College Physics 10th Edition by Raymond Serway,Chris Vuille

Exercise 24

As the Earth moves around the Sun, its orbits are quantized. (a) Follow the steps of Bohr's analysis of the hydrogen atom to show that the allowed radii of the Earth's orbit are given by
where n is an integer quantum number, M S is the mass of the Sun, and M E is the mass of the Earth. (b) Calculate the numerical value of n for the Sun Earth system. (c) Find the distance between the orbit for quantum number n and the next orbit out from the Sun corresponding to the quantum number n + 1. (d) Discuss the significance of your results from parts (b) and (c).