I had the same thought: if there was another planet inside mercury's orbit, that would be the mostest closest planet to all the planets, stealing mercury's status, and so you keep iterating on that until you reach smallest and smallest orbits around the sun center of mass (which is inside the sun).

So, if you when you say "the sun" you mean the sun surface, then yes, the sun is always the mostest closest celestial body, to all planets

Why do you complicate it talking of surface vs center of sun. Sun is sun. That's it.

just because it made it easier for me to reason about the fact that since the sun has some actual width it's exactly equivalent to a body that would orbit at that distance. If you frame it that way then it's rather obvious that the sun also fits the bill as the "mostest closest body" (albeit not planet)

The center of the sun has the same property, with simpler 0 size orbit.

it's not intuitively clear to me whether that is on average closer to the earth or if it's on average exactly as far as something orbiting around that center.

Furthermore, since the sun is also orbiting around the shared center of mass of the whole solar system, this displacement albeit very small, is still enough for me to not intuitively understand if it makes the sun's center of mass closer or farther away on average than the closest orbiting body to the sun

Yes, a hypothetical planet located at the centre of the sun would be every planet's closest neighbour, by virtue of never getting as far away as others.

Nit: located at the gravitational centre of the solar system. Which is not the perfect center of the sun (though still inside it) since all the planets pull on the sun too.

Since that gravitational center, and the center of the pairwise systems is not the same, I wonder if a planet at that place is really the best solution.

The concept of a hypothetical planet at the centre of the sun made me laugh. Cheers

I don't understand why we need to introduce this planet. Is the Sun not our neighbor? And it's closer than Mercury, isn't it?

> Is the Sun not our neighbor? And it's closer than Mercury, isn't it?

It's not half the time and it is half the time. If you include the Sun as well as one of the possible answers (which I'd argue you shouldn't because neighbour implies same significance, not higher), the answer would've been an even split between Mercury and the Sun (on a large enough time scale).

If Mercury's year somehow lasted longer than a year on another planet, only then would Sun be the clear winner.

Actually the sun still edges out Mercury.

Think of it this way: If we take the Earth as stationary and just look at the respective motions of the Sun and Mercury, then the Sun is also (roughly) stationary* and Mercury moves around and around it, sometimes close to us and sometimes far.

Now, if Mercury actually yo-yo'ed through the Sun, then you'd be right: exactly half the time it would be closer to us, and half the time it would be further from us.

But it doesn't yo-yo through the Sun, it moves in a circle. When it's 90º from us and the Sun, it's still further away from us than the Sun is. So it has to get even closer before it's equidistant. So it's actually closer to us only less than half of the time.

*Yes, the Sun would also appear to orbit around the gravitational center of mass, but this doesn't affect the thinking above.

Other posters seem to be treating planets as point masses but not the sun.