What’s the closest earth like planet or moon to earth we have discovered in our galaxy?
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Well, this really does depend on what is considered an Earth-like planet. For instance, one could conclude that Venus is an Earth-like planet based off of them being similar in mass and also in regards to the similarities in radius. As for Earth-like moon, Titan would be a great candidate if located inside the so-called Goldilocks zone.
Counting planets outside our solar system, the nearest planet I could find was about 4.243 light-years away. Astronomers found it on August 24, 2016. It is a rocky planet in the habitable zone of its parent star Proxima Centauri, the closest star to Earth. The name of the planet is Proxima b, this planet is approximately 1.3 times the mass of Earth and possesses an orbital period of roughly 11.2 Earth days.
However, since Proxima Centauri is classified as a red dwarf this casts reasonable doubts on whether Proxima b is habitable. To be habitable Proxima b would have to deal with low stellar flux, which causes a high probability of tidal locking, and high stellar variation.