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Currently, most explorations about new planets are pointing to area outside Neptune's orbit, but how about inside Mercury orbit? Can we say for certain there are no planets inside Mercury's orbit?

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Yes, Vulcanoids larger than 5.7 km diameter are considered to be ruled out: A Search for Vulcanoids with the STEREO Heliospheric Imager.

An object sufficiently large to be called "planet Vulcan" would change Mercury's orbit in a detectable way by gravity.

So, there are two lines of evidence, that such a planet doesn't exist.

More to read in Wikipedia: https://en.wikipedia.org/wiki/Vulcan_(hypothetical_planet)

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