If an asteroid's orbit is nearly circular, meaning its elliptical path is almost centered around the Sun, then its eccentricity would be very close to zero.

Here's why:

* Eccentricity is a measure of how much an ellipse deviates from a perfect circle.

* Eccentricity of 0 represents a perfect circle.

* Eccentricity of 1 represents a completely flattened ellipse (a straight line).

* Values between 0 and 1 represent increasingly elongated ellipses.

Since the asteroid's orbit is almost circular, the deviation from a perfect circle is minimal, resulting in an eccentricity value very close to zero.