question_answer

The time period of the satellite of the earth is 5 hours. If the separation between the earth and the satellite is increased to 4 times the previous value, then what will be the new time period of the satellite?

Answer:

                According to Kepler's law of periods, \[{{\left( \frac{{{T}_{2}}}{{{T}_{1}}} \right)}^{2}}={{\left( \frac{{{R}_{2}}}{{{R}_{1}}} \right)}^{3}}\] or \[{{\left( \frac{{{T}_{2}}}{5} \right)}^{2}}={{\left( \frac{4{{R}_{1}}}{{{R}_{1}}} \right)}^{3}}\]                 or            \[{{T}_{2}}=\sqrt{64\times 25}=\mathbf{40h}.\]