The Interplanetary Alignment Celebration Day

Classical Mechanics Level pending

In the XYZ-11 planetary system there are two planets, of which the closest to the XYZ-11 star is inhabited. It takes 1.5 terrestrial years for the inner planet to make a revolution around the star, while it takes 2.5 terrestrial years for the outer planet.

On the inner planet, \( \eta \beta \), a big celebration is made every time the two planets are aligned. How many terrestrial years does it take for this event to take place?

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