Why are the orbits of our planets not equally eccentric?

How fitting that the 2 planets with the most circular orbits (lowest eccentricities) are named after Venus, the goddess of love and fertility, and Neptune, the god of fresh water and sea, while those with the least circular orbits honor the gods of commerce (Mercury) and the underworld (Pluto)!

There is a reason behind the differences in eccentricities, but the connection to names is a coincidence. The Romans had no notion of elliptical orbits or eccentricity when they named Mercury and Venus, and although I am not sure if the eccentricities were measured before Neptune and Pluto were named in 1846 and 1930, respectively, I am willing to bet that their elliptical nature did not influence the choice of names. Besides, Venus, at least from up close, does not inspire love. Without water to wash away any carbon dioxide from its atmosphere, Venus has a runaway greenhouse effect with an average surface temperature of 464 o C and to boot, clouds of sulfuric acid hover over its surface. Although Neptune is as blue as our oceans, its color comes from the methane in its atmosphere. There is water in its -200 o C icy surface, but it’s mixed with methane and ammonia.

On the left are the two planets with the greatest eccentricities, Mercury and Pluto. The least eccentric orbit is that of Venus, top right, followed by Neptune. Art works are by (clockwise from top left) Jean-Baptiste Pigalle, Alexandre Cabanel, Michel Anguier and Giovanni Battista di Jacopo.

How is eccentricity measured and why does it exist for planets?

An ellipse is a flattened circle with less symmetry than its counterpart. You can draw a circle with one taut string and one nail to keep it focused at the the center. But to draw an ellipse we have to attach a loose string to a pair of nails and then it pull it taut throughout its 360 degree journey.

The nails’ positions are the two focal points of the ellipse. If you put the shape of an ellipse on an xy plane and place the origin at the center, each focal point is said to be “c” units way from the origin. The horizontal distance from the center to the widest point of the ellipse is often denoted as “a” ; and the equivalent in the vertical direction is called “b”.

Drawing an ellipse is made possible with the above nail-set up because the total length of the string is constant. In fact, if you think about it, the length is equivalent to the entire horizontal ” diameter, equal to 2a. That in turn implies that a, b and c are related by the Pythagorean theorem, although the hypotenuse in this case is a and not the conventional c .

By using the relation a2 = b2 + c2 and applying the distance formula from the point, P = (x,y), to the focus (0, c), with the knowledge that half the string’s length is equal to “a”, we could derive, after some algebraic mud-wrestling,

x2 /a2 + y2/b2 = 1.

If we shift the graph so that one of the foci is at the origin, then we get (x – c)2 /a2 + y2/b2 = 1, which looks like this:

But how do you measure eccentricity(e) from all of this? The simplest way is to express it as a fraction of the focal distance, c, over the distance a, so e= c/a. (Incidentally, the purpose of shifting the focus to the origin is to make it more similar to the polar coordinate-system used in astronomy, given that the sun is at one of the foci. The planet’s closest approach(perihelion) and farthest (aphelion) become the distances to F1. The ratio of their differences to that of their sum ends up being equivalent to the ratio of a/c.) So in the case to the left, the eccentricity for the ellipse would be quite high at 4/5 = 0.8. To reduce it, we would have to move the middle of the ellipse closer to its foci, which would round it out. Of course, if we want to keep the focus’s value fixed we would have to change b’s value accordingly since it is bound by the relationship a2 = b2 + c2 . Here’s what an eccentricity or e value of 0.2 looks like—it’s far more circular.

The adjacent figure is a close representation of Mercury’s orbit (e=0.204). But it’s the second most elliptical orbit after that of the dwarf planet Pluto. Scaled down to the scale of a page, the orbits of Venus (e = 0.007), Neptune(0.009) and even that of Earth(0.017) would look like perfect circles.

What then is behind the discrepancies? It’s the particular details of each planet’s history of formation, very loosely akin to the way the micro-environment of each snowflake affects its shape and the way its coming to existence will in turn affect the conditions of another flake.

An artist’s conception of the solar nebula.

Our planets’ family history began with a dense cloud of interstellar dust particles and gas molecules. A nearby supernova may have compressed the gas-dust cloud into a spinning, swirling disk of material known as a solar nebula. Gravity acted from the nebula’s center of mass, pulling in an increasing number of particles. At one point the most abundant particles, hydrogen atoms, fused at the core leading to the birth of our sun, which used up most of the nebula’s mass.

Farther out in the disk the remaining matter also clumped together. The clumps violently collided with one another, growing in size the way the mass of dead insects got larger on the radiators of old 1970s cars as they sped on highways through forests. The collisions increased the eccentricity of the bigger clumps’ orbits around the newborn sun. But as the surrounding bodies and debris stuck to the growing planets, they worked to have the opposite effect and decreased the eccentricity.

Just as the way that the order and arrangement of the planets and other bodies in our solar system is rooted in its history, so are the eccentricities of the planets. None of them experienced the same collisions or scooped up the same amount of mass. The four terrestrial planets planets, Mercury, Venus, Earth and Mars, the ones with rocky material that could withstand the heat from the young solar system close to the sun, each had different neighborhoods that influenced their orbits and continue to do so. The changes are just smaller than those they experienced in their youth.

Meanwhile, materials such as ice, liquid or gas could only survive the heat at a greater distance from the sun. They too were pulled together by gravity. In these outer regions of the solar system, Jupiter, Saturn, Uranus and Neptune formed. At the beginning, these planets also amassed more matter from the swirling disk. This made them migrate because of the angular momentum that was exchanged. Simulations reveal that Jupiter was forced to move inward, while Saturn, Uranus and Neptune drifted further away from the Sun. Before they moved, their eccentricities were as low as those of Venus and Earth, but when Jupiter and Saturn became locked into a 1:2 orbital resonance, the eccentricities of the giants and Uranus quickly escalated to the ones we observe today. That of Neptune, which was further away, remained low.

Having said all that, we should not go away without reiterating that eccentricities are still in flux. They constantly change, albeit very slowly and not too wildly. Here’s that of Mars as an example, which changes mostly due to the influence of Jupiter. According to the Solex program, it takes a couple of million years for Mars to go through a full cycle from its minimum (an eccentricity as low as Venus’s current one) to a maximum ( 30% more than its present one, but still much lower than Mercury’s.)

From the Solex program https://web.archive.org/web/20080218133456/http://chemistry.unina.it/~alvitagl/solex/index.html

Earth’s variations in eccentricity are more minor and have very few consequences, unlike those of other Milankovitch cycles. Hence we have another way of rationalizing our feelings for the most startling of planets: its eccentricity is, and will forever be, low, sometimes even lower than that Venus, and unlike the latter, our planet is fertile and covered with clouds that help sustain it.

From Nature: https://www.nature.com/scitable/knowledge/library/milankovitch-cycles-paleoclimatic-change-and-hominin-evolution-68244581/

Other Sources:

NASA: https://solarsystem.nasa.gov/solar-system/our-solar-system/in-depth

Origin of the orbital architecture of the giant planets of the Solar System. K. Tsiganis1, R. Gomes and al. Vol 435|26 May 2005|doi:10.1038/nature03539

Formation and Accretion History of Terrestrial Planets From Runaway Growth Through to Late Time: Implications for Orbital Eccentricity. Ryuji Morishima and Max W. Schmidt. The Astrophysical Journal, 685:1247Y1261, 2008 October 1

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