The earth revolves round the sun due to gravitational attraction. Suppose that the sun and the earth are point particles with their existing masses and that Bohr’s quantization rule for angular momentum is valid in the case of gravitation.

(a) Calculate the minimum radius the earth can have for its orbit.


(b) What is the value of the principal quantum number n for the present radius? Mass of the earth = 6.0 × 1024 kg, mass of the sun = 2.0 × 1030 kg, earth-sun distance =1.5 × 1011 m.


Given: Mass of the earth = me = 6.0 × 1024 kg


Mass of the sun = ms = 2.0 × 1030 kg


earth-sun distance = r =1.5 × 1011 m


Applying Bohr’s quantization rule for angular momentum



And due to gravitational force balancing centripetal force.



Using both the equations we get



And


(a) For minimum value of r, n=1



(b) For present radius



After substituting the values as above



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