Suppose the gravitational force varies inversely as the ${n^{th}}$ power of distance. Then the time period of a planet in circular orbit of radius $R$ around the sun will be proportional to
Suppose the gravitational force varies inversely as the ${n^{th}}$ power of distance. Then the time period of a planet in circular orbit of radius $R$ around the sun will be proportional to
${R^{\left( {\frac{{n + 1}}{2}} \right)}}$
${R^{\left( {\frac{{n - 1}}{2}} \right)}}$
${R^n}$
${R^{\left( {\frac{{n - 2}}{2}} \right)}}$
Suppose the gravitational force varies inversely as the ${n^{th}}$ power of distance. Then the time period of a planet in circular orbit of radius $R$ around the sun will be proportional to
$m{\omega ^2}R \propto \frac{1}{{{R^n}}}$
$m\left( {\frac{{4{\pi ^2}}}{{{T^2}}}} \right)R \propto \frac{1}{{{R^n}}}$
${T^2} \propto {R^{n + 1}}$
$T \propto {R^{\left( {\frac{{n + 1}}{2}} \right)}}$
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