InterviewSolution
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InterviewSolution
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A planet of mass m revolves around the sun of mass M in an elliptical orbit. The maximum and minimum distances of the planet from the sun are r1 and r2, respectively. The time period of the planet in terms of r1 and r2 is(a) T ∝ (r1 + r2)2(b) T ∝ (r1 + r2)3(c) T ∝ (r1 + r2)1/2(d) T ∝ (r1 + r2)3/2 |
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Answer» Answer is : (d) \(T\propto (r_1+r_2)^{\frac{3}{2}}\) The semi-major axis of the elliptical orbit around the sun is given by \(r=\frac{r_1+r_2}{2}\) According to Kepler’s third law, \(T^2\propto r^3\) \(\Rightarrow T^2\propto (\frac{r_1+r_2}{2})^3\) \(or\: T\propto (\frac{r_1+r_2}{2})^\frac{3}{2}\) \(or\:T\propto (r_1+r_2)^{\frac{3}{2}}\) |
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