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. 57


b) 0. 27


c) 0. 65


d) 0. 48

Answer 1

If rp is 0.27ra, then a moon's orbital eccentricity is 0.57. Thus, option (a) is the correct answer.

Though the moon does not move around andra in a perfect ellipse, here, we assume that the moon's orbit is in the shape of an ellipse, we know that:

$e = \frac{ra - rp}{ra + rp}$ ... (i)

where e ⇒ eccentricity of the ellipse

ra ⇒ apoapsis i.e., the longest distance between the moon and its planet

rp ⇒ periapsis i.e., the shortest distance between the moon and its planet

From the question, we know

rp = 0.27 ra

Putting this value in equation (i) we get:

$e = \frac{ra-0.27ra}{ra+0.27ra}$

$e=\frac{0.73ra}{1.27ra}$

e = 0.57

Hence, if rp is 0.27 of ra, the moon's orbital eccentricity is 0.57.

To know more about eccentricity, click:

brainly.com/question/28991074

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