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!

Answer 1

Answer: D. 0.57

Step-by-step explanation:

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

`e=(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=(r_(a)-0.27 r_(a))/(r_(a)+0.27 r_(a))`

`e=(0.73 r_(a))/(1.27 r_(a))`

`e=0.57` This is the moon's orbital eccentricity