Q.The following photographs are taken from the recent lunar eclipse which occurred on January 31, 2018. Is it possible to prove that Earth is a sphere from these photographs?

What happens during a total lunar eclipse. The Sun, Earth and Moon line up, and the Moon passes through the Earth's shadow. The fully-dark inner region of that shadow is the umbra; a lighter, partially-shadowed outer region is the penumbra. A Moon fully inside the umbra typically appears reddish (sunlight bent through Earth's atmosphere still reaches it), and as it exits the umbra it briefly appears as a crescent shape.

Measuring the umbra's size from a photograph. By photographing the eclipse and measuring the apparent radius of the umbra shadow ($R_s$) against the Moon's own apparent radius ($R_m$) directly on the image, their ratio can be found (about $R_s/R_m\approx2.56$, from the January 2018 eclipse visible from Tamil Nadu). Since the Moon's true radius is already known ($R_m=1737\ \text{km}$), this ratio immediately gives the umbra's true radius: $R_s\approx2.56\times1737\approx4446\ \text{km}$, within about $3.5\%$ of the correct value of $4610\ \text{km}$ -- an impressively accurate result from a very simple photographic measurement, with the accuracy improving with a higher-quality telescope image. …