The Mystery of the Missing Planets : L4 and L5 Lagrange Points in a Solar System

List members , there is a possibility that the L4 & L5 Lagrange Points in any given Solar System , are well suited for the presence of "Trojan" planets - it's an intriguing line of research being done . Lagrange Points have been called "Gravitational Parking Lots" , as well :-

The Mystery of the Missing Planets


There is an unsolved problem I want to tell you about: The case of the missing Trojans. You might be thinking of the mythical horse with soldiers hidden inside. Or maybe you’re thinking of a sports team. Or a type of computer virus, or, let’s be honest, of the condoms. (Note that I said, “Case of the missing Trojans,” not, “the Missing case of Trojans.”)

But there is another type of Trojan: an orbit. A swarm of thousands of asteroids share an orbit with Jupiter. They are not right next to the planet, like moons, but rather clustered in two clumps, one ahead of Jupiter on its orbit and one behind. The leading clump is called the “Greeks” and the trailing clump the “Trojans,” but they are usually just lumped together and simply called Jupiter’s Trojans. Many of them are named after mythological figures from the Trojan wars.

The inner Solar System. The planets are labeled and the blue lines show their orbits. The small dots are asteroids. The main asteroid belt is shown in white. The green dots—called “Greeks” and “Trojans”—what we call Jupiter’s “Trojans.”Wikipedia user Mdf

Jupiter is more than 300 times more massive than Earth. Its gravity has almost completely emptied out the asteroid belt, which we think once contained 1,000 times more material than it does now. How can these Trojans survive so close to a gas giant and yet remain on stable orbits?

It turns out that this was figured out way back in 1772 by French mathematician Joseph-Louis Lagrange. If we visualize a planet’s orbit around a star, there are a few special points where an extra body can orbit at the same rate as the planet. These are called the Lagrange points, and there are five of them, named L1 through L5.

Lagrange points of a planet (blue) orbiting a star. L4 and L5 are the place where Trojan planets can survive. The other points (L1, L2 and L3) and not stable. Credit: WikipediaWikipedia user Cmglee

Only two of the Lagrange points are stable: L4 and L5. A body that is located at or near these points will happily orbit the Sun, remaining roughly 60 degrees in front or behind Jupiter. (More precisely, the extra body will actually oscillate with a typical amplitude of about 20 degrees around its Lagrange point, and there is even a class of orbit called a “horseshoe” that goes all the way around between L4 and L5.) Jupiter has Trojans simply because its L4 and L5 are stable despite the gravitational kicks of the other planets. They are islands of stability in a huge unstable ocean. If asteroids were sprinkled uniformly across the inner Solar System, the only ones that would survive near Jupiter are the Trojans.

Jupiter is not the only planet in the Solar System to have Trojans, although it has by far the most. Uranus (1 Trojan) and Neptune (13) each have them. So does Mars (7). And Earth even has one! Surprisingly, Saturn does not have any; the reason appears to be that Jupiter’s gravity de-stabilizes Saturn’s Trojans on millionyear timescales. Saturn’s Trojan island has sunk under the ocean of instability (though Saturn’s moons actually have four Trojan), as has Venus’.

Let’s take this Trojan idea a step farther. The objects trapped near the stable islands at L4 and L5 don’t need to be puny little asteroids. They can be full-grown planets! If two planets lie in the same orbit, separated by 60 degrees, they form a pair of Trojan planets.

Trojan planets are commonly found in computer simulations that try to explain how planets orbiting other stars (“exoplanets”) are created. Many of the known exoplanets have orbits very close to their stars. Astronomers think that many of these planets formed farther away and were pushed closer in by a process called orbital migration. It is the disks of gas and dust from which the planets were born that are causing the planets to migrate. And it is during this migration that adjacent planets can be trapped in Trojan configurations. Trojan planets don’t form during every simulation but they do pop up every third or fourth time.

Snapshot from a computer simulation of a pair of Trojan planets—each 10 times as massive as Earth—migrating in a gaseous protoplanetary disk. The image shows the wakes created by the planets in the disk; the planets are at the center of the light green swirls, at the center of the wakes. Gory details here.Arnaud Pierens

So we think that Trojan planets should exist. We don’t have any in the Solar System, but Trojan planets should definitely exist around other stars, and they should be detectable with current telescopes! The best tool for the job is Kepler, NASA’s planet-finding space telescope extraordinaire. So what has Kepler found?

Drumroll…and a big frowny face. Kepler has not found any Trojan planets. There was one announced discovery of a four-planet system called KOI-730 (now named Kepler-223) with two Trojan planets sharing an orbit plus two more planets, one interior and one exterior to the Trojan pair.

Unfortunately, this system was later determined to be in a different configuration with no Trojan planets. Bummer.

The search for Trojan exoplanets has been ongoing for several years, and it continues, but things are looking grim. Trojan planets are supposed to be relatively easy to detect, so their absence stands out. It’s a cosmic mystery: The case of the missing Trojans!

So why aren’t we finding any Trojan planets? There are two possibilities: Either the Trojans are there but we aren’t finding them, or they simply aren’t there.

Could Trojan pairs be harder to find than we thought? Well, two planets on the same orbit each produce a signal with the same frequency and, if you aren’t expecting this, it can make both planets look like noise. But we are expecting it. Plus, the gravitational tug of war between Trojan planets also changes the phase of their signal, but we know this, too, and can actually use it as a tool to try to find Trojans.

Perhaps Trojan configurations are destroyed either as planets migrate inward or, for planets very close to their stars, because of tidal interactions between the planets and star. However, these destruction mechanisms should only affect a small fraction of the planets that Kepler is finding.

My own pet theory goes like this. Planets migrate inward in cohorts, often with Trojan pairs. But when the gaseous protoplanetary disk dissipates, the orbits of the migrated planets go haywire. There is a phase of giant collisions between planets that both destroys Trojan pairs and re-organizes the orbits of the survivors. This model matches what we see in the dataset of exoplanets, so that’s encouraging. Plus, once in a while, planets migrate in and do not go haywire, so according to the model there should indeed be some Trojan pairs out there, and we can predict where we should find them. Of course, it’s just a model so we’ll see how it stands the test of time, as more data floods in.

Lagrange Points: Parking Places in Space

By Elizabeth Howell almost 4 years ago

Diagram of the sun-Earth Lagrange points

Diagram of the Lagrange points associated with the sun-Earth system. (Image credit: NASA / WMAP Science Team)

A Lagrange point is a location in space where the combined gravitational forces of two large bodies, such as Earth and the sun or Earth and the moon, equal the centrifugal force felt by a much smaller third body. The interaction of the forces creates a point of equilibrium where a spacecraft may be "parked" to make observations.

These points are named after Joseph-Louis Lagrange, an 18th-century mathematician who wrote about them in a 1772 paper concerning what he called the "three-body problem." They are also called Lagrangian points and libration points.

Structure of Lagrange points

There are five Lagrange points around major bodies such as a planet or a star. Three of them lie along the line connecting the two large bodies. In the Earth-sun system, for example, the first point, L1, lies between Earth and the sun at about 1 million miles from Earth. L1 gets an uninterrupted view of the sun, and is currently occupied by the Solar and Heliospheric Observatory (SOHO) and the Deep Space Climate Observatory.

L2 also lies a million miles from Earth, but in the opposite direction of the sun. At this point, with the Earth, moon and sun behind it, a spacecraft can get a clear view of deep space. NASA's Wilkinson Microwave Anisotropy Probe (WMAP) is currently at this spot measuring the cosmic background radiation left over from the Big Bang. The James Webb Space Telescope will move into this region in 2018.

The third Lagrange point, L3, lies behind the sun, opposite Earth's orbit. For now, science has not found a use for this spot, although science fiction has.

“NASA is unlikely to find any use for the L3 point since it remains hidden behind the sun at all times,” NASA wrote on a web page about Lagrange points. “The idea of a hidden 'Planet-X' at the L3 point has been a popular topic in science fiction writing. The instability of Planet X's orbit (on a time scale of 150 years) didn't stop Hollywood from turning out classics like 'The Man from Planet X.'”

L1, L2 and L3 are all unstable points with precarious equilibrium. If a spacecraft at L3 drifted toward or away from Earth, it would fall irreversibly toward the sun or Earth, "like a barely balanced cart atop a steep hill," according to astronomer Neil DeGrasse Tyson. Spacecraft must make slight adjustments to maintain their orbits.

Points L4 and L5, however, are stable, "like a ball in a large bowl," according to the European Space Agency. These points lie along Earth's orbit at 60 degrees ahead of and behind Earth, forming the apex of two equilateral triangles that have the large masses (Earth and the sun, for example) as their vertices.

Because of the stability of these points, dust and asteroids tend to accumulate in these regions. Asteroids that surround the L4 and L5 points are called Trojans in honor of the asteroids Agamemnon, Achilles and Hector (all characters in the story of the siege of Troy) that are between Jupiter and the Sun. NASA states that there have been thousands of these types of asteroids found in our solar system, including Earth’s only known Trojan asteroid, 2010 TK7.

L4 and L5 are also possible points for a space colony due to their relative proximity to Earth, at least according to the writings of Gerard O'Neill and related thinkers. In the 1970s and 1980s, a group called the L5 Society promoted this idea among its members. In the late 1980s, it merged into a group that is now known as the National Space Society, an advocacy organization that promotes the idea of forming civilizations beyond Earth.

Benefits of Lagrange points

If a spacecraft uses a Lagrange point close to Earth, there are many benefits to the location, the Jet Propulsion Laboratory's Amy Mainzer told

Mainzer is principal investigator of NEOWISE, a mission that searches for near-Earth asteroids using the Wide-field Infrared Survey Explorer (WISE) spacecraft that orbits close to our planet. While WISE is doing well with its current three-year mission that concludes in 2016, Mainzer said, a spacecraft placed at a Lagrange point would be able to do more.

Far from the interfering heat and light of the sun, an asteroid-hunting spacecraft at a Lagrange point would be more sensitive to the tiny infrared signals from asteroids. It could point over a wide range of directions, except very close to the sun. And it wouldn't need coolant to stay cool, as WISE required for the first phase of its mission between 2009 and 2011 — the location itself would allow for natural cooling. The James Webb Space Telescope will take advantage of the thermal environment at the sun-Earth L2 point to help keep cool.

L1 and L2 also “allow you to have enormous bandwidth” because over conventional Ka-band radio, the communication speeds are very high, Mainzer said. “Otherwise, the data rates just become very slow,” she said, since a spacecraft in orbit around the sun (known as heliocentric orbit) would eventually drift far from Earth.

Lagrange point science

Multiple astronomical and Earth observatories are located at Lagrange points, providing a vantage point of our planet and space that you can't get from close-up. Scientists also perform periodic studies of small bodies naturally occurring at Lagrange points. Here are some recent science results:

In 2016, NASA released a video of the Earth spinning through an entire year. The time-lapse was based on 3,000 pictures taken every two hours by the EPIC camera on the Deep Space Climate Observatory (DSCOVR) satellite, which was at L1. Besides showing pretty views, EPIC provides scientists with metrics on climate such as cloud height, ultraviolet reflectivity, or ozone and aerosol levels.

In February 2017, the OSIRIS-REX mission — then on its way to asteroid Bennu — spent about 10 days looking for additional Trojan asteroids in Lagrange points near Earth. "That would be the most fascinating thing we could discover," mission lead scientist Dante Lauretta, a planetary scientist with the University of Arizona's Lunar and Planetary Laboratory, told a NASA science advisory group in January. The search revealed no new Trojans, but perhaps other spacecraft will look again in the future.

A 2017 study suggests that Trojan asteroids near Mars are from the planet, and not captured asteroids from other regions in space. The smoking gun is that at least three of Mars' nine Trojan asteroids are high in olivine. This mineral is rare in asteroids, but common on larger bodies (including Mars, which has it in impact basins). While Earth and Venus have olivine as well, lead author David Polishook, a researcher at the Weizmann Institute in Israel, told that it's much easier for Mars to capture asteroids from its own surface.