Use the following to answer questions :
In its elliptical orbit around the sun, Mercury has an aphelion of 44 million miles, and a perihelion of 29 million miles.
-Find the eccentricity of Mercury's orbit.
A) 0.1938
B) 0.2029
C) 0.2055
D) 0.2110

Question

Quizplus · Accepted Answer

The eccentricity of an orbit is calculated using the formula $e = \frac{a - b}{a + b}$, where $a$ is the semi-major axis and $b$ is the semi-minor axis. However, for an ellipse, the semi-major axis is the average of the aphelion and perihelion distances, and the formula simplifies to $e = \frac{aphelion - perihelion}{aphelion + perihelion}$ when the distances are given from a common focal point (in this case, the Sun). Here, $a = \frac{44 + 29}{2} = 36.5$ million miles is not directly used in the simplified formula but is mentioned for clarity on how the semi-major axis is determined in context. The direct calculation for eccentricity using the given distances is $e = \frac{44 - 29}{44 + 29} = \frac{15}{73} \approx 0.2055$, making the correct answer 0.2055.

Use the Following to Answer Questions