Final answer:
The calculated eccentricity of the asteroid's orbit, based on the given perihelion of 2.0 and aphelion of 4.0, is approximately 0.333, which does not match any of the provided options exactly. The closest provided option is (A) 0.5, though this is not the precise answer.
Step-by-step explanation:
To calculate the eccentricity of the asteroid's orbit, we need to use the definition of eccentricity for an elliptical orbit. The eccentricity (e) is given by the formula:
e = (aphelion - perihelion) / (aphelion + perihelion)
Where the perihelion is the closest point to the Sun in the orbit, and the aphelion is the furthest point. Plugging in the given values:
e = (4.0 - 2.0) / (4.0 + 2.0)
Which simplifies to:
e = 2.0 / 6.0
Which gives us an eccentricity of:
e = 0.333...
Since none of the provided options (A) 0.5, (B) 1.0, (C) 0.0, or (D) 2.0 match the calculated eccentricity of 0.333..., it seems there might be an error in the question or in the provided options. If precision is not essential, one could argue that option (A) 0.5 is the closest to the calculated value, but technically, it is not the correct answer based on the values given.