Elliptical orbits
An elliptical orbit is the elliptical path followed by a celestial body— planet, comet, or satellite—follows around another body under the influence of gravity. First described mathematically by Johannes Kepler in the early 17th century, elliptical orbits are the norm in the solar system: all the planets follow elliptical paths around the Sun, which occupies one of the two foci of each ellipse.
Kepler’s Laws
Kepler’s first law states that planets move in ellipses with the Sun at one of the foci. The second law states that the line segment connecting a planet to the Sun sweeps out equal areas in equal times—which means that themoves faster when it is close to the Sun (at perihelion) and slower when it is farther away (at aphelion). The third law relates the orbital period to the semi-major axis of the ellipse.
Eccentricity and Shape of the Orbit
The eccentricity of an ellipse measures its degree of flattening, ranging from 0 (a perfect circle) to 1 (a parabola). The Earth’s orbit is nearly circular, with an eccentricity of 0.017. Comets often have highly elongated orbits with eccentricities close to 1, which bring themvery close to the Sun before carrying them out to the outer reaches of the solar system.
Importance in Astronomy
Understanding elliptical orbits is fundamental to predicting the positions of planets, planning space missions, and assessing the risk of asteroid impacts. The trajectories of space probes skillfully exploit orbital mechanics—particularly gravitational assists—to reach distant destinations with minimal fuel.
Concrete Example
Halley’s Comet has a highly elliptical orbit with an eccentricity of 0.967. Its perihelion (the point closest to the Sun) is located at 0.59 AU (between Venus and the Sun), while its aphelion (the farthest point) is located at 35 AU, beyond Neptune. This extremely elongated orbit explains its orbital period of 76 years.
Frequently Asked Questions
Why are orbits elliptical rather than circular?
This is a direct consequence of Newton’s law of universal gravitation. An ellipse—and more generally, a conic section (ellipse, parabola, hyperbola)—is the mathematical solution to the equations of motion under a gravitational force proportional to 1/r². A circle is a special case of an ellipse (zero eccentricity).
Are the orbits stable indefinitely?
Not perfectly. Gravitational interactions between planets perturb the orbits over long periods. These perturbations are generally small, and the orbits remain stable for billions ofyears, but over very long timescales they can cause instabilities in the solar system.
Do artificial satellites also follow elliptical orbits?
Yes. Most artificial satellites follow elliptical orbits. A circular orbit is a limiting case that is achieved in practice with a certain degree of precision. The International Space Station, for example, follows a nearly circular orbit at an altitude of about 400 kilometers.