Why are orbits elliptical and not circular?

Why aren't orbits perfect circles?

A perfectly circular orbit would require an ideal balance between speed and gravity, a condition almost impossible to achieve in reality. This is why celestial bodies follow elliptical trajectories, whose shape is measured by eccentricity (e). The closer e is to 0, the more circular the orbit (Earth: 0.0167). The larger e, the more elongated the orbit (Mercury: 0.206). This eccentricity creates the apsides: the perihelion (closest point to the Sun) and the aphelion (farthest point), whose distances vary according to the formula r = a(1 ± e).

Finally, orbits are not fixed: under the effect of gravitational perturbations, the line of apsides precesses slowly. The precession of Mercury's perihelion (43 arcseconds per century) is one of the historical proofs of Einstein's general relativity.

Inner orbits of the solar system

General characteristics of inner planets

The inner planets (Mercury, Venus, Earth, Mars) have orbits relatively close to the Sun, which intensifies tidal effects and interactions with the solar wind. Their apsides are measured with great precision thanks to modern ephemerides.

Mercury: a highly elliptical orbit

Mercury, with its high eccentricity \(e \approx 0.206\), has a very elliptical orbit: its perihelion is at 46 million km, and its aphelion at 70 million km. This imbalance generates a highly variable orbital speed, ranging from 59 km/s near the Sun to about 39 km/s at aphelion.

The precession of Mercury's perihelion

The precession of Mercury's perihelion is an emblematic phenomenon. While Newton's laws predict a certain advance due to perturbations from other planets, observations show an excess of 43 arcseconds per century, perfectly explained by the curvature of space-time in Einstein's formalism.

Earth: a nearly circular orbit

Earth, with a nearly circular orbit \(e \approx 0.0167\), shows a modest variation between perihelion (147.1 million km) and aphelion (152.1 million km). This difference influences the amount of solar energy received (the solar constant varying by ~6%) but is not the main cause of the seasons, which depend on the axial tilt of 23.5°.

Mars: a marked eccentricity

Mars, farther out, has an eccentricity of 0.093, almost six times that of Earth. Its perihelion (206 million km) and aphelion (249 million km) show a much more pronounced seasonal variability, notably visible in its asymmetric climate between hemispheres.

Venus: an almost perfect orbit

Venus is an interesting case: its orbit is almost perfectly circular \(e \approx 0.0068\). As a result, the variation between its apsides is negligible, but it plays an important role in transits observed from Earth when alignments are exact at the node passage.

Outer orbits of the solar system

General characteristics of outer planets

The outer planets (Jupiter to Neptune) describe wider and generally more circular orbits than the inner planets. Nevertheless, they are subject to mutual gravitational resonances that slowly modify their apsides. Jupiter, the dominant giant, strongly influences the architecture of the solar system. Its perihelion is at 740 million km, and its aphelion at 816 million km, with a moderate eccentricity \( e \approx 0.049 \).

Stability of the orbits of Saturn, Uranus and Neptune

Saturn, Uranus and Neptune have relatively small apsis gaps (a few tens of millions of km) relative to their average distances, making their motion more stable over the long term. However, their orbit is also subject to a slow precession of their apsidal lines, detected by spectroscopic analysis of rings or satellite tracking.

Trans-Neptunian objects: extreme eccentricities

Trans-Neptunian objects show more extreme eccentricities. Pluto, with \(e \approx 0.2488\), goes from 4.4 billion to 7.3 billion km depending on whether it is at perihelion or aphelion. This variation is such that Pluto can temporarily be closer to the Sun than Neptune. Its apsidal line is inclined (~17°) and highly mobile, reflecting a chaotic regime.

Distant objects: Sedna, Eris and the Oort cloud

Other distant objects like Eris, Sedna or extreme objects in the Oort cloud, reach aphelions greater than 500 AU. Sedna, for example, has a highly eccentric orbit \(e \approx 0.854\), with a perihelion at 76 AU and an estimated aphelion at 937 AU. These objects are fossil witnesses of past perturbations, possibly linked to nearby stars or a hypothetical planet not yet detected.

Importance of distant apsides

These distant apsides are essential for understanding the boundaries of the solar system and the gravitational forces that prevail there. They are studied by numerical simulation, as their trajectory cannot be described by a simple analytical method, especially when relativistic effects, resonances and galactic tides are taken into account.

Comparison of aphelions and perihelions of planets in the solar system in millions of kilometers

FAQ: Everything you need to know about apsides and orbital eccentricity

What is the difference between perihelion, aphelion and their general equivalents?

Perihelion is the point in an orbit where an object is closest to the Sun. Aphelion is the farthest point from the Sun. These terms are specific to the solar system. Their general equivalents, valid for any central body, are periapsis (closest point to the gravitational focus) and apoapsis (farthest point). For example, we speak of perigee and apogee for an orbit around the Earth, and periastron and apastron for an orbit around any star.

How does eccentricity influence a planet's orbital speed?

Eccentricity determines the variation of orbital speed along the orbit. According to Kepler's second law (law of areas), a planet moves faster when it is near perihelion (minimum distance) and slower at aphelion. For example, Mercury, with an eccentricity of 0.206, reaches 59 km/s at perihelion and slows to about 39 km/s at aphelion. Earth, with a much lower eccentricity (0.0167), has a much less marked speed variation: about 30.3 km/s at perihelion versus 29.3 km/s at aphelion. This speed variation is a direct consequence of the conservation of angular momentum.

What is apsidal precession and why is it important?

Apsidal precession is the slow rotational movement of the line joining perihelion and aphelion in the orbital plane, under the effect of gravitational perturbations (notably interplanetary). This effect is particularly noticeable for Mercury: Newton's laws predict a certain advance of the perihelion due to other planets, but observations show an excess of 43 arcseconds per century. This excess was perfectly explained by Einstein's general relativity as a consequence of the curvature of space-time by the Sun's mass. Apsidal precession is therefore a sensitive indicator of non-Newtonian effects and a crucial test for theories of gravitation.