Here’s a procedure for observing the curvature of the Earth right where you stand, assuming you select a good spot, without getting on a rocket that takes you out beyond the atmosphere.
Or, if one is more ambitious, one may also calculate how much of a distant feature gets obscured by the curving surface of the globe and then compare this estimate with real-world observations.
There are variations of these procedures scattered piecemeal across the web. Although most of them are accurate, I’ve found them to be fragmentary (pieces scattered) and either overly complex or lacking in detail. I also wanted to work out the geometry and algebra for myself and develop a spreadsheet that does the calculations for any location desired. I also describe a supplementary procedure for calculating the radius of the Earth based on a sighting of a distant tall feature.
Yes, you too can do low-tech geodesy like Persian scholars did a millennium ago or like the ancient Greeks of over 2 millennia ago. Yes, a low-tech, old-school, analog activity! Click down below on the PDF instructions and on the Excel spreadsheet for performing the calculations.