reflector’s distance from the sun (regarding the sunlight intercepted by it) times the square of its distance from us (for the light we receive). For sources very far away, the product of these factors implies dimming inversely with distance to the fourth power. On the other hand, an artificial source that produces its own light acts like a light bulb and dims only inversely with the square of its distance from us. By checking whether a Kuiper belt object dims inversely with distance to the second or fourth power as it recedes away along its orbit, one can infer whether it emits its own light.

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