Given: Diameter (D) = 3474 km
∴ Radius of moon (R) = 1737 km
= 1.737 × 106 m
Distance from Earth r = 3.84 × 108 m
To find: Solid angle (dΩ)
Formula: dΩ = \(\frac{dA}{r^2}\)
Calculation:
From formula,
dΩ = \(\frac{\pi R^2}{r^2}\) ……..( cross-sectional area of disc of moon = πR2)
dΩ = \(\frac{\pi\times(1.737\times10^5)^2}{(3.84\times10^8)^2}\)
= \(\frac{3.412\times(1.737)^2\times10^{10}}{(3.84)^2\times10^{16}}\)
= antilog{log(3.142) + 2log(1.737) – 2log(3.84)} × 10-6
= antilog {0.4972 + 2(0.2397) – 2(0.5843)} × 10-6
= antilog{0.4972 + 0.4794 – 1.1686} × 10-6
= antilog{\(\overline{1}\) .8080} × 10-6
= 6.428 × 10-1 × 10-6
= 6.43 × 10-5 sr
Solid angle subtended by moon at Earth is 6.43 × 10-5 sr