Earlier quoted context omitted.
Trash is full of valuable materials! Right now it may not be economical to recover those, but I would be surprised if we aren't mining our landfills in the next 100 years. That said, the CO2 emissions from launching anything non-essential into orbit are huge, I'd wait until we have a space elevator to (intentionally) throw trash into space.
Or a rail gun. My understanding for why we don't use those for spacecraft is because people and fine machinery can't take the Gs. Trash could.
https://en.wikipedia.org/wiki/Project_HARP
https://en.wikipedia.org/wiki/Project_Babylon
[Edit] Also the German V-3. An important note is that the V3 and Babylon (unsure of HARP) were designed to have multiple charges go off as the projectile proceeded down the barrel, which gives an acceleration profile more like a railgun than a traditional cannon.
https://en.wikipedia.org/wiki/V-3_cannon
Solid-fuel rocket boosters were used instead of explosive charges because of their greater suitability and ease of use. These were arranged in symmetrical pairs along the length of the barrel, angled to project their thrust against the base of the projectile as it passed. This layout spawned the German codename Tausendfüßler ("millipede").