Estimate a Lunar Cycle

Pick a clear night and track the moon's phase over the next week. Day 1 it might be a thin crescent. By day 7 it is near first quarter, and by day 14 it is full. The complete cycle takes about 29.5 days — Earth's first calendar.

Try an estimation game. The Moon is 384,000 km away and about 3,474 km across. That ratio gives its angular size: 3474 ÷ 384000 ≈ 0.009 radians, or roughly half a degree. Hold a pencil at arm's length and its width covers about the same angle.

One week of watching the sky, and you have re-derived ancient astronomy.