Huh? "The Moons?" Do we have more than one? Well yes, at least, for some time, we did have two and we might yet again. Not so long ago, the Earth, with some help of our Moon #1, did grab a second moon.
So here's what's happened, a tragic story of passion, fatal attraction and final rejection.
It all began in September 2002, when the American astronomer Bill Yeung discovered a new asteroid, or thought he had. But when the orbit of that body - it was named J002E3 - was determined, it turned out no be not on an orbit around the Sun (a heliocentric orbit), but on a highly elliptical orbit around the Earth.
That's a problem because such orbits are unstable, so no natural body can remain on them more than just a fairly short time. The apogee of these orbits is so high that it is in that gravitational no-man's-land where a body is undecided whether it shall orbit the Earth or rather the Sun.
What's more, such orbits cross the Moon orbit and will be subject to large perturbations. Sooner or later, it will hit the Earth or get kicked into escape. So J002E3 could not have been in that orbit long.
Then, spectroscopic analysis showed that its surface was blinding white ... and covered with titanium dioxide. A highly unliely set-up for a natural body but quite typical for a rocket stage, for which titanium dioxide based paint is commonly used.
But nobody had launched a large rocket into such a highly elliptical orbit orbit in or shortly before the year 2002. There was no recent unaccounted-for rocket stage. The last launches of this nature were those of the mighty Saturn V rockets of the Apollo program, but those were long past.
The Saturn V rocket's upper stage was the S-IVB. Its size and colour matched the J002E3 observations. However, from Apollo 12 onwards, all S-IVB stages had been crashed on the lunar surface. The impacts were duly registered with seismic instruments left by earlier missions.
So that stage had to come from an earlier moon flight. Die S-IVB-stages of Apollo 8, 10 und 11 had been soundly inserted into heliocentric orbits. With Apollo 12 however, a problem with the ullage motors delayed the escape manoeuvre so much that it did not achieve escape; the Apollo 12 S-IVB remained stranded in a highly elliptical Earth orbit on November 14, 1969.
That piece of hardware could hardly have survived more than 30 years in an unstable orbit. It had been "lost" following its lunar flyby on November 18, 1969 - Space is vast, even that small chunk that surrounds our tiny blue planet - but numerical trajectory simulation showed that it must have escaped into a heliocentric orbit eventually.
Backwards calculation of the orbit of J002E3 in 2002 (yes, numerical calculations of orbits also work "backwards in time") showed that that object must have been captured into an Earth-bound orbit in May 2002, coming from the direction of the Lagrange Point L1, i.e., from towards the Sun. The above animation displays the result of the numerical simulation, showing that the Moon was involved in the capture (ca. June 20, 2002). The essential point is that the original escape and also the eventual re-capture occurred at a low relative velocity. Otherwise, this could not have happened.
J002E3 then completed a series of complete orbits. The apparent flower petal trajectory is a bit misleading - it's just an artifact, due to the fact that the chosen coordinate system is one that rotates with the Earth position on its path around the Sun. In an inertial (=non-rotating) frame, the orientation of the ellipse would appear largely unchanged. However, it would be difficult the Sun direction and L1 location in an inertial frame, and those are essential in the given case.
One year later, J002E3 escaped Earth orbit, again with some help from the Moon (ca. June 1, 2003), and again through the L1 region. This indicates that its heliocentric orbit must be heading the Earth. The object is initially slightly ahead of the Earth and Earth's gravity keeps pulling it back, exerting a steady braking force and thus removing orbital energy.
A lower-energy orbit has a lower radius and therefore higher speed - one of the apparent paradoxes of celestial mechanics. So due to the Earth's braking force, the object will be speeding on ahead of the Earth. With growing distance, the Earth's influence will cease. The object's orbit is still similar to the Earth's; it will move on, passing through the farthest point on the other side of the Sun, almost 300 million kilometers distant and then catching up with the Earth from behind. As the saying goes: what goes around, comes around.
Notre that a heading orbit was selected for one of the NASA solar observation craft in the NASA"STEREO" mission. Conversely, STEREO-B is in an Earth-trailing orbit, as is NASA's infrared space telescope "Spitzer".
The process of drifting out ahead and eventually catching up from behind lasts around 30 years, so if J002E3 is in fact the Apollo 12 S-IVB, it would have to have escaped in the early 1970s. It was then re-captured in 2002, re-escaped in 2003 and may be back in the early 2030's.
Interesting, eh? That's quite a career for a spent rocket stage: a major showcase for various complex effects of multi-body celestial mechanics and an alien space ship suspect.
Note:The process of capture into a bound orbit around the planet from a heliocentric orbit is all that unusual. Jupiter and Saturn have acquired some of their outer moons in this way. Also, comets get captured into Jupiter orbit, the last known such example was the ill-fated but famous Shoemaker-Levy 9.
Collection of animations of the simulated trajectory of J002E3 from 2002 - 2003