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An artificial satellite is revolving round a planet of mass M and radius R in a circular orbit of radius 'r' . If its period of revolution T obeys Kepler's law i.e. T^(2)propr^(3). What is relation for the period of revolution in terms of R,r and "g" the accelerations due to gravity on the planet ? |
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Answer» `T=kr^(3/2)R^(1/2)g^(1/2)` `:.Tpropr^(3//2)...(2)` ALSO let `Tpropg^(a)R^(b)` `:.Tpropr^(3//2)g^(a)R^(b)` Putting the DIMENSIONS `M^(0)L^(0)T^(1)=k[L]^(3//2)[L^(1)T^(-2)]^(a)[L^(1)]^(b)` `=kL^(3//2+a+b)T^(-2a)` Comparing the dimension `3//2+a+b=0` `3//2-(1)/(2)+b=0` `:.b=-1` `-2a=1` `a=-(1)/(2)` `:.T=kr^(3//2)g^(-1//2)R` `=(k)/(R)sqrt((r^(3))/(g))` HENCE `(C )` is correct. |
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