The variation in the speed of the planets in their orbits about the sun can be explained on the basis of the conservation of angular momentum .How?

Dear Student, 
Please find below the solution to the asked query: 
$$\begin{gathered} \mathrm{Law} \mathrm{of} \mathrm{conservation} \mathrm{of} \mathrm{momentum}: \\ \mathrm{In} \mathrm{the} \mathrm{absence} \mathrm{of} \mathrm{external} \mathrm{torque}, \mathrm{the} \mathrm{angular} \mathrm{mometnum} \mathrm{of} \mathrm{the} \mathrm{system} \mathrm{is} \mathrm{constant}. \\ \mathrm{L} = \mathrm{constant} \\ \mathrm{r} \mathrm{p} = \mathrm{constant} \\ \mathrm{r} \mathrm{m} \mathrm{v} = \mathrm{constant} \\ \mathrm{v} \mathrm{\alpha } \frac{1}{\mathrm{r}} \\ \mathrm{The} \mathrm{speed} \mathrm{of} \mathrm{the} \mathrm{planets} \mathrm{is} \mathrm{inversely} \mathrm{proportional} \mathrm{to} \mathrm{radius} \mathrm{of} \mathrm{the} \mathrm{orbit}. \\ \mathrm{Hence}, \\ \mathrm{speed} \mathrm{of} \mathrm{the} \mathrm{planet} \mathrm{is} \mathrm{larger} \mathrm{when} \mathrm{it} \mathrm{is} \mathrm{closure} \mathrm{to} \mathrm{sun} \mathrm{and} \\ \mathrm{speed} \mathrm{of} \mathrm{the} \mathrm{planer} \mathrm{is} \mathrm{smaller} \mathrm{when} \mathrm{it} \mathrm{is} \mathrm{away} \mathrm{from} \mathrm{sun} \end{gathered}$$
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