Solution Found!
a) Using elementary Newtonian mechanics find the period of
Chapter 8, Problem 8.7(choose chapter or problem)
a) Using elementary Newtonian mechanics find the period of a mass m1 in a circular orbit of radius r around a fixed mass m2. (b) Using the separation into CM and relative motions, find the corresponding period for the case that m2 is not fixed and the masses circle each other a constant distance r apart. Discuss the limit of this result if m2 oo. (c) What would be the orbital period if the earth were replaced by a star of mass equal to the solar mass, in a circular orbit, with the distance between the sun and star equal to the present earthsun distance? (The mass of the sun is more than 300,000 times that of the earth.)
Questions & Answers
QUESTION:
a) Using elementary Newtonian mechanics find the period of a mass m1 in a circular orbit of radius r around a fixed mass m2. (b) Using the separation into CM and relative motions, find the corresponding period for the case that m2 is not fixed and the masses circle each other a constant distance r apart. Discuss the limit of this result if m2 oo. (c) What would be the orbital period if the earth were replaced by a star of mass equal to the solar mass, in a circular orbit, with the distance between the sun and star equal to the present earthsun distance? (The mass of the sun is more than 300,000 times that of the earth.)
ANSWER:Step 1 of 7
Part (a)
The gravitational forces between two masses can be represented as,
The centripetal force acting on first mass can be given as,
The gravitational force is balanced by the centripetal force which can be represented as,
