* Natural Satellites (Moons): There are many natural moons orbiting the planets in our solar system. The exact number depends on how you count small, recently discovered objects. But we're talking about hundreds.

* Artificial Satellites: These are the ones humans have launched. There are thousands of these orbiting Earth, and a handful orbiting other planets (like Mars and Venus).

So, to answer your question directly, it's impossible to give a single number. It would be the sum of:

* Natural Satellites: Hundreds, maybe thousands.

* Artificial Satellites: A few thousand around Earth, and a handful around other planets.

Let me know if you'd like a more detailed breakdown of the moons around each planet!