Earth's 'Second Moon' in a 'ménage à trois' ( Forwarded)
Andrew Yee
http://sci.esa.int
26 Oct 1999
Earth's 'Second Moon' in a 'ménage à trois'
We will never see it but the Earth has at least one other natural satellite. In
discovering several new types of orbital motion, a team of British scientists
has shown that the gravitational forces of our planet and of the Sun allow
our planet to capture passing asteroids. One of them is named 'Cruithne', and
can be considered -- at least for the next 5000 years -- as 'Earth's second
Moon'.
The work of coorbital dynamics by a team from Queen Mary and Westfield
College in London was published 27 September in the US publication 'Physical
Review Letters'. Fathi Namouni, Apostolos Christou and Carl Murray have
taken even further the discoveries of Joseph-Louis Lagrange.
The 18th century French mathematician gave his name to the five special
points of equilibrium between the gravitational forces of a planet like our
Earth and those of the Sun. The 'Lagrangian points' -- also known as libration
points -- demonstrate the so-called 'three-body problem' when a planet and
its Sun can catch a third companion (see diagram).
The first point L1 is situated on a line between the planet and its Sun. SOHO,
the ESA-NASA Solar and Heliospheric Observatory is the first spacecraft
to exploit such a position. It is currently orbiting the inner L1 position 1.5
million km from Earth using this vantage point to study the Sun. L2 is on the
same line but on the outer side from Earth.
The L3 point is precisely on the other side of the Sun. L4 and L5 are at the
summit of two equilateral triangles with a common base being the line
between the Earth and the Sun. Joseph-Louis Lagrange had already shown
that objects turning around L4 and L5 could easily stay there. This
configuration applies to other planets of the solar system. Indeed Jupiter
has hundreds of Trojan asteroids and Mars has at least two. Although Saturn
itself has none, its own moons Tethys and Dione maintain Trojan asteroid
satellites at Lagrangian points.
The orbits of these third bodies are exotic. The Trojan asteroids describe
a 'tadpole-shaped' pattern around the L4 and L5 points. Even more peculiar
is the 'horseshoe orbit' in which the third body turns around the three
points of equilibrium, L3, L4 and L5.
Cruithne is such an object. Discovered in 1997, it is a 5-km diameter
asteroid that takes 770 years to complete its horseshoe orbit. Thus every
385 years it comes to its closest point to Earth, some 15 million kilometres.
Last time was in 1900, next -- if you can wait -- will be in 2285.
The British team integrated Cruithne's parameters into their mathematical
models, deducing that it can remain in its present state for 5,000 years
before leaving. They have even calculated that 'Earth's second moon' is
likely to be a second-comer having been trapped in a similar orbit some
time in the past 100,000 years. "Cruithne is a case example, proof that
our work is not just abstract calculations," says Carl Murray. "The
mathematical model that we have developed has been able, not only to
predict several new types of previously unsuspected motion, but has it has
subsequently been confirmed by investigating numerically the orbits of real
solar system objects. Nature has already provided examples of every kind
of orbit that the theory can provide."
Examining existing catalogues of near-Earth objects to see whether there
were any other similar cases, the Queen Mary and Westfield College team
have discovered four: three concerning Earth and one for Venus.
The main significance of the work is that it provides a complete
classification of coorbital motions. It could lead to a greater understanding
of other asteroids, including their likelihood of hitting Earth and of how
the planets were formed. Space mission planners could devise new
gravitational tricks for their space probes. Murray himself is one of the
European members of the Imaging Science Subsystem team on the Cassini
orbiter part of the Cassini-Huygens mission.
The team also shows that the forces of attraction in the three-body problem
are also present in other domains of science -- such as chemistry where,
for instance, two electrons of an atom of helium display a similar 'ménage
à trois' around their nucleus.
USEFUL LINKS FOR THIS STORY
* Physical Review Letters abstract
http://ojps.aip.org/journal_cgi/getabs?KEY=PRLTAO&cvips=PRLTAO000083000013002506000001&gifs=Yes
* More about SOHO
http://sci.esa.int/soho
* More about Huygens
http://sci.esa.int/huygens
* The Lagrange points (NASA webpage)
http://map.gsfc.nasa.gov/html/lagrange.html
[NOTE: Illustrations supporting this release are available at
http://sci.esa.int/categories/newsitem.cfm?TypeID=5&ContentID=7331]
--
Andrew Yee
ay...@nova.astro.utoronto.ca
Mike Dworetsky
>
> ESA Science News
> http://sci.esa.int
>
> 26 Oct 1999
>
> Earth's 'Second Moon' in a 'ménage à trois'
Does it occur to anyone else that such an object would be very easy to
visit and investigate, due to its orbit being tied to one of Earth's
Trojan points? Ideal for a low-continuous-thrust speaccraft.
It could even be a remarkably good target for a future manned mission.
Dynamically it is practically on our doorstep.
--
Mike Dworetsky
Brian Davis
> Does it occur to anyone else that such an object would be very easy to
> visit and investigate, due to its orbit being tied to one of Earth's
> Trojan points? Ideal for a low-continuous-thrust speaccraft.
If you mean easy as in, "very nearly the same orbital energy", yes.
But there is the problem of travel time and launch opertunities, which
at least for manned missions is a serious contraint. NEO's with orbital
periods close to 1 year have *very* infrequent launch windows for most
specific trajectories (like minimum energy or minimum time).
--
Brian Davis
Peter Munn
>Andrew Yee wrote:
>>
>> Earth's 'Second Moon' in a 'ménage à trois'
>
>visit and investigate, due to its orbit being tied to one of Earth's
>Trojan points?
Yes it occurred to me. Actually, as the article says of course,
Cruithne wanders around the whole circuit of the three distant
Lagrangian points.
>It could even be a remarkably good target for a future manned mission.
If the object gains popular credence as Earth's second moon (not that
I'm comfortable with that designation myself), I wouldn't put it beyond
_private_ efforts at a manned landing circa 2090. The first man/woman
to stand on the Earth's "other moon" would be quite a prize.
>Dynamically it is practically on our doorstep.
Of course, for a manned landing you don't want long journey times, so
when it is not nearby, the dynamical advantage is less pertinent.
>> The Trojan asteroids describe
>> a 'tadpole-shaped' pattern around the L4 and L5 points. Even more peculiar
>> is the 'horseshoe orbit' in which the third body turns around the three
>> points of equilibrium, L3, L4 and L5.
>>
>> Cruithne is such an object. Discovered in 1997, it is a 5-km diameter
>> asteroid that takes 770 years to complete its horseshoe orbit. Thus every
>> 385 years it comes to its closest point to Earth, some 15 million kilometres.
>> Last time was in 1900, next -- if you can wait -- will be in 2285.
Right! Who has the proper low-down on this? 770 years sounded too long
for a two-way trip around the horseshoe, and that 1900-1997 interval
seemed suspiciously like about one eighth of 770 to me: four round trips
in 770 years would make that 1997 observation occur when Cruithne was
relatively close to us.
So, I investigated. I get a horseshoe orbit, not inclined to the
ecliptic, which gets to 0.1 AU of the Earth to have a period of about
170 years. Can anyone confirm? An inclined orbit would feel less of
the Earth's gravitational influence and have a somewhat longer period.
770/4 = 192.5 feels a reasonable figure.
So, can anyone confirm that 770 years represents a cycle of four,
presumably slightly different, trips around the horseshoe? And that
Cruithne will therefore be close at hand again around 2090/2095?
--
,---. __
_./ \_.'
'..l.--''7
|`---' Peter Munn
| Software Designer
| Staffordshire UK
Brian Davis
> So, I investigated. I get a horseshoe orbit, not inclined to the
> ecliptic, which gets to 0.1 AU of the Earth to have a period of about
> 170 years. Can anyone confirm?
Try putting your object into an orbit with a lower "eccentricity" (if
such a term has any menaing in this case). In other words, the closer it
is to a circular orbit (the smaller the "tadpole", in a co-rotating
reference frame), the longer between connjunctions. I suspect the 770
year relative period is correct.
--
Brian Davis
Mike Dworetsky
>
> Mike Dworetsky wrote:
>
> > Does it occur to anyone else that such an object would be very easy to
> > visit and investigate, due to its orbit being tied to one of Earth's
>
> If you mean easy as in, "very nearly the same orbital energy", yes.
> But there is the problem of travel time and launch opertunities, which
> at least for manned missions is a serious contraint. NEO's with orbital
> periods close to 1 year have *very* infrequent launch windows for most
> specific trajectories (like minimum energy or minimum time).
To visit the main asteroids would be a big deal energetically and
temporally. This object is practically on our doorstep. By 'easy' I
mean within the range of current technology, without the sort of cost
that would be involved in a Mars or asteroids mission.
I wasn't necessarily thinking of manned missions, but maybe these will
be the first objects reached and exploited for commercial reasons.
It doesn't need to be in the close part of its orbit to be easy to
visit. Yes it might take a bit longer to get there.
Also saw recently a paper on the existence of a few stable asteroids in
the zone between Earth and Mars. These would be easy to reach also.
Compared to flyby missions to most asteroids, going into a parking orbit
around one of these would be a 'cheap' mission.
--
Mike Dworetsky
Peter Munn
>Peter Munn wrote:
>> So, I investigated. I get a horseshoe orbit, not inclined to the
>> ecliptic, which gets to 0.1 AU of the Earth to have a period of about
>> 170 years. Can anyone confirm?
>
> Try putting your object into an orbit with a lower "eccentricity" (if
>such a term has any menaing in this case). In other words, the closer it
>is to a circular orbit (the smaller the "tadpole", in a co-rotating
>reference frame), the longer between connjunctions.
Yes, the first ones I tried had more circular "orbits" in the co-
rotating frame. The first I tried gave a period of about 460 years, but
only approached to about 0.34 AU of Earth, which is the general problem.
Having tried a couple more things, the only way I'm getting close to
meeting both the 0.1 AU and 770 year values, is to give the asteroid a
large eccentricity, in the normal sense.
I didn't try this before, probably because the description in the
article created an image of the asteroid passing serenely around the
horseshoe. In fact, drawing its path in the co-rotating frame [1] it
will appear as a sequence of large, heavily overlapping loops with only
the centre of the loops staying in the horseshoe proper. This could
bring the asteroid to 0.1 AU of Earth even though the path mapped by the
centre of the loops never gets within 0.5 AU.
>I suspect the 770
>year relative period is correct.
I've shoved the orbital eccentricity up to nearly 0.25 (root 0.06,
actually) but my last effort was still only up to about 650 years on
period and down to about 0.14 AU on approach distance. Perhaps
inclining the orbit will help. (I know I could probably look up the
actual parameters for Cruithne, but that would be less instructive for
understanding the generality of orbits like these.)
I still feel I'm going to need an eccentricity of over 0.25, which will
bring it pretty close to Venus from time to time. Orbital inclination
could help mitigate that, too, but only as long as inclination stays in
synchronisation with perihelion - and I imagine the Earth-interactions
might play havoc with that. All this seems to suggest that Venus
interactions may be a big player in trapping asteroids in horseshoe
orbits with Earth, and in kicking them out again.
Anyway, assuming Cruithne has an eccentricity in the region of 0.25, we
can forget the idea of it being in our immediate dynamical
neighbourhood. Plus that 770 year period puts it near the far side of
our orbit for the next two centuries, so I'll hurriedly revise downward
my speculation about manned visits circa 2090.
I'm going to quietly hope a larger asteroid, currently in the distant
part of a horseshoe orbit with us, comes into view in the next 20 years,
and becomes a much more attractive target. Cruithne could turn out to
be no more than the third or fourth largest such body.
You never know...
[1] note to lurkers: imagine filming it from, say, North of the solar
system and keep turning the camera so the Earth and Sun appear still.