# How was Cruithne's orbital time calculated?

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How was it determined that Cruithne takes 770 years to complete its cycle with Earth? Janus and Epimetheus were disovered long enough ago, and have short enough cycle times, that we've had time to directly observe their 8 year cycle more than 6 times over. But Cruithne was only discovered 30-ish years ago, so certainly it's cycle time wasn't determined by simple observation.

So what method was used to arrive at this 770 year number?

It's a good question!

I went to the JPL Horizons web page and looked up 3753 Cruithne and saw that the current orbital solution is based on observations from 1973 to 2018, about 45 years. That's a fraction of an orbit, but very careful measurements of it's position on the celestial sphere (RA, Dec) over time will allow astronomers to calculate its position and speed by fitting those observations to many possible trajectories and finding the one that's the best fit.

JPL/HORIZONS 3753 Cruithne (1986 TO) 2019-Feb-14 23:48:43 Rec #: 3753 (+COV) Soln.date: 2018-Sep-27_06:26:23 # obs: 677 (1973-2018)

The orbit is elliptical but has a nearly-identical semimajor axis as Earth, so it's period around the Sun is one year just like Earth. That means that it in 45 years it has been possible to observe about 45 orbits around the Sun, allowing astronomers to nail down its orbit with great precision.

I plotted the distance from Earth to Cruithne from 1973 to 2018 below from the Horizons data. At a half of an AU and 0.1 arcsec astrometric position precision (averaging over many observation) that gives the position to tens of kilometers over a span of decades.

Then using accurate orbital modeling using the gravity of all the solar system's bodies as described here it is possible to project the position with great accuracy, as long as non-gravitational forces like unpredictable outgassing aren't too strong, and predictable non-gravitational forces like solar radiation pressure can be modeled as described here.

Over time the orientation of the elliptical orbit slowly precesses around the Sun due to the gravitational effects of Earth. This is the ~770 year period you've mentioned.

In the video Near-Earth Asteroid 3753 Cruithne they hold the position of the Earth fixed and you can see how Cruithne's orbit sloshes back and forth.

This GIF is too large to embed here, but it demonstrates the sloshing nicely: https://en.wikipedia.org/wiki/File:Animation_of_3753_Cruithne_orbit.gif">ShareImprove this answeredited Feb 15 '19 at 0:21answered Feb 15 '19 at 0:02uhoh28.5k6 gold badges55 silver badges172 bronze badges

## Earth's orbital companion: Asteroid Cruithne

Sen&mdashThe asteroid Cruithne, around 5 km in size, was first spotted in 1983 by Giovanni de Sanctis and Richard M. West of the European Southern Observatory, Chile. It was given the inital designation 1983 UH. But they never saw the object again, so were unable to track its motion. It was in October 1986 that amateur astronomer Duncan Waldron, working with Robert McNaught, Malcolm Hartley and Michael Hawkins at the Siding Spring Observatory in Australia, spotted the object again. What do we know now about the asteroid Cruithne (named by Waldron and colleagues and officially accepted by the International Astronomical Union), a body that's even been dubbed 'Earth's second moon'?

Although first spotted by de Sanctis and West, Waldron, McNaught, Hartley and Hawkins have been credited as Cruithne's official discoverers. The reason is because they were the first who were able to track its motion and prove it was indeed an asteroid. This is the tradition in astronomy. Waldron was examining photographic plates from the UK Schmidt Telescope at Siding Spring when he spotted 1983 UH. Conrad Bardwell, who would later work at the Minor Planet Center, realised that this and the 1983 object were one and the same and calculated its initial orbital parameters. Waldron et al then used Bardwell's calculations to determine a more accurate result.

They found Cruithne's orbit around the Sun is highly elliptical, with the Sun 'off-centre'. Its closest approach to the Sun, known as perihelion, is 72,405,369 km&mdash0.48 times that of Earth's mean distance from it. The furthest Cruithne gets, known as aphelion, is 226,042,383 km&mdash1.51 AU, where 'AU' is one Astronomical Unit, theEarth-Sun distance of 150 million km, a standard unit of measurement used in astronomy.

The orbits of Cruithne and Earth over the course of a year (from September 2007 to August 2008). Cruithne's location is indicated by the red box as it is too small to be seen at this distance. Earth is the white dot moving along the blue circle. The yellow circle in the centre is our Sun. Credit:From Wikimedia Commons, the free media repository

There is a large overlap between Cruithne's orbit and that of Earth's&mdashsuch that if you were to trace a 'top-down' view of both orbits they would resemble a Venn diagram. Whereas Earth takes 364.25 days to complete one orbit around the Sun, Cruithne takes 363.99 days. It completes a full rotation about its axis in 27.31 hours. However, Cruithne's orbital plane is tilted from Earth's by 19.81°. Thus its orbital path never coincides with Earth's, so there is no danger it will collide with our planet.

From Earth, Cruithne appears to be ahead of our planet in its solar orbit. Because both bodies orbit the Sun across similar distances&mdashwith Cruithne's orbit being very elliptical&mdashand because the asteroid's orbital period is slightly different from Earth's, it appears to trace out a bean-shaped orbit from our perspective, as illustrated by the graphic below.

The red path represents the path that Cruithne takes as it revolves around the sun. Since the camera is rotating with Earth, Cruithne appears to move along a bean-shaped path. This illusion is known as a horseshoe orbit. Credit: From Wikimedia Commons, the free media repository

But Cruithne's orbit is stranger and more complex still&mdashthe true nature of which was only realised 11 years after Waldron et al's calculations. In 1997 Seppo Mikkola of Turku University, Finland, and Paul Weigert and Kimmo Innanen of York University, Toronto, Canada found that Cruithne's bean-shaped orbit slowly moves in a horseshoe-shaped pathalong Earth's solar orbit. So currently it is moving away from us. The closest Cruithne ever gets to Earth is 12,000,000 km&mdashnearly 32 times the Earth-Moon distance. As it slowly moves away from Earth over the centuries it will end up right around the other side, before appearing to move away again. Cruithne completes one such horseshoe orbit every 770 to 780 years.

Although Cruithne has very unusual orbital characteristics, it does not actually orbit the Earth. Thus it is incorrect to labelit Earth's second moon. A better term is that Cruithne's a 'companion body' to Earth. Although our planet has captured one object into its orbit before to form a natural satellite&mdashthe three meter-wide 2006 RH120&mdashit was only there for a year. Earth only has one permanent moon.

## Contents

### Orbital data Edit

Shortly after the discovery by LINEAR, Scientists at the Jet Propulsion Laboratory (JPL), the Athabasca University (Canada), the Queen's University in Kingston (Ontario, Canada), the York University in Toronto and the Tuorla Observatory of the University of Turku in Finland determined the unusual orbit of 2002 AA29 , and through further observations at the Canada–France–Hawaii Telescope in Hawaii it was confirmed that:

• Its orbit lies for the most part inside Earth's orbit. The orbits of most asteroids lie in the asteroid belt between Mars and Jupiter. Through orbital disturbances by the gas giant planets, mainly Jupiter and the Kirkwood gaps, and through the Yarkovsky effect (force due to asymmetrical absorption and emission of infra-red radiation) asteroids are diverted into the inner Solar System, where their orbits are further influenced by close approaches with the inner planets. 2002 AA29 has probably been brought in the same way from the outer Solar System into Earth's influence. However, it is also suggested that the asteroid has always been on a near-Earth orbit and thus that it or a precursor body was formed near Earth's orbit. In this case one possibility is that it could be a fragment from a collision of a middle-sized asteroid with Earth or the Moon. [5]
• Its mean orbital period is one sidereal year. After it was diverted into the inner Solar System – or formed on a path near Earth's orbit – the asteroid must have been moved into an orbit corresponding with Earth. In this orbit it was repeatedly pulled by Earth in such a way that its own orbital period became the same as that of Earth. In the current orbit, Earth thus holds the asteroid in synchronicity with its own orbit.
• The orbit of the asteroid is almost circular, with an eccentricity of 0.012 which is even lower than that of the Earth at 0.0167. The other near-Earth asteroids have on average a significantly higher eccentricity of 0.29. Also, all other asteroids in 1:1 resonance with Earth known before 2002 have very strongly elliptical orbits – e.g. the eccentricity of (3753) Cruithne is 0.515. At the time of its discovery the orbit of 2002 AA29 was unique, because of which the asteroid is often called the first true co-orbital companion of Earth, since the paths of previously discovered asteroids are not very similar to Earth's orbit. The very low orbital eccentricity of 2002 AA29 is also an indication that it must always have been on a near-Earth orbit, or the Yarkovsky effect must have comparatively strongly caused it to spiral into the inner Solar System over billions of years, since as a rule asteroids which have been steered by planets have orbits with higher eccentricity.
• The orbital inclination with respect to the ecliptic (orbital plane of Earth) of 2002 AA29 is a moderate 10.739°. Hence its orbit is slightly tilted compared with that of Earth.

### Shape of the orbit Edit

If one looks at the orbit of 2002 AA29 from a point moving with the Earth around the Sun (the reference frame of the Earth–Sun system), it describes over the course of 95 years an arc of almost 360°, which during the next 95 years it retraces in reverse. The shape of this arc is reminiscent of a horseshoe, from which comes the name "horseshoe orbit". As it moves along the Earth's orbit, it winds in a spiral about it, in which each loop of the spiral takes one year. This spiral motion (in the Earth–Sun reference frame) arises from the slightly lower eccentricity and the tilt of the orbit: the inclination relative to the Earth's orbit is responsible for the vertical component of the spiral loop, and the difference in eccentricity for the horizontal component.

When 2002 AA29 is approaching the Earth from in front (i.e. it is moving slightly slower, and the Earth is catching it up), the gravitational attraction of the Earth shifts it onto a slightly faster orbit, a little nearer the Sun. It now hurries ahead of the Earth along its new orbit, until after 95 years it has almost lapped the Earth and is coming up from behind. Again it comes under the Earth's gravitational influence this time it is lifted onto a slower orbit, further from the Sun. On this orbit it can no longer keep pace with the Earth, and it falls behind until in 95 years it is once again approaching the Earth from in front. The Earth and 2002 AA29 chase each other in turn around the Sun, but do not get close enough to break the pattern.

On 8 January 2003, the asteroid approached the Earth from in front to a distance of 0.0391 AU (5,850,000 km 3,630,000 mi), [6] its closest approach for nearly a century. Since that date, it has been hurrying ahead (with a semi-major axis less than 1 AU), and will continue to do so until it has reached its closest approach from behind on 11 July 2097 at a distance of 0.037712 AU (5,641,600 km 3,505,500 mi). [6] As a result of this subtle exchange with the Earth, unlike other Earth orbit crossing asteroids, we need have no fear that it could ever collide with the Earth. Calculations indicate that in the next few thousand years it will never come closer than 4.5 million kilometres, or about twelve times the distance from the Earth to the Moon. [3]

Because of its orbital inclination of 10.739° to the ecliptic, 2002 AA29 is not always forced by the Earth on its horseshoe orbit however but can sometimes slip out of this pattern. It is then caught for a while in the neighbourhood of the Earth. This will next happen in about 600 years i.e. in the 26th century. It will then stay within the small gap in the Earth's orbit which it does not reach in its previous horseshoe orbit, and will be no further than 0.2 astronomical units (30 million km) away from the Earth. There it will slowly circle the Earth almost like a second moon, although it takes one year for a circuit. After 45 years it finally switches back into the horseshoe orbit, until it again stays near the Earth for 45 years around the year 3750 and again in 6400. In these phases in which it stays outside its horseshoe orbit it oscillates in the narrow region along the Earth's orbit where it is caught, moving back and forth in 15 years. Because it is not bound to the Earth like the Moon but is mainly under the gravitational influence of the Sun, it belongs to the bodies called quasi-satellites. This is somewhat analogous to two cars travelling side by side at the same speed and repeatedly overtaking one another but which are however not attached to each other. Orbital calculations show that 2002 AA29 was in this quasi-satellite orbit for 45 years from about 520 AD but because of its tiny size was too dim to have been seen. It switches approximately cyclically between the two orbital forms, but always stays for 45 years in the quasi-satellite orbit. Outside the time frame from about 520-6500 AD, the calculated orbits become chaotic i.e. not predictable, and thus for periods outside this time frame no exact statements can be made. [7] 2002 AA29 was the first known heavenly body that switches between horseshoe and quasi-satellite orbits.

### Brightness and size Edit

Relatively little is known about 2002 AA29 itself. With a size of about 20–100 metres (70–300 ft) it is very small, on account of which it is seen from the Earth as a small point even with large telescopes, and can only be observed using highly sensitive CCD cameras. At the time of its closest approach in January 2003 it had an apparent magnitude of about 20.4. [8]

So far nothing concrete is known about the composition of 2002 AA29 . Because of its nearness to the Sun, it cannot however consist of volatile substances such as water ice, since these would evaporate or sublime one can clearly observe this happening to a comet as this forms the visible tail. Presumably it will have a dark, carbon-bearing or somewhat lighter silicate-rich surface in the former case the albedo would be around 0.05, in the latter somewhat higher at 0.15 to 0.25. It is due to this uncertainty that the figures for its diameter cover such a wide range.

A further uncertainty arises from radar echo measurements at the Arecibo Radio Telescope, which could only pick up an unexpectedly weak radar echo, implying that 2002 AA29 is either smaller than estimated or reflects radio waves only weakly. In the former case it would have to have an unusually high albedo. [4] This would be evidence in support of the speculation that it, or at least the material of which it is composed, is different from most other asteroids so far discovered on near-Earth orbits, or represents a fragment thrown off by the collision of a medium-sized asteroid with the Earth or the Moon. [5]

### Rotational period Edit

Using radar echo measurements at the Arecibo radio telescope the rotational period of 2002 AA29 could be determined. In this radar astronomy procedure radio waves of known wavelength are emitted from a radio telescope aimed at an asteroid. There they are reflected, and because of the Doppler effect the part of the surface that is moving towards the observer (because of the asteroid's rotation) shortens the wavelength of the reflected waves, whilst the other part which is turning away from the observer lengthens the reflected wavelength. As a result, the wavelength of the reflected waves is "smeared out". The extent of the wavelength smearing and the diameter of the asteroid allow the rotational period to be narrowed down. 33 minutes is thus calculated as the upper limit of the rotational period for 2002 AA29 it probably rotates more quickly. This rapid rotation together with the small diameter and therefore low mass leads to some interesting conclusions:

• The asteroid rotates so quickly that the centrifugal force on its surface exceeds its gravitational pull. It is therefore under tension and so cannot be composed of an agglomeration of loosely bound debris or of fragments circling each other – as is supposed for several other asteroids and for example has been determined for the asteroid (69230) Hermes. Instead the body must be made of a single relatively strong block of rock or of pieces baked together. However, its tensile strength is probably considerably lower than terrestrial rock and the asteroid also very porous. [4]
• 2002 AA29 cannot possibly have been built up from individual small pieces, as these would be thrown apart by the rapid rotation. Therefore, it must be a fragment blown off in the collision of two heavenly bodies. J. Richard Gott and Edward Belbruno from Princeton University have speculated that 2002 AA29 might have formed together with Earth and Theia, the postulated planet that, according to the giant impact hypothesis, collided with Earth in its early history. [9]

Because its orbit is very similar to the Earth's, the asteroid is relatively easily reachable by space probes. 2002 AA29 would therefore be a suitable object of study for more precise research into the structure and formation of asteroids and the evolution of their orbits around the Sun. Meanwhile, further co-orbital companions of the Earth of this type on horseshoe orbits or on orbits as quasi-satellites have already been found, such as the quasi-satellite 2003 YN 107 . Furthermore, it is assumed that there are small trojan companions of the Earth with diameters in the region of 100 metres located at the L4 and L5 Lagrangian points of the Earth–Sun system.

## Contents

Cruithne was discovered on 10 October 1986 by Duncan Waldron on a photographic plate taken with the UK Schmidt Telescope at Siding Spring Observatory, Coonabarabran, Australia. The 1983 apparition (1983 UH) is credited to Giovanni de Sanctis and Richard M. West of the European Southern Observatory in Chile. [5]

It was not until 1997 that its unusual orbit was determined by Paul Wiegert and Kimmo Innanen, working at York University in Toronto, and Seppo Mikkola, working at the University of Turku in Finland. [6]

Cruithne is approximately 5 kilometres (3 mi) in diameter, and its closest approach to Earth is 12 million kilometres (0.080 AU 7,500,000 mi), approximately thirty times the separation between Earth and the Moon. From 1994 through 2015, Cruithne made its annual closest approach to Earth every November. [7]

Although Cruithne's orbit is not thought to be stable over the long term, calculations by Wiegert and Innanen showed that it has probably been synchronized with Earth's orbit for a long time. There is no danger of a collision with Earth for millions of years, if ever. Its orbital path and Earth's do not cross, and its orbital plane is currently tilted to that of the Earth by 19.8°. Cruithne, having a maximum near-Earth magnitude of +15.8, is fainter than Pluto and would require at least a 320-millimetre (12.5 in) reflecting telescope to be seen. [8] [9]

Cruithne is in a normal elliptic orbit around the Sun. Its period of revolution around the Sun, approximately 364 days at present, is almost equal to that of the Earth. Because of this, Cruithne and Earth appear to "follow" each other in their paths around the Sun. This is why Cruithne is sometimes called "Earth's second moon". [10] However, it does not orbit the Earth and is not a moon. [11] In 2058, Cruithne will come within 0.09 AU (13.6 million kilometres or 8.5 million miles) of Mars. [7]

Due to a high orbital eccentricity, Cruithne's distance from the Sun and orbital speed vary a lot more than the Earth's, so from the Earth's point of view Cruithne actually follows a kidney-bean-shaped horseshoe orbit ahead of the Earth, taking slightly less than one year to complete a circuit of the "bean". Because it takes slightly less than a year, the Earth "falls behind" the bean a little more each year, and so from our point of view, the circuit is not quite closed, but rather like a spiral loop that moves slowly away from the Earth. [ citation needed ]

After many years, the Earth will have fallen so far behind that Cruithne will then actually be "catching up" on the Earth from "behind". When it eventually does catch up, Cruithne will make a series of annual close approaches to the Earth and gravitationally exchange orbital energy with Earth this will alter Cruithne's orbit by a little over half a million kilometres—while Earth's orbit is altered by about 1.3 centimetres (0.51 in)—so that its period of revolution around the Sun will then become slightly more than a year. The kidney bean will then start to migrate away from the Earth again in the opposite direction – instead of the Earth "falling behind" the bean, the Earth is "pulling away from" the bean. The next such series of close approaches will be centred on the year 2292 – in July of that year, Cruithne will approach Earth to about 12.5 million kilometres (0.084 AU 7,800,000 mi). [ citation needed ]

After 380 to 390 years or so, the kidney-bean-shaped orbit approaches Earth again from the other side, and the Earth, once more, alters the orbit of Cruithne so that its period of revolution around the Sun is again slightly less than a year (this last happened with a series of close approaches centred on 1902, and will next happen with a series centered on 2676). The pattern then repeats itself. [ citation needed ]

More near-resonant near-Earth objects (NEOs) have since been discovered. These include 54509 YORP, (85770) 1998 UP 1 , 2002 AA 29 , and 2009 BD which exist in resonant orbits similar to Cruithne's. 2010 TK 7 is the first and so far only identified Earth trojan.

Other examples of natural bodies known to be in horseshoe orbits (with respect to each other) include Janus and Epimetheus, natural satellites of Saturn. The orbits these two moons follow around Saturn are much simpler than the one Cruithne follows, but operate along the same general principles.

Mars has four known co-orbital asteroids (5261 Eureka, 1999 UJ 7 , 1998 VF 31 , and 2007 NS 2 , all at the Lagrangian points), and Jupiter has many (an estimated one million greater than 1 km in diameter, the Jovian trojans) there are also other small co-orbital moons in the Saturnian system: Telesto and Calypso with Tethys, and Helene and Polydeuces with Dione. However, none of these follow horseshoe orbits.

Cruithne plays a major role in Stephen Baxter's novel Manifold: Time, which was nominated for the Arthur C. Clarke Award for best science fiction in 2000.

Cruithne is mentioned on the QI season 1 episode "Astronomy", in which it is incorrectly described as a second moon of Earth. In a later episode, this mistake was rectified and it was added that Earth has over 18,000 mini-moons.

In Astonishing X-Men, Cruithne is the site of a secret lab assaulted by Abigail Brand and her S.W.O.R.D. team. It contains many Brood before Brand destroys it. [12]

In the Insignia trilogy, 3753 Cruithne has been moved into an orbit around Earth to serve as a training ground for the Intrasolar Forces. In the third novel, Catalyst, it is intentionally directed at the Earth. While it is destroyed before impact, its fragments rain down on the Earth's surface, killing nearly 800 million people across the world.

In the science-fiction book series Aeon 14, Cruithne appears as an inhabited moonlet, home to 'privateers', smugglers, Terran Space Fleet (TSF) outposts and corporate headquarters. [13] Notable inhabitants have included Ngoba Starl and Petral Dulan. [14]

## Similar minor planets

More near-resonant near-Earth objects (NEOs) have since been discovered. These include 54509 YORP, (85770) 1998 UP 1 , 2002 AA 29 , and 2009 BD which exist in resonant orbits similar to Cruithne's. 2010 TK 7 is the first and so far only identified Earth trojan.

Other examples of natural bodies known to be in horseshoe orbits (with respect to each other) include Janus and Epimetheus, natural satellites of Saturn. The orbits these two moons follow around Saturn are much simpler than the one Cruithne follows, but operate along the same general principles.

Mars has four known co-orbital asteroids (5261 Eureka, 1999 UJ 7 , 1998 VF 31 , and 2007 NS 2 , all at the Lagrangian points), and Jupiter has many (an estimated one million greater than 1 km in diameter, the Jovian trojans) there are also other small co-orbital moons in the Saturnian system: Telesto and Calypso with Tethys, and Helene and Polydeuces with Dione. However, none of these follow horseshoe orbits.

## Earths second Moon Cruithne

Cruithne is a comparatively near-Earth asteroid which, although it does not technically orbit the Earth, does – because of its location in the sky – seem to semi-circle the Earth in a rough horseshoe shape. However, horseshoe orbits are effectively optical illusions created by our own relative position in space, rather than true orbits for this reason, Cruithne is not truly the Earth’s second moon.

Cruithne is about an asteroid about 3 miles wide. Currently it comes closest to Earth every November, at which time it is still several dozen times as far away from us as the Moon is – far enough away that, given its size, it can never be seen with the unaided eye. It is inclined and slightly offset relative to ours, which means that it never actually crosses the precise orbital path of the Earth. For that reason, the likelihood that Cruithne would ever collide with Earth is considered negligible. However, it will also never become Earth’s second moon – because it never actually orbits the Earth, simply appearing to do so because its orbit is very close to our own.

The asteroid’s orbit around the Sun is actually 364 days, not 365 days like Earth’s, so that there is a centuries-long pattern which astronomers believe it will follow. Right now, Cruithne is spiralling away from Earth a little farther with every orbit. In a few centuries’ time, we will have fallen behind far enough that Cruithne’s orbits begin to approach ours from the other direction, as though it were spiralling closer and closer. However, current calculations indicate that it will never collide: after the closest approach orbit, it will begin to spiral away again, as it is doing now. Each time this cycle occurs, Earth’s gravity pulls Cruithne a few hundred thousand miles off course. Cruithne’s gravity also pulls Earth, although its effect on our orbit is calculated to be just a centimeter or so.

Cruithne was found in 1986 by the Siding Spring Observatory in Australia. It was named after the Cruithne, an early Irish ethnic group related to the Scottish Pict people. However, it took about a decade for its strange orbit to be fully charted, by a team of Canadian and Finnish astronomers.

– Searching for Second Moons –

Since the dawn of modern astronomy, astronomers have searched for a body worthy of the name “Earth’s second moon.” It is not implausible that such an object could exist: all it would take is a small asteroid getting trapped in a slow, distant orbit, nowhere near as luminous as our Moon but certainly fitting the scientific criteria for being Earth’s second moon.

The first generation of moon searchers, in the 1800s, quickly identified a number of these asteroid candidates. In 1918, Walter Gornold, who in his career as an astrologer went by the pseudonym Sepharial, even argued that he had found Earth’s second moon, and named it Lilith. Subsequent searchers have never found Lilith again, and the claim is considered to have been bogus.

Other interesting near-Earth objects that, for brief periods of time, were thought to meet the qualifications for being Earth’s second moon include 1998 UP1, 2002 AA29, and 2003 YN107, which also orbit the Sun close to Earth and occasionally seem to follow horseshoe orbital paths. Another, 2006 RH120, orbits just beyond the range at which Earth’s gravity could truly capture it, so that every few years it actually gets caught, spun into Earth orbit for a few rotations, and then escapes again. If it ever did get truly captured, RH120, not Cruithne, would become the best candidate for Earth’s second moon (and would presumably deserve a new name, as well).

## How was Cruithne's orbital time calculated? - Astronomy

I was recently watching a program about popular misconceptions which stated that the Earth has two moons. Apparently the second moon was discovered in 1994, has a diameter of 3 km and orbits the Earth once every 770 years. I would like to know if this is true and if so, why is there no information about it in modern amateur astronomy books.

I'm really glad you sent this email, because we've received several questions about a second moon of Earth, and I wasn't sure what people were referring to or where they had heard it, but the details you included made it possible to figure it out!

Anyway, to answer your question, I think the object that you're referring to is called Cruithne, which is a 3 mile (5 km) object in a horseshoe orbit "around" Earth that has a period of 770 years. You can read a press release about it at Space.com (archived from the original). It was discovered in 1986, but it took a lot of observations in order to figure out its complicated orbit, which was determined in 1997.

In the press release, one of the scientists involved with the study called the object a "moon", because it shares Earth's orbit however, it's definitely not a moon like our Moon. First, a horseshoe orbit is much different from the elliptical orbit that the Moon makes around Earth. The Moon actually orbits the planet Earth, while Cruithne just shares the Earth's orbit around the Sun. You can read more about its motion and about horseshoe orbits at a question previously answered by Dave, or at this page about Cruithne. The orbit of Cruithne is also very inclined with respect to Earth's orbit around the Sun, so it moves in and out of the plane that the most of the planets orbit in. This large inclination is part of the reason that Cruithne won't collide with Earth.

Second, objects trapped in orbits like Cruithne's are only expected to remain in the orbit for a few thousand to tens of thousands of years, which may sound like a long time, but it's actually fairly short in the timescale of Solar System history. After Cruithne escapes from its present orbit, it may become a Near Earth Asteroid on a different close-to-Earth orbit, or move onto an orbit more similar to our Moon's orbit, in which case it would be more like a "real" moon. No one seems quite sure which scenario will happen.

So I guess I would think of Cruithne as more of a Near-Earth Asteroid that's trapped by Earth's gravity, not as a moon. And in fact, it's classified by astronomers as an Aten asteroid, which is a group of Near-Earth Asteroids on similar orbits. But Cruithne is a good example of the fact that Earth's gravity can interact with nearby asteroids, bringing them closer to Earth or forcing them onto different, strange, orbits.

Update (2016): Astronomers have discovered several other quasi-satellites of Earth, with small asteroid 2016 HO3 apparently being the most stable. Here are a few related links:

## How was Cruithne's orbital time calculated? - Astronomy

Who discovered the speed of light? When was it discovered? How was it calculated or derived?

Scientists have been trying to study the speed of light since the ancient Greeks. Most ancient Greek astronomers believed, amongst other things, that the speed of light was effectively infinite. They had no way to test this educated guess, however. Nevertheless, it was generally taken for granted that light-speed was infinite until the astronomer Galileo in the early 1600's. Galileo supposedly attempted to quantify the speed of light, by using distant lanterns with shutters, which an assistant opened at specified times. Galileo would try to record how long it took light to get to him from across the field on which the experiment was done. His only conclusion was that light-speed was too fast to be measured by that experiment. (In fact, with what we now know about the speed of light, we can say that if Galileo and his assistant were standing about a mile apart, it would only take light about five microseconds - five millionths of a second - to travel from Galileo to his assistant. This was much too short to be measured with the technology of that time.)

The first true measurement of the speed of light came in 1676 by a fellow named Ole Roemer (Rømer). Roemer was observing Jupiter's moon Io, the innermost of the Galilean satellites. As seen by an observer on Earth, Io suddenly disappears when it moves into Jupiter's shadow, and it suddenly reappears when it moves out of Jupiter's shadow (back into the sunlight). Roemer was interested in predicting the times at which Io would be observed to emerge from Jupiter's shadow. His goal was to use those observations to determine Io's orbital period more accurately he was not initially trying to determine the speed of light.

Roemer noticed that the time elapsed between eclipses of Io became shorter as the Earth moved closer to Jupiter and became longer as the Earth and Jupiter moved farther apart. He realized that the discrepancies between the observed and calculated Io emergence times could be explained by a finite speed of light. Since the Earth was moving away from Jupiter over the course of Roemer's observations, it would take the reflected light from Io slightly longer to reach Earth, and this would affect the exact time at which Io was observed to emerge from Jupiter's shadow.

Based on these observations, Roemer calculated that it would take light about 22 minutes to cross the diameter of Earth's orbit. Combining that value with earlier measurements of the Earth's semimajor axis (orbital radius) (described here and here) gives a speed of light of about 210,000 kilometers per second. This is about 30% lower than the modern value for the speed of light, but considering its antiquity, method of measurement, and 17th century uncertainty in the exact sizes of the planetary orbits, this value is remarkably close to the modern value of 299,792.458 kilometers per second.

Here are some pages with more information on Roemer's calculation, including some illustrations of the observing geometry:

This page was last updated by Sean Marshall on January 17, 2016.

#### Dave Kornreich

Dave was the founder of Ask an Astronomer. He got his PhD from Cornell in 2001 and is now an assistant professor in the Department of Physics and Physical Science at Humboldt State University in California. There he runs his own version of Ask the Astronomer. He also helps us out with the odd cosmology question.

## Johannes Kepler

Johannes Kepler was born into a poor family in the German province of Württemberg and lived much of his life amid the turmoil of the Thirty Years’ War (see Figure 1). He attended university at Tubingen and studied for a theological career. There, he learned the principles of the Copernican system and became converted to the heliocentric hypothesis. Eventually, Kepler went to Prague to serve as an assistant to Brahe, who set him to work trying to find a satisfactory theory of planetary motion—one that was compatible with the long series of observations made at Hven. Brahe was reluctant to provide Kepler with much material at any one time for fear that Kepler would discover the secrets of the universal motion by himself, thereby robbing Brahe of some of the glory. Only after Brahe’s death in 1601 did Kepler get full possession of the priceless records. Their study occupied most of Kepler’s time for more than 20 years.

Through his analysis of the motions of the planets, Kepler developed a series of principles, now known as Kepler’s three laws, which described the behavior of planets based on their paths through space. The first two laws of planetary motion were published in 1609 in The New Astronomy. Their discovery was a profound step in the development of modern science.

## クルースン (小惑星)

クルースンは、実際には地球の周りを回っているわけではない。その代わり、地球の軌道の周りを螺旋状に動く。クルースンの（見かけ上）馬蹄形の軌道 (Horseshoe orbit) はあたかも準衛星のような軌跡になる [7] が、その両端では、それぞれ地球の反対側に接近はしても接触はしない。近日点は金星よりも太陽に近く、遠日点は火星軌道の長半径とほぼ等しい。クルースンは地球を周回せず、時には太陽を挟んだ反対側 [1] 、すなわち地球のヒル球の外側にある。水星の軌道内と火星の軌道外を通る [1] 。

SF作家のスティーヴン・バクスターは、クルースンの奇妙な軌道のためか、著書『Manifold:Time』 （英語） （多様体：時間）のなかでクルースンを舞台に取り上げている。 同作は2000年、アーサー・C・クラーク賞ノミネート作。