Astronomy

Orbits of Trojan Asteroids

Orbits of Trojan Asteroids



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I understand that the Trojan points are located 60 degrees ahead and behind a planet in its orbit. However, since there are quite a number of Trojans in Jupiter's orbit, they cannot all be exactly at that point. Presumably they orbit around it.

So what sort of orbits do they have? Are they circular or anywhere near so, or are they elongated along the orbit of Jupiter? If the latter how far can they get from the 60 degree point?


Trojan asteroids are in roughly circular orbits around the Sun at roughly the same distance as Jupiter, that are in 1:1 resonance with Jupiter and stay very roughly 60 degrees away from it.

Scott Manley's video below shows two classes of asteroids in resonance with Jupiter. The first one shown is confusing because it is in a 3:2 resonance and in the rotating frame it looks like they are cycling between L3, L4 and L5. Skip ahead to 33 seconds and you can see what "normal Trojan asteroids" do. Most of them stay within +/-20 degrees of L4 or L5, only a few exotic stragglers go farther than that away from their Lagrange points. There is some out-of-plane motion as well, as there is for all asteroids.

@JamesK's answer showing a rather exotic asteroid in 1:1 resonance with Earth is an extreme case, but the GIF does help to give some illustration of the back-and-forthness, even though it's pretty exaggerated compared to what normally happens.

After watching, go back to the beginning and see the more confusing 3:2 resonance orbits.

update: There's this!


As an example, look at Earth's only confirmed Trojan

By Phoenix7777 - Own work Data source: HORIZONS System, JPL, NASA, CC BY-SA 4.0, source

Now, to understand what is happening here. The yellow dot is the sun. The blue dot is the Earth. Although the Earth is orbiting the sun, the "camera" is turning so that it appears that the Earth is roughly stationary (it wobbles slightly due to the eccentricty of the earth's orbit)

The pink dot is the asteroid 2010 TK7. It has an orbit that is eccentric, and so sometimes it is much closer to the sun than the Earth, and at other times it is further, but its orbit takes nearly exactly one year. However the exact shape of the orbit changes, sometimes it moves around the sun in slightly less than a year, so it starts to catch up with the Earth, but as it nears the Earth, the Earth's gravity tends to pull it forward, and out, causing it to slow down and move away from the earth. The whole cycle takes hundreds of years.

Note, the actual shape of the orbits are elliptical about the sun, the odd shapes is a result of the camera turning at one revolution per year.

This kind of orbit is said to librate about the L4 point. It is called a "tadpole orbit" Trojans don't have to remain exactly at the L4 point, they can stably orbit in a tadpole orbit around the L4 point.


Trojan Asteroids

Asteroids Beyond the Main Belt

The Trojan asteroids move in the same orbit as Jupiter, though they keep either well ahead of or well behind the Giant Planet and are in no danger of being engulfed. Mars has several Trojans, and Neptune one. No true Earth Trojans are known, though 3753 Cruithne has almost the same orbital period and describes a curious sort of ‘horseshoe’ path with respect to the Earth. There are also asteroids, such as 944 Hidalgo and 5335 Damocles, with very eccentric orbits, very like those of comets. For example, Damocles has a period of 40.9 years its orbit crosses those of Mars, Jupiter, Saturn, and Uranus, but is in no danger of collision as its orbital inclination is 61°. It is no more than 15 km in diameter.

The ‘Centaur’ asteroids remain well beyond the Main Belt the first to be found (in 1977) was 2060 Chiron, which moves mainly between the orbits of Saturn and Uranus, in a period of 50 years. It shows traces of a coma at times, but seems much too large to be classed as a comet, even though it has been given a cometary number.


Trojan asteroid

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Trojan asteroid, also called Trojan planet, any one of a number of asteroids that occupy a stable Lagrangian point in a planet’s orbit around the Sun.

In 1772 the French mathematician and astronomer Joseph-Louis Lagrange predicted the existence and location of two groups of small bodies located near a pair of gravitationally stable points along Jupiter’s orbit. Those are positions (now called Lagrangian points and designated L4 and L5) where a small body can be held, by gravitational forces, at one vertex of an equilateral triangle whose other vertices are occupied by the massive bodies of Jupiter and the Sun. Those positions, which lead (L4) and trail (L5) Jupiter by 60° in the plane of its orbit, are two of the five theoretical Lagrangian points in the solution to the circular restricted three-body problem of celestial mechanics. The other three stable points are located along a line passing through the Sun and Jupiter. The presence of other planets, however—principally Saturn—perturbs the Sun-Jupiter-Trojan asteroid system enough to destabilize those points, and no asteroids have been found near them. In fact, because of that destabilization, most of Jupiter’s Trojan asteroids move in orbits inclined as much as 40° from Jupiter’s orbit and displaced as much as 70° from the leading and trailing positions of the true Lagrangian points.

In 1906 the first of the predicted objects, (588) Achilles, was discovered by German astronomer Max Wolf near L4. Within a year two more were found: (617) Patroclus, located near L5, and (624) Hektor, near L4. It was later decided to continue naming such asteroids after participants in the Trojan War as recounted in Homer’s epic work the Iliad and, furthermore, to name those near the leading point after Greek warriors and those near the trailing point after Trojan warriors. With the exception of the two “misplaced” names already bestowed (Hektor, the lone Trojan in the Greek camp, and Patroclus, the lone Greek in the Trojan camp), that tradition has been maintained.

As of 2020, of the more than 7,000 Jupiter Trojan asteroids discovered, about two-thirds are located near L4, and the remainder are near L5. Astronomers estimate that 1,800–2,200 of the total existing population of Jupiter’s Trojans have diameters greater than 15 km (10 miles).

Nearly all of Jupiter’s Trojans are dark, having albedos (percentage of visual light reflected) between 0.04 and 0.10. (However, one Trojan, [4709] Ennomos, has an albedo of 0.15, which is greater than that of the Moon [0.12].) The majority belong to two compositionally distinct groups that are similar to the most-common classes of outer main-belt asteroids.

Since the discovery of Jupiter’s orbital companions, astronomers have searched for Trojan objects of Earth, Mars, Saturn, Uranus, and Neptune as well as of the Earth-Moon system. It was long considered doubtful whether truly stable orbits could exist near the Lagrangian points of the smaller planets because of gravitational perturbations by the major planets. However, in 1990 an asteroid later named (5261) Eureka was discovered librating (oscillating) about the L5 point of Mars, and since then eight others have been found, one at L4 and seven at L5. Twenty-four Trojans of Neptune, all but three associated with L4, have been discovered since 2001. The first Earth Trojan asteroid, 2010 TK7, which librates around L4, was discovered in 2010, and the first Uranus Trojan, 2011 QF99, which librates around L4, was discovered the next year. Although Trojans of Saturn have yet to be found, objects librating about Lagrangian points of the systems formed by Saturn and its moon Tethys and Saturn and its moon Dione are known.


Dec 13th: Small Asteroids in Earth-like Orbits & Jupiter Trojan Confusion

Description: Today’s 2 topics:

  • Four days after it made its closest approach to Earth, I found a 10 foot diameter asteroid with the NASA funded University of Arizona 60 inch telescope on Mt. Lemmon.
  • Humans know of approximately half million main belt asteroids orbiting the Sun between Mars and Jupiter. We have also found approximately 11,000 Earth approaching asteroids.

Bio: Dr. Al Grauer is currently an observing member of the Catalina Sky Survey Team at the University of Arizona. This group has discovered nearly half of the Earth approaching objects known to exist. He received a PhD in Physics in 1971 and has been an observational Astronomer for 43 years. He retired as a University Professor after 39 years of interacting with students. He has conducted research projects using telescopes in Arizona, Chile, Australia, Hawaii, Louisiana, and Georgia with funding from NSF and NASA.

He is noted as Co-discoverer of comet P/2010 TO20 Linear-Grauer, Discoverer of comet C/2009 U5 Grauer and has asteroid 18871 Grauer named for him.

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91E: Small Asteroids in Earth-like Orbits

Four days after it made its closest approach to Earth, I found a 10 foot diameter asteroid with the NASA funded University of Arizona 60 inch telescope on Mt. Lemmon. At that point it was 838,000 miles from us and was moving away at about 3 miles/second. Previously, It had been about half the distance to the Moon from planet Earth. This small asteroid orbits the Sun every 349 days on a path which crosses our orbit twice a year. Calculations by the NASA – JPL group indicate that it can come within 2 Earth diameters of us.

A week later my Catalina Sky Survey Survey team leader, Eric Christensen found a slightly larger small asteroid. It orbits the Sun in 388 days and can closer than 4 Earth diameters to us.

Either of these small asteroids would fit into the bed of a dump truck. Their speeds relative to Earth are well within our rockets ability to catch them.

These two asteroids do not pose a threat to humans. If they ever did enter the Earth’s atmosphere, they would likely burn up at high altitude producing a supersonic boom. They are interesting because they could be targets for NASA’s Asteroid Redirect Mission. The concept for this project is to redirect a small asteroid into orbit around the Moon where it would be visited by Astronauts using the Orion Spacecraft. This mission will provide us with scientific data about Earth approaching objects and develop the capability for humans to explore the planet Mars.

92E: Jupiter Trojan Confusion

Humans know of approximately half million main belt asteroids orbiting the Sun between Mars and Jupiter. We have also found approximately 11,000 Earth approaching asteroids. Members of these two groups can be recognized by briefly observing their motion since their paths about the Sun are very different. Jupiter Trojans, on the other hand, occupy a point either 60 degrees in front or behind Jupiter as it moves about the Sun. Their orbit around the Sun takes about 5 and a half years so short pieces of one of their orbits can mimic the path of an Earth approaching object. When Jupiter Trojans are opposite to the Sun, their little full moon faces are pointing towards Earth. When they are in this position in the sky we have to sort through a number of them so we can separate them from real near Earth objects.

The Jupiter Trojans oscillate about a stable point 60 degrees in front of or behind a planet as it orbits the Sun. This geometry was predicted by Joseph-Louis Lagrange in 1772. More than 100 years later Astronomers began to discover Jupiter Trojans. Today we know of almost 6,000 of the perhaps several hundred thousand of these asteroids which are larger than a kilometer in diameter. The largest one, Hektor. It is about 120 miles in diameter. Most of the Jupiter Trojans are much smaller than Hektor and may be fragments of larger ones which collided with each other.

Someday humans may visit these distant asteroids and find them to be a rich sources of raw materials.

For Travelers in the Night this is Dr. Al Grauer.

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How were the Trojan asteroids discovered and named?

Illustration of the Lucy mission's seven targets: the binary asteroid Patroclus/Menoetius, Eurybates, Orus, Leucus, Polymele, and the main belt asteroid DonaldJohanson. Credit: NASA's Goddard Space Flight Center Conceptual Image Lab

On Feb. 22, 1906, German astrophotographer Max Wolf helped reshape our understanding of the solar system. Again.

Born in 1863, Wolf had a habit of dramatically altering the astronomy landscape. Something of a prodigy, he discovered his first comet at only 21 years old. Then in 1890, he boldly declared that he planned to use wide-field photography in his quest to discover new asteroids, which would make him the first to do so. Two years later, Wolf had found 18 new asteroids. He later became the first person to use the "stereo comparator," a View-Master-like device that showed two photographs of the sky at once so that moving asteroids appeared to pop out from the starry background.

It is perhaps unsurprising, then, that on Feb. 22, 1906, Wolf made another important discovery: an asteroid with a particularly unusual orbit. As Jupiter moved, this asteroid remained ahead of Jupiter, as though it was somehow trapped in Jupiter's orbit around the Sun. German astronomer Adolf Berberich observed that the asteroid was nearly 60 degrees in front of Jupiter. This specific position reminded Swedish astronomer Carl Charlier of a peculiar behavior predicted by the Italian-French mathematician Joseph-Louis Lagrange over 100 years earlier. Lagrange argued that if a small body (such as an asteroid) is placed at one of two stable points in a planet's orbit around the Sun (called the L4 and L5 Lagrange Points), the asteroid would remain stationary from the planet's perspective due to the combined gravitational forces of the planet and the Sun. Charlier realized that Wolf's asteroid was actually caught in Jupiter's L4 Lagrange point. Until Wolf's discovery, Lagrange's prediction had only been a mathematical exercise. Now, these astronomers had photographic proof that Lagrange was right.

Eight months later, one of Wolf's graduate students August Kopff discovered an asteroid in Jupiter's other stable Lagrange point L5, as well as another asteroid caught in L4 a few months afterward.

Once three of these Lagrange point-inhabiting asteroids had been discovered, astronomers began wondering what to call them. At this point, most asteroids were given the names of women from Roman or Greek mythology, unless their orbits were particularly strange. The asteroids in question certainly had bizarre orbits, so Austrian astronomer Johann Palisa suggested the names Achilles, Patroclus, and Hektor after characters from The Iliad. Achilles was a nigh-invulnerable Greek hero (except for his heel), and Patroclus was a friend of his. Hektor, prince of the Trojans, eventually killed Patroclus, and Achilles exacted revenge by killing Hektor. The recently discovered asteroids were then given Iliad-inspired names.

As astronomers continued discovering asteroids hiding in Jupiter's Lagrange points, they continued naming them after heroes of the Trojan War and began referring to them as "Trojan asteroids." ("Trojan asteroids" would eventually refer to asteroids inhabiting any planet's stable Lagrange points, though names from The Iliad are reserved for Jupiter's Trojans.) It later became convention to name Jupiter's L4 asteroids after Greek characters and Jupiter's L5 asteroids after Trojan characters, so L4 and L5 became the "Greek camp" and the "Trojan camp" respectively. Palisa apparently did not foresee this tradition, for his naming of first three asteroids led to a Greek "spy" residing in the Trojan camp (Patroclus) and a confused Trojan (Hektor) who probably wandered into the Greek camp hoping to order some of their famous custom-built wooden horses.

No spacecraft has ever been to this population of small bodies, called the Trojan asteroids. Now, a new NASA Discovery Program mission called Lucy will fly by seven Trojan asteroids, plus a main belt asteroid, to survey the diversity of this population in a single 12-year record-breaking mission. The Lucy spacecraft launch window opens Oct. 16, 2021.


Asteroids sharing an orbit with a planet, but which are located at the leading (L4) and trailing (L5) Lagrangian points, are known as Trojan asteroids. Although Trojan asteroids have been discovered for Mars (4 to date, 1 at L4 and 3 at L5) and Neptune (8 Trojans, 6 at L4 and 2 at L5) and even Earth (1 Trojan at L4), the term ‘Trojan asteroid’ generally refers to the asteroids accompanying Jupiter.

There are currently over 4,800 known Trojan asteroids associated with Jupiter. About 65% of these belong to the leading group (L4) located 60 o in front of Jupiter in its orbit, while the other 35% cluster around the L5 Lagrangian point and trail 60 o behind Jupiter. Although their orbits are stabilised at the Lagrangian points by gravitational interactions with Jupiter and the Sun, their actual distribution is elongated along the orbit. Perturbations by the other planets (primarily Saturn) cause the Trojans to oscillate around L4 and L5 by ∼20° and at inclinations of up to 40° to the orbital plane. These oscillations generally take between 150 and 200 years to complete.

Such planetary perturbations may also be the reason why there have been so few Trojans found around other planets. In particular, we assume that the Trojans formed at their present positions at the same time as Jupiter emerged from the solar nebula. If this is correct, we would also expect Saturn to be accompanied by families of Trojan asteroids. That no Trojans are found at the Lagrangian points of Saturn is most likely the result of Jupiter removing them from these stable orbits through gravitational perturbations.

The term ‘Trojan asteroid’ was coined when it was decided to name all asteroids discovered at the L4 and L5 points of Jupiter after warriors in the Trojan war, Greek and Trojan respectively. The exceptions are Hector (a Trojan spy in the Greek camp) and Patroclus (a Greek spy in the Trojan camp), the first two Trojan asteroids discovered and named before the two camps were established.

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All material is © Swinburne University of Technology except where indicated.


Why are they called Trojan Asteroids?

On February 22, 1906, German astrophotographer Max Wolf helped reshape our understanding of the solar system. Again.

Born in 1863, Wolf had a habit of dramatically altering the astronomy landscape. Something of a prodigy, he discovered his first comet at only 21 years old. Then in 1890, he boldly declared that he planned to use wide-field photography in his quest to discover new asteroids, which would make him the first to do so. Two years later, Wolf had found 18 new asteroids. He later became the first person to use the “stereo comparator,” a View-Master-like device that showed two photographs of the sky at once so that moving asteroids appeared to pop out from the starry background.

It is perhaps unsurprising, then, that on February 22, 1906, Wolf made another important discovery: an asteroid with a particularly unusual orbit. As Jupiter moved, this asteroid remained ahead of Jupiter, as though it was somehow trapped in Jupiter’s orbit around the Sun. German astronomer Adolf Berberich observed that the asteroid was nearly 60° in front of Jupiter. This specific position reminded Swedish astronomer Carl Charlier of a peculiar behavior predicted by mathematician Joseph-Louis Lagrange over 100 years earlier. Lagrange argued that if a small body (such as an asteroid) is placed at one of two stable points in a planet’s orbit around the Sun (called the L4 and L5 “Lagrange Points”), the asteroid would remain stationary from the planet’s perspective due to the combined gravitational forces of the planet and the Sun. Charlier realized that Wolf’s asteroid was actually caught in Jupiter’s L4 Lagrange point. Until Wolf’s discovery, Lagrange’s prediction had only been a mathematical exercise. Now, these astronomers had photographic proof that Lagrange was right.

Eight months later, one of Wolf’s graduate students August Kopff discovered an asteroid in Jupiter’s other stable Lagrange point L5, as well as another asteroid caught in L4 a few months afterward.

Once three of these Lagrange point-inhabiting asteroids had been discovered, astronomers began wondering what to call them. At this point, most asteroids were given the names of women from Roman or Greek mythology, unless their orbits were particularly strange. The asteroids in question certainly had bizarre orbits, so Austrian astronomer Johann Palisa suggested the names Achilles, Patroclus, and Hektor after characters from The Iliad. Achilles was a nigh-invulnerable Greek hero (except for, you know…), and Patroclus was a friend of his. Hektor, prince of the Trojans, eventually killed Patroclus, and Achilles exacted revenge by killing Hektor.

As astronomers continued discovering asteroids hiding in Jupiter’s Lagrange points, they continued naming them after heroes of the Trojan War and began referring to them as “Trojan asteroids.” (“Trojan asteroids” would eventually refer to asteroids inhabiting any planet’s stable Lagrange points, though names from The Iliad are reserved for Jupiter’s Trojans.) It later became convention to name Jupiter’s L4 asteroids after Greek characters and Jupiter’s L5 asteroids after Trojan characters, so L4 and L5 became the “Greek camp” and the “Trojan camp.” Palisa apparently did not foresee this tradition, for his naming of first three asteroids led to a Greek “spy” residing in the Trojan camp (Patroclus) and a confused Trojan (Hektor) who probably wandered into the Greek camp hoping to order some of their famous custom-built wooden horses.

  • Cornish, N. J. (2020, January 4). What is a Lagrange Point? Retrieved June 8, 2020, from https://solarsystem.nasa.gov/resources/754/what-is-a-lagrange-point/ Editors of Encyclopaedia Britannica. (2019, September 29). Max Wolf. Retrieved June 8, 2020, from https://www.britannica.com/biography/Max-Wolf
  • Lowell Observatory. (2016, June 8). Naming Asteroids. Retrieved June 8, 2020, from https://lowell.edu/sga/naming-asteroids/
  • Michel, P., DeMeo, F. E., & Bottke, W. F. (2015). Asteroids IV. Tucson: The University of Arizona Press.
  • Murdin, P. (2016). Rock Legends: the Asteroids and Their Discoverers. Springer International Publishing AG. doi: 10.1007/978-3-319-31836-3
  • Nicholson, S. B. (1961). The Trojan Asteroids. Astronomical Society of the Pacific Leaflets, 8(381), 239–246.
  • Tenn J. S. (1994) Max Wolf: The twenty-fifth Bruce Medalist. Mercury, 23(3), 27-28.

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Trojan Asteroids Are in a Class of Their Own

By: Christopher Crockett October 26, 2018 0

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Hordes of debris trapped by Jupiter and Neptune have distinct colors that mark them as possibly the last remnants of the material that built the giant planets.

Trojan asteroids lead and trail Jupiter along its orbit around the Sun in this illustration.
NASA / JPL-Caltech

There’s a color conundrum among some of the smaller members of our solar system.

Jupiter and Neptune drag pockets of rocky debris on their treks around the Sun. Known as Trojans, these asteroid-like objects were likely swept up by the gravity of these two worlds. Swept up from where and when, though, has long been a mystery that could reveal details about how the young solar system evolved.

Well, the mystery keeps getting deeper. New observations build on previous hints that the Trojans at Jupiter and Neptune — despite being separated by billions of kilometers — have remarkably similar colors that don’t match any other small bodies in the solar system.

“Nature is giving us a little punch in the eye,” said David Jewitt (UCLA) during an October 23rd press conference at a meeting of the American Astronomical Society’s Division for Planetary Sciences.

Trojan asteroids lead and trail a planet as it orbits the Sun. They congregate at special points known as Lagrange points, where gravitational and orbital forces balance. One leading idea (of several) for their origin is that Trojans are lost souls from the Kuiper belt, the field of frozen debris beyond Neptune.

To test this idea, Jewitt compared the colors of 13 Neptunian Trojans to the colors of bodies in the Kuiper belt. They didn’t match. Neptune’s Trojans do, however, have similar colors to the Trojans near Jupiter, implying a common origin for both.

Astronomers have known for a while that Jupiter’s Trojans don’t match the Kuiper belt. Some researchers suspected that warmer temperatures near Jupiter could modify the surfaces of any visitors from the frigid Kuiper belt, thus changing their colors. But Jewitt said that doesn’t explain the color mismatch at Neptune, where the temperature is nearly the same as the Kuiper belt.

(Story continues after animation.)

Jupiter's Trojans (green) follow the giant planet (orange) on its orbit around the Sun. This animation shows their movements (along with the inner planets) during the course of NASA's Lucy mission to the Trojans.
Petr Scheirich (Astronomical Institute of the Czech Academy of Sciences)

“The Trojans are probably the last remnants of what formed the planets,” says Scott Sheppard (Carnegie Institution for Science). The planets are thought to have formed from lots of little things smashing together to make big things. The stuff that didn’t make it into a planet continued to orbit the Sun, and some of that debris could have gotten trapped where the Trojans live today.

Sheppard published a paper in 2006, along with Chad Trujillo (Northern Arizona University), that presented colors of the first four known Neptunian Trojans. Even then, there were hints that the Trojans were a separate family from everything else in the solar system. In the years since, that case has continued to build. “This new result doubles the sample size,” says Sheppard. “It continues to show this trend of being a very different population.” (See Sheppard's article in our June 2016 issue.)

Sarah Sonnett (Planetary Science Institute) agrees: “This is a very interesting result that provides constraints on where Neptune Trojans might have formed,” she says. “It consequently could help us understand how giant planets may have migrated early in solar system history.”

Most planetary scientists agree that the giant planets formed closer together and then migrated to their current orbits more than 4 billion years ago. If the Trojans were swept up during that time, they might have much to say about how the planets jockeyed for position. Some Jupiter Trojans, for example, are on highly inclined orbits. “That suggests a very chaotic environment,” Sheppard says. Planets effectively bouncing off one another could have stirred up the surrounding debris to create the Trojan orbits seen today.

“The Trojans have always been an overlooked population,” says Sheppard. They’re hard to observe and their spectra don’t reveal much. That’s where NASA’s Lucy mission might help. Scheduled to launch in 2021, it will spend seven years visiting six Jupiter Trojans (plus an asteroid in the belt between Mars and Jupiter), becoming the first probe to investigate this enigmatic population.


Asteroid Groups

Asteroids are grouped according to their orbit range, as follows:

Near-Earth Asteroids (NEAs)

Objects in near-earth orbit. There are about 9,000 objects known ranging from 1 meter to 32 meters in diameter. These asteroids can be further grouped as follows:

  • Atira group: Inside Earth's orbit semi-major axis less than 1.0 AU
  • Aten group: Cross Earth's orbit semi-major axis less than 1.0 AU
  • Apollo group: Cross Earth's orbit semi-major axis greater than 1.0 AU
  • Amor group: Outside Earth's orbit semi-major axis greater than 1.0 AU

Main-Belt Asteroids

The total mass of the asteroid belt is just 4% that of the moon. Millions of asteroids located between the orbits of Mars and Jupiter (1.8 to 4.0 AU) are in the "asteroid belt".

Trojan Asteroids

Mainly, two large groups of asteroids located along the orbital path of Jupiter, 60 degrees ahead and behind the planet at the trojan points. There are also eight Mars Trojans and one Earth Trojan known.

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Dwarf planet Ceres


Asteroid Vesta


Asteroid Pallas


Asteroid Eros


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