It's impossible to give an exact number, but astronomers estimate there are hundreds of billions of stars in the Milky Way galaxy. Since many stars are likely to have planets orbiting them, it's reasonable to assume there are billions of solar systems within our galaxy.

Here's a breakdown:

* Stars: The Milky Way has an estimated 100-400 billion stars.

* Planets: Recent studies suggest that most stars have at least one planet orbiting them.

* Solar Systems: This means there could be a similar number of solar systems to stars, potentially reaching into the trillions.

However, it's important to remember that these are just estimates. We've only been able to directly observe a small fraction of planets, and there are likely many more undiscovered planets and solar systems.