By Kenrick Vezina – Updated Mar 24, 2022

In astrophysics, the perihelion is the point in an orbit where a celestial body comes closest to the Sun. The term originates from the Greek words peri (near) and Helios (Sun). Its counterpart, the aphelion, marks the farthest distance from the Sun. While comets are the most iconic example—displaying bright comae and glowing tails when near perihelion—the same principles apply to every orbiting object.

Eccentricity: Why Most Orbits Aren’t Circular

Our common image of Earth’s path as a perfect circle is a simplification. In reality, almost all planetary orbits, including Earth’s, are slightly elliptical. The deviation from a perfect circle is quantified by the orbit’s eccentricity, a dimensionless number between 0 and 1. An eccentricity of 0 denotes a perfect circle; higher values indicate increasingly elongated ellipses. For example, Earth’s eccentricity is about 0.0167, while Halley’s Comet’s orbit has an eccentricity of 0.967.

Key Properties of an Ellipse

• Foci: Two points that define the ellipse’s shape; the Sun occupies one focus in a heliocentric orbit.
• Center: The midpoint of the ellipse.
• Major Axis: The longest diameter passing through both foci and the center; its endpoints are the vertices.
• Semi‑major Axis: Half the major axis, the distance from the center to a vertex.
• Vertices: The most extreme points on the ellipse; correspond to perihelion and aphelion in orbital terms.
• Minor Axis: The shortest diameter, perpendicular to the major axis and passing through the center; its endpoints are the co‑vertices.
• Semi‑minor Axis: Half the minor axis, the shortest distance from the center to a co‑vertex.

Calculating Eccentricity from Axes

When the lengths of the semi‑major and semi‑minor axes are known, eccentricity can be computed with:

\(\text{eccentricity}^2 = 1.0-\frac{\text{semi‑minor axis}^2}{\text{semi‑major axis}^2}\)

Astronomical distances are usually expressed in astronomical units (AU), where 1 AU ≈ 149.6 million km. The units of the axes must be consistent, but they need not be AU.

Determining Perihelion and Aphelion Distances

Once the semi‑major axis (a) and eccentricity (e) are known, the nearest and farthest orbital distances from the Sun are calculated as:

\(\text{perihelion} = a(1- e)\)

\(\text{aphelion} = a(1+ e)\)

Example: Mars

Mars has a semi‑major axis of 1.524 AU and an eccentricity of 0.0934.

\(\text{perihelion}_{\text{Mars}} = 1.524\,(1-0.0934) = 1.382\,\text{AU}\)

\(\text{aphelion}_{\text{Mars}} = 1.524\,(1+0.0934) = 1.666\,\text{AU}\)

These modest variations keep Mars at a relatively stable distance from the Sun, and Earth’s similarly low eccentricity maintains a consistent solar irradiance throughout the year.

Example: Mercury

Mercury’s semi‑major axis is 0.387 AU and its eccentricity is 0.205.

\(\text{perihelion}_{\text{Mercury}} = 0.387\,(1-0.205) = 0.307\,\text{AU}\)

\(\text{aphelion}_{\text{Mercury}} = 0.387\,(1+0.205) = 0.467\,\text{AU}\)

Mercury’s orbit brings it nearly two‑thirds closer to the Sun at perihelion compared to aphelion, causing dramatic shifts in temperature and solar flux across its orbit.

Why Eccentricity Matters

Understanding orbital eccentricity and its impact on perihelion and aphelion distances is essential for accurate modeling of planetary climates, spacecraft trajectory planning, and the study of cometary activity. While Earth’s slight eccentricity has minimal daily effects, more eccentric orbits—like that of Mercury—produce significant seasonal extremes.