This is a tricky question! It depends on what you consider an "object." Here's a breakdown:

* Planets: 8 (Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune)

* Dwarf Planets: 5 officially recognized by the IAU (Pluto, Ceres, Eris, Makemake, Haumea)

* Moons: Hundreds, if not thousands, orbiting planets and dwarf planets.

* Asteroids: Millions in the asteroid belt between Mars and Jupiter, with many more throughout the solar system.

* Comets: Thousands, with a vast, undiscovered population.

* Dust and Gas: The solar system is filled with vast amounts of dust and gas, much of it orbiting the Sun.

So, the answer is: a LOT! We've only discovered a fraction of the objects that orbit the Sun.

It's a constantly evolving answer as we discover more and more celestial bodies with better telescopes and technology.