Exoplanet is a planet that orbits a star different from our Sun.
Are there any planets (that we know of) which orbit something else? (Like different giant planet or black hole or maybe neutron star.)
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The very first exoplanets discovered were found orbiting a type of neutron star known as a pulsar. https://en.wikipedia.org/wiki/Pulsar_planet
There have also been planets found orbiting brown dwarfs. https://en.wikipedia.org/wiki/Brown_dwarf#Planets_around_brown_dwarfs
This is a brief argument from reasonable expectation, not experimental data.
There is good evidence that stars and planets form from interstellar dust clouds which are gravitationally unstable. If such a cloud is large enough then eventually a star would form. But I guess that if the cloud were of intermediate size then stuff could gather together into large ball-shaped lumps without ever getting pressure and temperature high enough for self-sustaining fusion reactions. So then you would have 'planets' without a star. Such planets could, I guess, include big rocky or watery bodies. Presumably they would all orbit and crash into one another in some complicated way to begin with, and I guess it is possible that they could eventually settle to a planetary system, since this has happened in many other cases involving stars.
This is, then, a reasonable guess from a non-expert. I would be interested to know if it proves to be wrong. (One could study this using simulations of course).
Here is a quote from Wiki concerning rogue planets:
"They found 474 incidents of microlensing, ten of which were brief enough to be planets of around Jupiter's size with no associated star in the immediate vicinity. The researchers estimated from their observations that there are nearly two Jupiter-mass rogue planets for every star in the Milky Way."