gen-define-orbital-eccentricity-and-give-one-short-worked-exampl-6b1d

Define orbital eccentricity and give one short worked example.

# Orbital Eccentricity **Orbital eccentricity** (e) is a dimensionless parameter that describes how much an orbit deviates from a perfect circle. It ranges from 0 to 1 for bound orbits: - **e = 0**: Perfect circle - **0 < e < 1**: Ellipse - **e = 1**: Parabola (unbound) - **e > 1**: Hyperbola (unbound) ## Formula For an elliptical orbit: $$e = \frac{r_a - r_p}{r_a + r_p}$$ where: - **r_a** = aphelion distance (farthest point from the focus) - **r_p** = perihelion distance (closest point from the focus) ## Worked Example **Problem:** Earth's orbit has a perihelion of 147.1 million km and an aphelion of 152.1 million km. Find its eccentricity. **Solution:** $$e = \frac{r_a - r_p}{r_a + r_p} = \frac{152.1 - 147.1}{152.1 + 147.1} = \frac{5.0}{299.2} = 0.0167$$ Earth's orbital eccentricity is **0.0167**, meaning its orbit is very nearly circular.