Lunar eclipse and measurements of shadow of Earth: On January 31, 2018 there was a total lunar eclipse which was observed from various place including Tamil Nadu. It is possible to measure the radius of shadow of the Earth at the point where the Moon crosses.
When the Moon is inside the umbra shadow, it appears red in colour. As soon as the Moon Schematic diagram of umbra disk radius exits from the umbra shadow, it appears in crescent shape.
By finding the apparent radii of the Earth’s umbra shadow and the Moon, the ratio of the these radii can be calculated.
The apparent radius of Earth’s umbra shadow = Rs = 13.2 cm
The apparent radius of the Moon = Rm = 5.15 cm
The radius of Moon Rm = 1737 km
The radius of the Earth’s umbra shadow is Rs = 2.56 × 1737 km ≅ 4446
The correct radius is 4610 km
The percentage of error in the calculation = \(\frac{46140 - 4446}{4610}\) x 100 = 3.5 %
The error will reduce if the pictures taken using a high quality telescope are used
