Question:
A satellite is in an elliptical orbit around a planet P. It is observed that the velocity of the satellite when it is farthest from the planet is 6 times less than that when it is closest to the planet. The ratio of distances between the satellite and the planet at closest and farthest points is:
A satellite is in an elliptical orbit around a planet P. It is observed that the velocity of the satellite when it is farthest from the planet is 6 times less than that when it is closest to the planet. The ratio of distances between the satellite and the planet at closest and farthest points is:
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Angular momentum about the planet is conserved; at the nearest and farthest points the velocity is perpendicular to the radius, so \(v_1 r_1 = v_2 r_2\).
Updated On: Nov 5, 2026
- \(1 : 2\)
- \(1 : 3\)
- \(1 : 6\)
- \(3 : 4\)
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The Correct Option is C
Solution and Explanation
Gravity is a central force, so angular momentum \(L = mvr\) is conserved.
At the closest and farthest points (apsides) \(\vec v\perp\vec r\): \(v_{c}\,r_{c} = v_{f}\,r_{f}\).
Given \(v_f = \frac{v_c}{6}\): \(\frac{r_c}{r_f} = \frac{v_f}{v_c} = \frac16\).
Answer: (3) \(1 : 6\)
At the closest and farthest points (apsides) \(\vec v\perp\vec r\): \(v_{c}\,r_{c} = v_{f}\,r_{f}\).
Given \(v_f = \frac{v_c}{6}\): \(\frac{r_c}{r_f} = \frac{v_f}{v_c} = \frac16\).
Answer: (3) \(1 : 6\)
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