question_answer 13)

How will you 'weigh the Sun', that is estimate its mass ? You will need to now the period of one of its planets and the radius of the planetary orbit. The mean orbital radius of the Earth around the Sun is . Estimate the mass of the Sun.  

Answer:

To estimate the mass of the Sun, we require, the time period of revolution T of one of its planets (say the Earth). Let be the masses of Sun and Earth respectively and r be the mean orbital radius of the Earth around the Sun. The gravitational force acting on Earth due to Sun is  Let, the Earth be moving in circular orbit around the Sun, with a uniform angular velocity , the centripetal  force acting on Earth is As this centripetal force is provided by the gravitational pull of Sun on Earth, so  Knowing r and T, mass My of the Sun can be estimated. In this question, we are given,