question_answer

The motion of planets in the solar system is an example of the conservation of :

A)  mass    

B)                        linear momentum                         

C)  angular momentum      

D)  energy

Correct Answer: C

Solution :

From Keplers second law a line joining any planet to the sun sweeps out equal areas in equal times, that is, the areal speed of the planet remains constant. dA = area of curved triangle SAB \[\pi \] \[{{Q}^{2}}(4\pi {{\varepsilon }_{0}}{{a}^{2}})\] The instantaneous areal speed of the planet is \[-{{Q}^{2}}(4\pi {{\varepsilon }_{0}}{{a}^{2}})\] where \[{{Q}^{2}}/(2\pi {{\varepsilon }_{0}}{{a}^{2}})\] is angular speed. Let J be angular momentum of planet about sun \[2\mu F\] \[{{T}_{2}}>{{T}_{1}}\] From Keplers law areal speed is constant therefore angular momentum J is constant. Hence, Keplers second law is equivalent to conservation of angular momentum.