The Planet Problem
Let's somewhere there is a star called Stella. There are two planets orbiting Stella - Planet A and Planet B. Their orbits are perfectly circular. Planet A has the outer orbit, and it takes it 8 years to do a complete circle. Planet B has the inner orbit, with a full circle taking 6 years. At the day our problem starts, the planets are positioned at a perfect right angle, the vertex of the angle being the Stella. Planet A is positioned directly under Stella, while Planet B is directly on the right. How many years will pass until Stella, Planet A, and Planet B are in a line?
Details:
- Planet A and B must be on the same side of Stella for the answer to be correct.
- Both planets spin clockwise.
The answer is 18.
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1 solution
The answer is yes because: as 18 years is divisible by 6, Planet B will be strictly where it started off. As Planet A has an orbiting time of 8 years, and 18 is divisible by 8 with a remainder of 2, it will have completed two full circles, ending up where it started off, and then use the remaining 2 years two complete 1/4, ending up strictly on the right of Stella. In that way, the two planets are in line, strictly in the right of Stella.