If a star appears to wobble back back and forth, or its light seems to change in brightness, what might be the cause?

The first method, known as the wobble method, looks for changes in a star's relative velocity caused by the gravitational tug of a nearby planet. ... If a planet's orbit crosses between its parent star and Earth, it will block some of the light and cause the star to dim.

Explanation:

We all know that the chains of gravity shackle a planet to its star. That star's enormous gravitational influence keeps its planetary family in orbit. But gravity works both ways: as the planets sweep around in their orbits, they tug on their parent stars to and fro, causing those stars to wobble

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