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Speeds at the nearest and farthest points of an elliptical orbit

This type of question, asked 2 times: 2021 Paper 5, 2021 Paper 14. All 2 questions below, oldest first.

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  1. Question 1

    2021 Paper 5

    7
    The maximum and minimum distances of a comet from the Sun are 1.6×1012 m1.6 \times10^{12}\text{ }m and 8.0×1010 m8.0 \times10^{10}\text{ }m respectively. If the speed of the comet at the nearest point is 6×104 ms−16 \times10^{4}{\text{ }ms}^{- 1}, the speed at the farthest point is :

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  2. Question 2

    2021 Paper 14

    2
    Earth moves around sun in elliptical orbit. If minimum and maximum distance between earth and sun are rmin⁡r_{\min} and rmax⁡r_{\max} respectively and minimum and maximum speed of earth are Vmin⁡V_{\min} and Vmax⁡V_{\max} respectively. Express Vmax⁡V_{\max} in terms of others parameters.

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