Denounce might be an option, but that usually refers to a commonly held belief being disproved. It also suggests its subject is non-scientific.
The other users suggested disprove and refute (which I like), which apply well in scientific experiments. More specifically, refute suggests you disproving a previously held belief, while disprove suggests your results turning out against a certain hypothesis or outcome.
In your example: "By careful observation, I have __ that the Earth orbits the sun.", I would probably go with disprove myself.
Definitions:
- disprove — to prove that something is false
- refute — to prove a statement or theory is wrong; disprove
- denounce — publicly declare to be wrong; inform against