is it possible to upgrade the software on a 2009 apple desktop computer

The oldest Macs that can run Catalina are the 2012 models.

"Early" and "Mid" 2009 iMacs can run no higher than macOS 10.11.X "El Capitan"

"Late" 2009 iMacs can run not higher than macOS 10.13.X "High Sierra." High Sierra is now out of date but has the advantage over El Capitan of most modern browsers still working with it.

You find whether your iMac is Early, Mid, or Late by doing "About this Mac..." from youe Apple menu:

If you have a Late 2009 model and would like to upgrade to High Sierra, the installer is available through this Apple Support article:

How to get old versions of macOS - Apple Support

A 2009 is VERY old by computer standards, it simply does not have the hardware to run more current versions of Mac OS. Before you ask, no the hardware cannot be updated. Your best bet is to upgrade to a more current Mac.

No, your Mac is just too old.