question_answer 60)

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

Answer:

                  Solid angle subtended by the sun at a point on earth, \[\Omega =\frac{\pi R_{S}^{2}}{R_{SE}^{2}}\]                                 Solid angle subtended by the moon at appoint on earth \[\Omega =\frac{\pi R_{m}^{2}}{R_{ME}^{2}}\].                 \[\therefore \]\[\frac{\pi R_{S}^{2}}{R_{SE}^{2}}=\frac{\pi R_{M}^{2}}{R_{ME}^{2}}\] or \[\frac{{{R}_{s}}}{{{R}_{M}}}=\frac{{{R}_{SE}}}{{{R}_{ME}}}\]                 \[\therefore \] \[\frac{\text{Radius}\,\text{of}\,\,\text{the}\,\text{sun}}{\text{Radium}\,\,\text{of}\,\,\text{the}\,\,\text{moon}}\]                 \[\text{=}\frac{\text{Distance of the sun from the earth}}{\text{Distance of the moon from the earth}}\]