Trigonometric parallax is a powerful method to work out the distance of celestial bodies, and it was used in the past to measure the distance of the Moon, Venus, Mars and nearby stars. We set up an observation campaign for high school and undergraduate students with the purpose to measure both the Moon's and Mars' parallax. To have a large enough baseline (or basis), we took simultaneous pictures of these celestial bodies from Italy and South Africa. Then, we estimated the apparent shift relative to background stars and, via trigonometry, we worked out the distances of the Moon and Mars. Reliable results were found. (Contains 7 figures and 8 footnotes.)