For a moon orbiting its planet, rp is the shortest distance between the moon and its planet andra is the longest distance between the moon a

Question

For a moon orbiting its planet, rp is the shortest distance between the moon and its planet andra is the longest distance between the moon and its planet. What is a moon’s orbital eccentricity if rp is equal to 0.27ra?
A. 0.65

B. 0.27

C. 0.48

D. 0.57

D. IS THE CORRECT ANSWER!

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Ngọc Khuê 1 week 2021-07-22T06:42:56+00:00 1 Answers 1 views 0

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    2021-07-22T06:44:45+00:00

    Answer: D. 0.57

    Explanation:

    The formula to calculate the eccentricity e of an ellipse is (assuming the moon’s orbit in the shape of an ellipse):

    e=\frac{r_{a}-r_{p}}{r_{a}+r_{p}}

    Where:

    r_{a} is the apoapsis (the longest distance between the moon and its planet)

    r_{p}=0.27 r_{a} is the periapsis (the shortest distance between the moon and its planet)

    Then:

    e=\frac{r_{a}-0.27 r_{a}}{r_{a}+0.27 r_{a}}

    e=\frac{0.73 r_{a}}{1.27 r_{a}}

    e=0.57 This is the moon’s orbital eccentricity

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