Kepler's third law states that square of period of revolution (T) of a planet around the sun is proportional to third power of average distance r between the sun and planet, i.e. $$T2$$ $$=$$ $$Kr3$$, here K is constant. If the masses of the sun and planet are M and m respectively, then as per Newton's law of gravitational force of attraction between them is $$F=GMmr2$$, here G is gravitational constant. The relation between G and K is described as [CBSE AIPMT $$2015$$]

Question

Kepler's third law states that square of period of revolution (T) of a planet around the sun is proportional to third power of average distance r between the sun and planet, i.e. $$T2$$ $$=$$ $$Kr3$$, here K is constant. If the masses of the sun and planet are M and m respectively, then as per Newton's law of gravitational force of attraction between them is  $$F=GMmr2$$, here G is gravitational constant. The relation between G and K is described as  [CBSE AIPMT $$2015$$]

Infinity Learn · Accepted Answer

The gravitational force of attraction between the planet and sun provides the centripetal force,i.e.,       $$GMmr2=mv2r$$⇒$$v=GMrThe$$ time period of planet will $$beT=2$$$$π$$rv⇒  $$T2=4$$$$π$$$$2r2GMr=4$$$$π$$$$2r3GM$$                                            …(i)Also$$, from the Kepler's third law,   $$T2=Kr3$$                        …$$(ii)From$$ Eqs. $$(i) and (ii), we $$get4$$$$π$$$$2r3GM=Kr3$$⇒$$GMK=4$$$$π$$$$2$$

Best Courses for You

Detailed Solution

courses

Get Expert Academic Guidance – Connect with a Counselor Today!

best study material, now at your finger tips!

download the app

Download the App