What observation confirmed to Galileo that the points of light were orbiting Jupiter rather than being distant, fixed stars?

Answer

They occasionally disappeared, suggesting they were eclipsed by Jupiter

The observation that these small points of light would periodically vanish indicated that Jupiter itself was passing between them and Galileo's telescope, proving they were satellites circling the planet.

What observation confirmed to Galileo that the points of light were orbiting Jupiter rather than being distant, fixed stars?

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