Eccentricity and Orbit Shapes

What is Eccentricity?

Eccentricity (e) is a single number that describes your orbit's shape:

e = 0: Perfect circle 0 < e < 1: Ellipse (closed orbit) e = 1: Parabola (exactly escape velocity) e > 1: Hyperbola (escape trajectory)

Most spacecraft orbits have e between 0 and 0.3.

Comets often have e > 0.9 (very elongated).

Escape trajectories have e ≥ 1.

Calculating Eccentricity

Eccentricity can be calculated from periapsis and apoapsis:

e = (ra - rp) / (ra + rp)

Where: - ra = apoapsis distance from planet center - rp = periapsis distance from planet center

Example: - 200 km × 200 km: e = 0.000 (circular) - 200 km × 400 km: e = 0.029 (slightly elliptical) - 200 km × 2000 km: e = 0.450 (very elliptical) - 200 km × ∞: e = 1.000 (escape)

Why Eccentricity Matters

Eccentricity affects:

1. Orbit stability: Low e = stable, high e = varying altitude 2. Communication: High e = satellite sometimes very far 3. Thermal control: High e = big temperature swings 4. Delta-V requirements: Higher e = more fuel to circularize 5. Mission planning: e determines orbit characteristics

Geostationary satellites: e ≈ 0.0001 (nearly perfect circles) Molniya orbits: e ≈ 0.74 (highly elliptical) Interplanetary transfers: e varies throughout mission