The curved path a planet takes as it travels around the Sun, known as its orbit, is mathematically defined as an ellipse. This shape is a slightly flattened or elongated oval, which represents a closed, stable path around a central star. Unlike open trajectories such as parabolas or hyperbolas, the elliptical path ensures the planet remains bound to the Sun. The distance between the planet and the Sun is constantly changing throughout this journey.
The Historical Shift from Circles to Ellipses
For over two millennia, the prevailing view held that celestial bodies must move in perfect circles. This belief was incorporated into early models, including the geocentric and Copernican heliocentric systems. These models used complex arrangements of circles within circles, known as epicycles, to explain observed planetary motions.
This assumption was challenged by the meticulous observational work of Danish astronomer Tycho Brahe, who collected precise, naked-eye measurements of planetary positions, particularly for Mars. Following Brahe’s death, his assistant, Johannes Kepler, inherited this data and spent years trying to fit Mars’s orbit into a perfect circle. Kepler found that the circular model consistently failed to match Brahe’s accurate observations.
Trusting the accuracy of the data, Kepler concluded that the orbit was an elongated oval. This finding became Kepler’s First Law of Planetary Motion, which states that the orbit of a planet is an ellipse with the Sun positioned at one of the two internal focal points.
Defining the Elliptical Path
An ellipse is defined by two points called foci, rather than a single center point like a circle. The mathematical property of an ellipse is that the sum of the distances from any point on the curve to the two foci is always constant. In a planetary orbit, the Sun is situated at one of these two focal points, while the other focus remains empty.
The degree to which an ellipse is stretched out compared to a perfect circle is quantified by eccentricity. A perfect circle has an eccentricity of zero, while an ellipse has an eccentricity between zero and one. The point in the orbit where the planet is closest to the Sun is called the perihelion, and the point where it is farthest away is called the aphelion. The size of the orbit is typically described by the semi-major axis, which is half the longest diameter of the ellipse.
What Governs the Shape
The physical reason that planetary orbits take the shape of an ellipse was explained later by Isaac Newton’s law of universal gravitation. The orbital path is the result of a dynamic balance between two primary factors: the Sun’s gravitational pull and the planet’s inertia. Inertia is the tendency of the planet to continue moving in a straight line, while gravity acts as the centripetal force, constantly pulling the planet toward the massive Sun.
The combination of the planet’s forward momentum and the Sun’s continuous inward tug causes the path to constantly curve around the Sun. This balance results in a stable, repeating path, which Newton’s mathematics proved must be a conic section, with the ellipse being the closed, bounded form. The gravitational force follows an inverse-square law, meaning the force weakens rapidly as the distance increases. This specific mathematical relationship compels the planet to trace out an elliptical path, with the Sun naturally positioned at one of the foci.
Variations in Planetary Orbits
While all planetary orbits are elliptical, the extent of their elongation varies significantly. The orbits of Earth and Venus are very close to circular, with eccentricities of about 0.017 and 0.0068, respectively. This low eccentricity means the distance from Earth to the Sun changes by only about three percent throughout the year. In contrast, the orbit of Mercury is notably more stretched out, possessing a higher eccentricity of approximately 0.205.
Dwarf planets and comets often exhibit much higher eccentricities, with some comets having values approaching one, resulting in extremely elongated paths. Furthermore, the elliptical paths are not perfectly fixed over cosmic timescales; they are subject to slight gravitational nudges from the other planets. These subtle, long-term interactions, particularly with the massive outer planets like Jupiter and Saturn, cause the orbital eccentricities to slowly oscillate. For Earth, this variation in eccentricity contributes to long-term climate cycles.