Answer:
The eccentricity of path of moon orbiting around its planet is 0.9628
Step by step explanation:
Given that a moon is orbiting around its planet
[tex]r_p[/tex] is the shortest distance between the moon and its planet
[tex]r_a[/tex] is the Longest distance between the moon and its planet
Relation between [tex]r_p[/tex] and [tex]r_a[/tex] is
[tex]r_p = 0.27 r_a[/tex]
We know that path of moon orbiting around its planet is ellipse.
Where, 2[tex]r_p[/tex] is minor axis of ellipse and 2[tex]r_a[/tex] is major axis of ellipse.
Also eccentricity of ellipse is given by
e=[tex]\frac{\sqrt{r_a^{2} -r_p^{2} } }{r_a}[/tex]
for [tex]r_a[/tex]>[tex]r_p[/tex]
Now, using given relation.
e=[tex]\frac{\sqrt{r_a^{2} -(0.27 r_a)^{2} } }{r_a}[/tex]
e=[tex]\frac{\sqrt{0.9271r_a^{2}} }{r_a}[/tex]
e=[tex]\frac{0.9628r_a}{r_a}[/tex]
e=0.9628
Thus
The eccentricity of path of moon orbiting around its planet is 0.9628
