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How is it confirmed that a radiation source (not in visible light) is either terrestrial or celestial?

If in-depth explanation and/or references are possible, I would be grateful.

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There's a few indicators where a source is located:

Direction: Radio waves are just like light waves only with longer wavelength: you have to look into the direction of the source in order to see it. Terretrial sources usually are not high up in the sky.

Apparent movement: Another important aspect is Earth's rotation: the sky rotates with respect to Earth's surface. Thus if the source moves with the rotation speed of Earth and remains stationary in a celestial reference frame, it is very likely a source outside of Earth - and vice versa.

Location / Parallax: If you have several receivers, they will disagree on the direction a signal comes from, but will agree much better the further away a source is. Celestial sources are far away enough that the direction will be (nearly) identical. The amount of disagreement, the so-called parallax gives you a geometric indicator about the distance to the source.

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To planetmaker’s excellent answer, add periodicity. This is useful if you can’t measure direction at all.

A signal whose intensity varies regularly over a 24-hour period is likely to be terrestrial.

A signal whose intensity varies regularly over a 23-hour-56-minute period is likely to be celestial.

For signals which (for whatever reason) can only be observed at a particular time of day - say, midnight - a 12-month period suggests “celestial” but you have to be careful because the weather has a 12-month period too, in most places.

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