The ancient Greek astronomer Aristarchus of Samos was the first to attempt to measure the relative distances of the Moon and Sun from Earth. He did this around 250 BC.

While his methods were not completely accurate, his work marked a significant step in understanding the scale of our solar system. He observed the Moon during a half-moon phase and used geometry to estimate the distance.

It's important to note that:

* His measurements were significantly off due to limitations in his observation techniques and the lack of accurate instruments.

* Later astronomers, such as Hipparchus and Ptolemy, built upon his work and made more accurate estimations.

Aristarchus's attempt, however, is crucial because it represented the first serious attempt to measure the distances in our solar system.