Q. 254.8( 8 Votes )

(a) The earth-moo

Answer :

(a) Given:

Distance between earth and moon = 60 x earth’s radius


The distance between the earth and moon can be treated as a radius of arc that is subtended by the diameter of the earth from the moon. Let θ be the angle subtended by the arc, R be the earth-moon distance and RE be the earth’s radius. Then,


2RE = length of the arc.


And distance between earth and moon = 60RE


Therefore the angle subtended by the arc




Therefore the diameter of earth as seen from earth will be 2°.


(b) Given:


Diameter of moon as seen from earth =


As calculated before the diameter of earth as seen from moon is approximately 2° and if moon is as seen from earth, then,



Therefore, earth’s diameter is 4 times that of moon’s diameter.


(c) Given:


Distance between sun and earth = 400 x earth-moon distance.


let rm � be the moon’s distance from earth and rS be the sun’s distance from earth, then we have



Let Ds, Dm � and De be the diameters of sun, moon and earth respectively. Since we know that the sun and the moon, appear to be the same size from the earth, we have




Also




Therefore, the sun’s diameter is 100 times larger than earth.


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