"Planetary dynamics is probably the oldest of the physical sciences. It goes back to when Kepler and Galileo realized that the planets' motions were not any mystical phenomena. That these were inherently physical, and they could derive the physical laws governing the motion of the planets. So, in a way, all of Modern Science started off with understanding the motion of the planets through simple Newtonian laws," says Prof. Renu Malhotra, Louise Foucar Marshall Science Research Professor and Regents Professor of Planetary Sciences at the University of Arizona.

In the spirit of these great pillars of Modern Science, physicists have continued to unravel more subtle phenomena in the Solar System. Their findings have drastically changed what we thought we knew about our immediate Solar neighborhood.

Planetary Migration

It was long believed that all the planets were formed precisely where we see them today. This was a simple assumption borne out of the fact that at present, we observe a very stable state of the Solar System. Thus, there was no reason to believe that any process that causes significant shifts in the planets' positions had ever occurred. However, the Planetary Migration hypothesis suggests the contrary.

A schematic map of the Solar System. Source: Lecture Materials, Prof. Renu Malhotra

Approximately 4.5 billion years ago, when our Solar System was newly formed, the empty regions between the planets were filled with leftover small celestial bodies like asteroids and comets called planetesimals. These planetesimals were eventually cleared up by the gravitational effects of the Giant planets, bringing the Solar System to its present state. The Migration hypothesis draws attention towards the reaction forces these planetesimals would have exerted on the planets due to the law of Conservation of Angular Momentum. Thus, for example, a planet flinging an asteroid towards the interior of the Solar System would be pushed slightly outwards due to this reaction.

Statistical scattering effects of all the small bodies present in the Solar System at that time suggest that Jupiter must have migrated about 0.5 AU towards the Sun, and the other Gas Giants would have migrated outwards by varying distances, with Neptune moving the largest distance by 10 AU (the Astronomical Unit is a standard unit of measurement on the Solar System scale. 1 AU is defined as the distance between the Earth and the Sun.)

Prof. Malhotra explains this significant shift in Neptune's orbit:

"Jupiter, being the largest planet, naturally has the strongest gravitational influence. Thus, it preferentially removes the planetesimals scattered inward by Neptune and the other planets. Because all the planetesimals that used to be interior to planets orbits have been scattered very quickly by all the other giant planets inward of Neptune, the main source of planetesimals for Neptune to scatter is outside its orbit. Now, these bodies' specific energy and angular momentum is larger than Neptune's because the specific energy and angular momentum increase as the orbital radius increases. So, all the planetesimals that Neptune encounters have larger specific energy and angular momentum than itself. That creates a bias. The planetesimals scattered inside are removed faster from the system leading to an overall increase in Neptune's angular momentum and consequently, its orbital radius."

Migration had far-reaching consequences for the four Jovian planets. It describes how the Solar System attained its fine-tuned state, which, by extension, has allowed life to thrive on Earth. It also seems to have had drastic effects on the small, far-away dwarf planet- Pluto.


Pluto has ever been the enigma of the Solar System. Ever since its discovery by Clyde Tombaugh in 1930, Pluto's peculiar properties had puzzled astrophysicists. Its unusually high orbital eccentricity and the fact that Pluto's orbital plane is tilted by 17 degrees to the mean orbital plane are some features that are extremely difficult to integrate with most Planetary Dynamics models.

Diagrams illustrating Pluto’s unusual eccentricity and inclination. Source: Lecture Materials, Prof. Renu Malhotra

Another fascinating property of Pluto's orbit is that it is in a perfect 3:2 ratio with that of Neptune. Such pairs of orbits having their semi-major axes in whole-number ratios are called resonant orbits. Celestial bodies revolving in resonant orbits mutually affect each other's motion due to their periodic gravitational interactions. In Pluto's case, these resonance effects make sure that it never collides with Neptune, even though their orbital paths intersect. Pluto performs small loops at its perihelion (the point where it is closest to the Sun), which changes its subsequent trajectory to avoid crashing into Neptune. However, resonance effects only go so far. Pluto's eccentricity and inclination are still left unexplained…

Pluto’s motion around the Sun as viewed from Neptune’s frame of reference. Source: Lecture Materials, Prof. Renu Malhotra

Breakthroughs by Prof. Malhotra in the early 1990s shed entirely new light on this subject. Using the Planetary Migration hypothesis, she theorized that Pluto's peculiar orbit could have evolved into its present state after being captured in orbital resonance with Neptune.

Prof. Malhotra explains how she came up with this idea.

"I had this idea that maybe the orbits of Neptune and Pluto had changed over time. And then, at some point, they got locked into this resonant state in which we observe them today. But, at the time I was thinking about it, there wasn't any physical mechanism that anybody had proposed to explain the change in the orbits of planets. It was believed that the planets formed where we see them today. Then I discovered a paper by a pair of planetary dynamicists, Fernandez and Ip.
They had proposed that the planetesimal debris present in the early Solar System could make planets migrate. But that paper hadn't received much attention. In fact, people working in Planetary Dynamics told me that it was all wrong! But I looked into it anyway...
I thought about it, and I realized that it wasn't wrong. That there was a very important insight in that paper. It's just that our computers were not powerful enough to do the calculations correctly.
And, I was young. I was a little rebellious, and I went ahead with the idea. I realized that Pluto being in this mode-locked state with Neptune could be the evidence for planetary migration, and that's how I wrote those papers."
Neptune captures Pluto in resonance as it migrates away from the Sun. Source: Lecture Materials, Prof. Renu Malhotra

In her research, Prof. Malhotra came up with a rather simple logarithmic equation that describes the change in Pluto's eccentricity in terms of the distance of Neptune from the Sun. This equation even helped her predict that Neptune must have migrated by at least 5 AU for Pluto to attain its high eccentricity of 0.25.

A simple equation relating Pluto’s eccentricity to Neptune’s semi-major axis. Source: Malhotra, R. 1993a, Nature, 365:819-821

In the subsequent paper, she extended her hypothesis to all the Kuiper belt objects. This is the collection of asteroids present just beyond Neptune. Planetary migration implied that the asteroids in this region would pile up in several resonant orbits, the most prominent being the orbits in 1:1, 4:3, 3:2(Pluto's), and 2:1 ratios. These predictions were eventually verified by cataloging the asteroids observed in the Kuiper Belt. Thus, resonance and planetary migration were found to have numerous applications in explaining the overall structure of the Solar System.

Experimental verification of the distribution of asteroids in the Kuiper Belt as predicted by the Planetary Migration hypothesis. Source: Lecture Materials, Prof. Renu Malhotra
Experimental verification of the distribution of asteroids in the Kuiper Belt as predicted by the Planetary Migration hypothesis ‌‌

While these changes were happening in the outer Solar System, terrestrial planets (Mercury, Venus, Earth, and Mars) suffered a tormenting era of meteorite impacts. The impact craters on these planets suggest large-scale scattering of asteroids from the region between Mars and Jupiter once occurred. This phenomenon can easily be associated with the Migration of the Jovian Planets leading to the formation of what we now call the Asteroid belt.

Formation of the Asteroid Belt

The present-day structure of the Asteroid Belt is crucial observational evidence for Planetary Migration. Numerical simulations show that the Asteroid belt could have attained its present form only if the Jovian planets migrated.

A comparison of observational data about the distribution of asteroids in the Asteroid Belt in orange, to numerically simulated results in gray shows close agreement. Source: Lecture Materials, Prof. Renu Malhotra

This transition of the Asteroid Belt from being completely filled with debris to a relatively clear state at present had dire consequences for the terrestrial planets. These newly formed planets were bombarded by asteroids scattered due to the gravitational influences of the moving Jovian planets. Dating and analysis of the impact craters on Mars and Moon confirms that they were formed due to planetesimals coming from the Asteroid Belt around 3.9 billion years ago.

The effects of large-scale changes in the outer Solar System on these nearby terrestrial planets provide strong evidence supporting the Migration hypothesis. Moreover, analysis of the craters also sets the time at which migration must have occurred at 3.9 billion years ago, making the hypothesis more coherent.

Another facet of the Asteroid Belt that supplements the Migration hypothesis is that it sets an upper limit on the time taken by the planets to migrate. Had that process been prolonged, almost all the asteroids in the Belt would have been cleared due to the strong gravitational forces of the Giant plants. For the Asteroid Belt to be as populated as it is today, Migration could have only lasted for a few million years.

Careful study of these features of the asteroid belt has brought the Migration hypothesis much closer to completion. These discoveries have significantly increased our understanding of how the Solar System has evolved over time and have also changed the course of Planetary Sciences, adding several new dimensions to explore.

Impact on subsequent Literature and Future Applications

Ever since it was brought to the forefront by Prof. Malhotra's radical efforts, Migration has become a mainstay in Planetary Sciences. "It has really affected all of Planetary Science. Everything we do nowadays, almost every paper you see, will say something about what their line of research has to do with Migration," she said.

“It's like everything is colored by the idea that the planets didn't form where we see them. That their positions have changed”

One of the Planetary Science community's present goals is to know how exoplanet systems form and evolve. Understanding these far-off planetary systems could go a long way in revealing more about how our own Solar System has evolved and whether planet systems like ours are rare or relatively common in the Universe.

We have come a long way since Kepler, Newton, and Galileo took to understanding the mysterious motion of the planets. A deeper understanding of the same planetary dynamics in the coming years could well be the key to Humanity's destiny among the stars.  

Note: This article was inspired by the lecture given by Prof. Renu Malhotra in the Mysteries of the Universe(MOU) Lecture Series hosted by IIT, Roorkee. For more information about this and other lectures in the series, please visit: https://new.iitr.ac.in/ils-mou/#/

Prof. Mahotra's lecture materials cited above can be found at https://drive.google.com/file/d/1p_qEvVNVWPkyjxJN7c8sn7kPT2QTn0CT/view