Asteroid 3753 Cruithne

3753 Cruithne is an asteroid that has an orbital period of 364 days and a semi-major axis of 0.998 AU, very similar to Earth. Therefore, it has a 1:1 resonance with the Earth, even though it does not orbit the Earth - Cruithne is NOT a moon of Earth. 

Globedia (note: this website is in Spanish)

 



But unlike Earth, its orbit is much more eccentric with a perihelion of only 0.484 AU (between the orbits of Mercury and Venus) and an aphelio of 1.51 AU (at the orbit of Mars). As shown in the next graphic, it has a normal, elliptical orbit.



"Orbits of Cruithne and Earth". Licensed under Creative Commons Attribution-Share Alike 3.0 via Wikimedia Commons -

However, when you compare the orbit of Cruithne with a stationary Earth, the orbit takes on a strange shape - it has a kidney bean shape relative to Earth. Again, this does not mean that it orbits the Earth and is another moon of Earth. What the kidney bean shape reveals is how the position of 3753 Cruithne compares to the Earth.

"Horseshoe orbit of Cruithne from the perspective of Earth". Licensed under Creative Commons Attribution-Share Alike 3.0 via Wikimedia Commons -

 

Next time, I'll be posting about an even stranger orbital path relative to Earth - a horseshoe shape.

Aten Asteroids

A simple schematic of the inner solar system, the yellow star in the middle is the Sun, the gray circle is Mercury, the grayish-yellow circle is Venus, the blue circle is Earth, the red circle is Mars, and the orange circle is Jupiter. The green band between Mars and Jupiter is the asteroid belt. The brown band covering area between the Sun and just outside of Earth's orbit are the location of Aten asteroids.

In the previous post, I discussed a little bit about near-Earth asteroids and the three different types that exist. In the next few posts, I will go into more detail about the three families of near-Earth asteroids. Today's topic is about Aten asteroids, the near-Earth asteroids that have a semi-major axis smaller than one AU (the semi-major axis of Earth).

Aten asteroids are named after the first one discovered, 2062 Aten. 2062 Aten was discovered by Eleanor F. Helin at Palomar Observatory in 1976. It is named after the Egyptian Sun god, Aten, whose name is seen in many the names of many pharoahs, most famously Tutankhaten (who renamed himself Tutankhamun to reflect his worship of Amun over Aten).

Despite having semi-major axes smaller than Earth's orbit, Aten asteroids can and do cross Earth's orbit. Remember that to be a near-Earth asteroid, the asteroid must come within 0.3 AU of Earth's orbit which means that Aten asteroids must have an aphelion of 0.7 AU or larger.  Aten asteroids that have an aphelion of less than 1 AU (but still greater than 0.7 AU) belong to a second group of asteroids called Apohele asteroids*.

*Apohele asteroids are asteroids that never cross the Earth’s orbit from within the Earth’s orbit, i.e. their aphelions are always less than 1 AU from the Sun. Another name for Apohele asteroids are inner-Earth objects or Atira asteroids. It should be noted that some Apohele asteroids can be Aten asteroids, but not all. There are only 13 known Apohele asteroids discovered, so far.

Of the known near-Earth asteroids, only 815 (6%) have been identified as Aten asteroids. There are some Aten asteroids that should be noted:

• (325102) 2008 EY5 has the smallest semi-major axis of 0.626 AU (between the orbits of Mercury and Venus)
• (137924) 2000 BD19 has the closest perihelion of 0.092 AU, which takes it within Mercury's orbit. It also has an aphelion of 1.66 AU, which is outside the orbit of Mars, giving it the largest eccentricity of any Aten asteroids (and possibly any solar system body) of e=0.895. It is believed that this may be an extinct comet that was captured by the Sun and was prevented from leaving the inner solar system.
  
• 2002 AA29 (which will have its own post) has a period around the Sun of one year and a semi-major axis of one AU, but does not share the same orbit as the Earth. Its unique position by the Earth actually causes it to have a horseshoe shaped orbit around the Earth.
• 3753 Cruithne has a semi-major axis of one AU and a period around the Sun of about a year as well. However, it has a highly eccentric orbit with its aphelion near 1.51 AU (close to Mars) and a perihelion of 0.484 AU (just outside the aphelion of Mercury). This eccentricity leads it to have a kidney-shaped orbit with respect to the Earth. This will also be discussed in a separate post.

 

Asteroid 2002 AA29

Time Lapse view of 2002 AA29 moving among distant galaxies

Paul Wiegert, Astronomy Dept, University of Western Ontario



 

Much like 3753 Cruithne, 2002 AA29 is an Aten asteroid with a semi-major axis of about one AU and an orbital period of approximately one year. However, the eccentrictiy is much lower (0.012 - almost circular), even lower than Earth's eccentricity.  Its perihelion is only 0.988 AU and its aphelion is 1.012 AU, keeping it very close to Earth's orbit.  But this object is never in danger of colliding with Earth. It is locked into a 1:1 resonance with Earth, and this resonance is very stable. Its inclination, orbital tilt with respect to the ecliptic, is 10.739°.

What makes this asteroid unique is its orbit with respect to the Earth. When it is just inside Earth's orbit, it is travelling faster than Earth and so will get farther and farther ahead of Earth until it will almost lap Earth. At this point, Earth's gravity will slow down 2002 AA29 which will cause it to move to a higher orbit. This is a consequence of the conservation of angular momentum. When an object is moving slower in a circular (or elliptical) orbit, it has to move farther away. This is just like Kepler's Second Law of Planetary Motion. As a planet moves closer to the Sun, it is moving faster. Farther away, it moves slower.

 

Now, since the Earth is moving faster in a lower orbit, 2002 AA29 lags farther and farther behind Earth until eventually Earth catches up from behind and almost laps the asteroid. Earth's gravity now accelerates the asteroid, causing it to move to a lower orbit, and the orbital dance continues. Each part of this dance (2002 AA29 moving farther and farther ahead of Earth and almost lapping Earth; lagging farther and farther behind till Earth almost laps it) takes approximately 95 years. Because the Earth and 2002 AA29 only approach each other and the orbits never cross, there is not danger of the asteroid hitting us.



Overhead view of the orbit of 2002 AA29 with repect to the Earth's (Erde) orbit

"2002aa29-orbit-3" by JPL/NEO, Daniel Arnold - NASA - Jet Propulsion Laboratory - Near Earth Object Program, labeling and size of bodies modified by Daniel Arnold

Licensed under Public domain via Wikimedia Commons -

Inclination of 2002 AA29 to Earth's orbit

"2002aa29-orbit-2" by JPL/NEO, Daniel Arnold - NASA - Jet Propulsion Laboratory - Near Earth Object Program, labeling and size of bodies modified by Daniel Arnold

Licensed under Public domain via Wikimedia Commons -

 



This speeding up and slowing down create a unique shape. Each of the loops in the image below is the position of AA29 with respect to the Earth's orbit every year. The whole series of loops has a shape like a horseshoe with the Earth being in the gap at the two ends of the horseshoe.

 



 

"2002aa29-orbit" by JPL/NEO, Daniel Arnold - NASA - Jet Propulsion Laboratory - Near Earth Object Program, labeling and size of bodies modified by Daniel Arnold

Licensed under Public domain via Wikimedia Commons -

 

Near Earth Asteroids

A simple schematic of the inner solar system, the yellow star in the middle is the Sun, the gray circle is Mercury, the grayish-yellow circle is Venus, the blue circle is Earth, the red circle is Mars, and the orange circle is Jupiter. The green band between Mars and Jupiter is the asteroid belt.

 

Besides the asteroid belt and the Greek and Trojan Asteroids, there are also asteroids that come close to Earth. These asteroids are called near-Earth asteroids, or near-Earth objects (NEOs). You have probably have heard of these asteroids on the news, telling us a new one has been discovered and it will make a near approach to Earth sometime in the future.

What actually defines what we mean by a near-Earth asteroid? By definition, a near-Earth asteroid is one that can come within 0.3 AU of Earth. We use 0.3 AU as a baseline, because at closest approach between Earth and Venus, the planets are only 0.27 AU apart (when Venus is at Aphelion of 0.728 AU and Earth is at perihelion of 0.983 AU). This number is rounded up to 0.3 AU to make it easier to define NEOs.

As mentioned in a previous post, asteroids are numbered sequentially, i.e. in what order it was discovered. Typically, near-Earth asteroids are not numbered until they have been observed at opposition at least twice. Recall, opposition is when an object (in this case, an asteroid) is 180° away from the Sun in the sky.

An asteroid (brown circle) at opposition

 

It should be noted that although these asteroids do come close to the Earth, they do not necessarily cross the orbit of the Earth and are not potentially harmful to the well being of the inhabitants or our planet.

 

There are three types of near-Earth asteroids which will all be discussed in their own blog posts. We refer to these asteroids as Aten, Amor, and Apollo asteroids, with each group named after the first asteroid discovered to fall into that group.

• Aten asteroids are asteroids that have semi-major axes smaller than one AU
• Amor asteroids are asteroids that have semi-major axes larger than one AU
• Apollo asteroids are asteroids that have semi-major axes around one AU.

Greek and Trojan Asteroids

Jupiter has a two groups of asteroids lagging behind it in its orbit and leading it as it goes around the Sun. These asteroids are called Trojan asteroids and the two groups are broken down into the two camps during the Trojan War; the Greek camp which is the leading group and the Trojan camp which are the ones lagging behind.

Both of these groups are situated at Lagrangian points which are gravitational balanced points in a three-body system. The Greek asteroids are located at L4 in the Sun-Jupiter system and the Trojan asteroids are at L5.



From our post about Lagrangian points, we know that the Greeks are at 60° ahead of Jupiter in its orbit and the Trojans are 60° behind. Where did these asteroids come from?

 

The leading theory is that these asteroids are remnants of the formation of the Solar System and in as they moved in space, the asteroids got caught in the L4 or L5 Lagrangian points, which we learned is stable. Once they got to those points, they were there permanently.

 

One last thing about Trojan and Greek asteroids is that all the ones that have been discovered are named after Greek or Trojan heroes from the Trojan war.

Lagrangian Points

In a three-body system in orbital mechanics, there are five points where the combined gravity of the two larger objects can affect the orbit of the smallest body in the system. The combined gravity will provide the right centripetal force to allow the small body to orbit with the other two objects. These points are called Lagrangian Points, after Joseph-Louis Lagrange who published an essay on three-body physics.

Three of these points are collinear, i.e. lie along the line connecting the centers of the two larger masses. However, these points are unstable. A slight deviation in the location or the speed will cause the smallest mass to move towards either other mass, depending on which direction it moves. The other two points are coplanar, i.e. lying in the same plane as the other two masses. These two points create an equilateral triangle with the two larger masses.

Note: there is a point between the yellow mass and the blue mass where the gravity from each mass is completely cancelled out. L1 is not at this point.

L1 is the first Lagrangian Point and is located between the two masses. It is closer to the smaller mass since an object would need to be closer to the smaller mass to have a larger influence from the smaller mass. For the Sun-Earth system, L1 is 1.5 million km from Earth, outside the radius of the Moon's orbit.

L2, the second Lagrangian point, is located opposite L1 around the smaller mass. Its distance is approximately the same as L1.

L3 is opposite the smaller mass on that mass's orbit. It may seem counterintuitive that L3 balances the forces from the two masses, but the small mass does have a gravitational influence on the larger mass, L3 has the same orbital period as the small mass. L3 is very unstable and it would be practically impossible to keep a satellite there for any extended period of time without making adjustments with small thrusts of rockets.

L4 and L5 lie approximately on the orbit of the small mass, either 60° ahead or 60° behind. These two points are the most stable because the distance from either mass is the same. The gravitational force from each object is at the same ratio as the two masses, causing the total net gravitational force to act through the common center of mass.



It should be noted, that L3, L4, and L5 do not lie exactly on the smaller mass's orbit, but a little outside.

This post is not intended to make you an expert on Lagrangian Points, but to give you an idea of what they are. The Greek asteroids and Trojan asteroids near Jupiter lie near the L4 and the L5 points of the Sun-Jupiter system and will be the next topic.

If you have any questions, please feel free to ask me. Post a comment here, write on my Google+ wall, or tweet me (patronaut0709). I'll try to answer your question as well as I can.

Ida and Dactyl

Galileo Probe image from NASA

Typically, asteroids are too small to have their own satellites. The gravitational force exerted by an asteroid is too minor to hold on to any object larger than a boulder if that object passes close by. The object are moving faster than the escape velocity of the asteroid. However, there are exceptions. The prime example is the dual system of Ida and Dactyl.

243 Ida was the 243rd asteroid discovered in the Asteroid Belt. It was originally discovered by Austrian astronomer Johann Palisa in 1884. Based on the spectroscopy, Ida is an S-type asteroid with an albedo of 0.2383. It has a semi-major axis of 2.862 AU, taking 4.84 Earth years to orbit the Sun. It has an average diameter 31.4 km across which is kinda weird to use since it is longer than it is wide.

In 1993, the space probe Galileo visited Ida on its way to explore Jupiter. It was in this visit where Dactyl was discovered. Dactyl is only 1/20th the size of Ida, only about 1.4 km in diameter. It is difficult to determine Dactyl's orbital characteristics without much more observation, but because it is so small in relation to Ida, to determine how it orbits Ida, Dactyl and Ida will have to be visited. Constraints to its orbit did allow a density to be roughly detemined and Dactyl is lacking metallic minerals. Ida and Dactyl share similar characteristics, so it is possible that they formed at the same time.