question_answer

The figure represents an elliptical orbit of a planet around the sun. The planet takes time \[{{T}_{1}}\]to travel from A to B and it takes time\[{{T}_{2}}\]to travel from C to D. If the area CSD is double that of area ASB, find the relationship between\[{{T}_{1}}\]and\[{{T}_{2}}\] (a) \[{{T}_{1}}={{T}_{2}}\]         (b) \[{{T}_{1}}=2{{T}_{2}}\] (c) \[{{T}_{1}}=0.5\,{{T}_{2}}\]      (d) data insufficient

Answer:

According to Kepler?s law of areas, \[\frac{dA}{dt}=\]constant (or) \[\frac{{{A}_{1}}}{{{T}_{1}}}=\frac{{{A}_{2}}}{{{T}_{2}}}\] As, area of\[CSD=2\times area\] of \[ASB\,\,{{T}_{1}}=2\times {{T}_{2}}\]