For a moon orbiting its planet, rp is the shortest distance between the moon and its planet and ra is the longest distance between the moon and its planet. What is a moon's orbital eccentricity if rp is equal to 0.27ra?
Responses:
a) 0.65
b) 0.57
c) 0.48
d) 0.27
To find the moon's orbital eccentricity, we can use the formula:
eccentricity (e) = (ra - rp) / (ra + rp)
Given that rp = 0.27ra, we can substitute this value into the formula:
eccentricity (e) = (ra - 0.27ra) / (ra + 0.27ra)
Simplifying this expression, we get:
eccentricity (e) = 0.73ra / 1.27ra
eccentricity (e) = 0.73 / 1.27
eccentricity (e) ≈ 0.574
Therefore, the moon's orbital eccentricity is approximately 0.57.
Therefore, the correct answer is b) 0.57.
To find the moon's orbital eccentricity, we can use the formula:
Eccentricity (e) = (ra - rp) / (ra + rp)
Given that rp is equal to 0.27ra, we can substitute this value into the formula:
Eccentricity (e) = (ra - 0.27ra) / (ra + 0.27ra)
Simplifying the expression, we have:
Eccentricity (e) = 0.73ra / 1.27ra
Now, we can cancel out the ra terms:
Eccentricity (e) = 0.73 / 1.27
Calculating the value, we get:
Eccentricity (e) ≈ 0.57
Therefore, the correct answer is b) 0.57.