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No. A star's class on the main sequence is ultimately predetermined by its mass, so a star cannot change its position on the main sequence. Epsilon Eridani is about 82% the mass of the sun, which limits it to a lower rate of fusion and thus a lower temperature and luminosity than a G-type star like the sun. Epsilon Eridani's only change in class will come when it leaves the main sequence to become a red giant.

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Q: Will the K-type Epsilon Eridani star eventually evolve into a G-type main sequence star like the Sun?
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