question_answer 56)

                  (a) The earth-moon distance is about 60 earth radius. What will be the diameter of the earth (approximately in degrees) as seen from the moon?                 (b) Moon is seen to be of \[{{({\scriptstyle{}^{1}/{}_{2}})}^{o}}\] diameter from the earth. What must be the relative size compared to the earth?                 (c) From parallax measurement, the sun is found to be at a distance of about 400 times the earth-moon distance. Estimate the ratio of sun-earth diameters.                

Answer:

                  (a) \[\theta =\frac{\text{Diameter of earth}}{R}\]                 \[=\frac{2{{R}_{E}}}{60{{R}_{E}}}\]                 \[=\frac{1}{30}\text{red}\]                 \[=\frac{1}{30}\times \frac{360{}^\circ }{2\pi }\]                 \[=1.91{}^\circ \approx 2{}^\circ \]                 (b) Diameter of earth as seen from moon \[={{2}^{o}}\]                 Diameter of earth as seen from moon \[=\frac{{{1}^{o}}}{2}\]                 \[\therefore \]\[\frac{\text{Diameter of earth}}{\text{Diameter of moon}}=\frac{2{}^\circ }{1/2{}^\circ }=4\]                 (c) \[\frac{{{R}_{S}}}{{{R}_{M}}}=400,\] Now \[\frac{{{D}_{S}}}{{{D}_{M}}}=\frac{{{R}_{S}}}{{{R}_{M}}}=400\]                 Also \[\frac{{{D}_{E}}}{{{D}_{M}}}=4\]\[\therefore \]\[\frac{{{D}_{s}}}{{{D}_{E}}}=\frac{{{D}_{S}}/{{D}_{M}}}{{{D}_{E}}/{{D}_{M}}}\]                 \[=\frac{400}{4}=100\]