Question

During a total solar eclipse the moon almost entirely covers the sphere of the sun. write the relation between the distance and sizes of the sun and moon.

Answer 1

R_me = distance of moon from earth 

R_se = distance of sun from earth 

Let θ be angle made by sun and moon and 

A_s= area of sun, 

A_m= area of moon

⇒ \( θ=\frac{A_s}{R^2_{se}}=\frac{A_m}{R^2_{me}}\)

⇒ \( θ=\frac{\pi R^2_s}{R^2_{se}}=\frac{\pi R^2_m}{R^2_{me}}\)

⇒\((\frac{R_s}{R_m})^2=(\frac{R_m}{R_{me}})^2\)

⇒ \(\frac{R_s}{R_m}=\frac{R_{se}}{R_{me}}\)