Quasi-Satellites: Companions That Only Look Captured

What a quasi-satellite actually is

A quasi-satellite is a small body locked in a 1:1 mean-motion resonance with a planet. Its heliocentric semi-major axis is essentially the planet's — for Earth's companions, a ≈ 1.00 au — so by Kepler's third law its year matches the planet's year to within a fraction of a percent. The diagnostic quantity is the resonant angle σ = λ − λ_planet, the difference in mean ecliptic longitude. For a quasi-satellite, σ does not circulate through 360°; it librates, oscillating about 0° indefinitely. The object is permanently near conjunction, hovering at the same heliocentric ecliptic longitude as the planet for centuries.

What it is not is a moon. At Kamo'oalewa's closest approach to Earth, about 1.5 × 10⁷ km, Earth's gravitational acceleration on it is GM_⊕/r² ≈ 1.8 × 10⁻⁶ m s⁻², while the Sun pulls on it at GM_☉/(1 au)² ≈ 5.9 × 10⁻³ m s⁻². Earth contributes roughly 0.03 percent of the total force. The companion is a solar orbiter that Earth merely nudges — and that nudge, applied at the same phase every year, is exactly what keeps the resonance locked.

The dynamics are old: J. Jackson described stable retrograde satellite orbits in MNRAS in 1913, Michel Hénon catalogued them as family f of the Hill problem in 1969, Seppo Mikkola and Kimmo Innanen analysed planetary quasi-satellites in 1997, and Fathi Namouni's 1999 Icarus paper mapped the compound orbits that let objects switch between quasi-satellite, horseshoe and tadpole states.

The mechanism: eccentricity turns a shared orbit into a loop

Put two bodies on identical circular orbits and nothing happens: same radius, same speed, fixed separation, no loop. The loop is manufactured by eccentricity. Give the asteroid an orbit more eccentric than the planet's and it spends half of each year inside the planet's orbit and half outside. Near perihelion its speed is v = na√((1+e)/(1−e)); for Kamo'oalewa (e = 0.104) that is 33.0 km s⁻¹ against Earth's 29.8 km s⁻¹, so it sprints ahead. Near aphelion it falls to 26.9 km s⁻¹ and drops behind. Ahead, behind, ahead, behind — once per year, forever.

The linearised solution is the classical epicycle (the Hill or Clohessy–Wiltshire equations). Measuring the offset from the planet in radial (ξ, positive outward) and along-track (η, positive in the direction of motion) coordinates, and to first order in e:

• ξ = −a e cos M
• η = +2 a e sin M

where M is the mean anomaly. That is a closed ellipse with semi-axes ae radially and 2ae along-track — the 2:1 aspect ratio is forced by Kepler's third law, which ties the along-track drift to the radial displacement. Trace the sequence: sunward of the planet → leading it → anti-sunward → trailing → sunward again. That circulation runs opposite to the planet's own orbital direction, which is why the loop looks retrograde from the planet even though the asteroid's heliocentric orbit is perfectly prograde.

For Kamo'oalewa the numbers fall out immediately: ae = 0.104 au ≈ 1.56 × 10⁷ km, and 2ae ≈ 3.1 × 10⁷ km. Fold in its 7.8° inclination, which adds an out-of-plane swing of order a sin i ≈ 0.14 au, and the predicted excursion is roughly 14 to 40 million km — 38 to 100 lunar distances, precisely what JPL's ephemeris shows. At the real eccentricity the first-order ellipse distorts: the perihelion passage is fast and pinched, so the true path is the familiar kidney or bean shape rather than a clean ellipse, and because σ itself librates the loop slowly opens, closes and drifts instead of retracing exactly.

The numbers that prove it is not captured

The clean test is the Hill sphere, the region where a planet's gravity dominates the Sun's tidal field: R_H = a (m_p/3M_☉)^1/3. For Earth, (3.0 × 10⁻⁶/3)^1/3 ≈ 0.0100, so R_H ≈ 0.010 au ≈ 1.5 million km. The Moon orbits at 384,400 km — a comfortable 0.26 R_H. Kamo'oalewa's minimum distance is about ten Hill radii, and it typically loiters at twenty to twenty-five. It is never even close to being inside.

Energy makes the same point more brutally. Escape speed from Earth at 1.5 × 10⁷ km is √(2GM_⊕/r) ≈ 0.23 km s⁻¹. The actual relative speed there is a few km s⁻¹: the epicyclic estimate 2aen gives ≈ 6 km s⁻¹, and Öpik's relation U = v_⊕√(3 − T) applied to Kamo'oalewa's Tisserand parameter with respect to Earth, T_⊕ ≈ 2.97, gives ≈ 5 km s⁻¹. Its kinetic energy relative to Earth therefore exceeds the depth of Earth's potential well at that distance by a factor of several hundred. On a two-body reckoning the asteroid is screaming past on a hyperbola with v_∞ ≈ 5 km s⁻¹.

So why does it never leave? Because the two-body reckoning is the wrong frame. In the rotating frame the Coriolis and centrifugal terms — that is, the Sun's influence, not Earth's — curve the trajectory back around. The confinement is solar; Earth only sets the phase. This also explains the resonance's protective role: the epicycle guarantees a separation of at least ~ae at conjunction, so even though Kamo'oalewa's orbit-to-orbit minimum distance (its Earth MOID) is only a few hundredths of an au, the 1:1 lock ensures Earth is never at the crossing point when the asteroid is.

How quasi-satellites are found and confirmed

Nobody photographs the loop; a quasi-satellite is identified by computation. Discovery astrometry comes from the survey telescopes — Pan-STARRS 1 (1.8 m, Haleakalā), the Catalina Sky Survey, ATLAS, and historically LINEAR and LONEOS — and goes to the Minor Planet Center, where a heliocentric orbit is fitted. Classification then follows from numerical integration.

The standard procedure, used by Carlos and Raúl de la Fuente Marcos, Paul Wiegert, Apostolos Christou and others, is a clone ensemble: draw ~10³ virtual asteroids from the orbit solution's covariance matrix, integrate them for 10³–10⁶ years with all planets, the Moon as a separate body, general-relativistic corrections and (for small objects) a Yarkovsky term, and watch σ. If every clone keeps σ librating about 0°, the state is robust; if the clones diverge after a few centuries, the future is genuinely chaotic — Lyapunov times for Earth co-orbitals are typically decades to centuries.

Observing them is hard. Kamo'oalewa has an absolute magnitude H ≈ 24.3, a diameter of roughly 40–100 m depending on albedo, and brightens to V ≈ 22–23 only for a few weeks each April, requiring 4-to-10-metre apertures; radar is hopeless at 15 million km for a 50-metre rock. The key measurements came from spectroscopy: in 2021 Ben Sharkey, Vishnu Reddy and colleagues used the twin 8.4 m Large Binocular Telescope and the 4.3 m Lowell Discovery Telescope to show a reddened, feldspathic silicate spectrum matching Apollo lunar samples rather than ordinary near-Earth S-types, with light curves giving a fast ~28-minute rotation. The Gaia-based astrometric reference frame, which pushed star-catalogue systematics to the milliarcsecond level and typical NEO residuals down to a few tens of milliarcseconds, has since extended the trustworthy integration horizon, and the Vera C. Rubin Observatory's LSST should multiply the known Earth co-orbital population.

The real objects: Kamo'oalewa, Zoozve and the rest

469219 Kamo'oalewa (2016 HO3) was found by Pan-STARRS 1 on 27 April 2016 and named in 2019 from the Hawaiian creation chant, the Kumulipo, for an oscillating celestial fragment. Its orbit — a ≈ 1.001 au, e ≈ 0.104, i ≈ 7.8° — has kept it a quasi-satellite of Earth since roughly the start of the twentieth century, and integrations show it remaining one for several centuries more. Its total residence in Earth's co-orbital region is estimated at ~10⁵–10⁶ years. The lunar hypothesis has grown steadily stronger: Sharkey et al. (2021) on spectra, Castro-Cisneros, Malhotra et al. (2023) on a viable delivery pathway for lunar impact ejecta, and Jiao et al. (2024, Nature Astronomy) pointing to the ~22 km farside crater Giordano Bruno as a plausible source. China's Tianwen-2 launched on 28 May 2025 from Xichang to rendezvous with it, collect samples and return a capsule to Earth around late 2027 before continuing to comet 311P/PANSTARRS.

Earth has several others: 164207 (2004 GU9), 277810 (2006 FV35), 2013 LX28, 2014 OL339 and 2023 FW13, which integrations suggest has been a quasi-satellite since around 100 BCE and will remain one until roughly 3700 CE — the longest-lived yet identified.

Other planets have them too. 524522 Zoozve (2002 VE68), discovered by Brian Skiff with LONEOS on 11 November 2002, was shown by Mikkola, Brasser, Wiegert and Innanen in 2004 to be a quasi-satellite of Venus — the first identified for any planet. It has held the state for roughly 7,000 years and should leave in about 500; the IAU gave it its whimsical name in February 2024. Neptune has the temporary quasi-satellite (309239) 2007 RW10, good for some 12,500 years; Jupiter hosts long-lived cases such as 2001 QQ199 and 2004 AE9 plus several Jupiter-family comets passing through quasi-satellite episodes; and Christou and Wiegert showed in 2012 that even Ceres and Vesta capture temporary co-orbital companions.

The look-alikes, and how objects switch between them

Quasi-satellites are chronically confused with three different things.

• Horseshoe companions. 3753 Cruithne, found by Duncan Waldron at Siding Spring on 10 October 1986 and identified as an Earth co-orbital by Wiegert, Innanen and Mikkola in Nature in 1997, is the perennial "Earth's second moon" headline. It is not a quasi-satellite: its σ executes a huge libration that swings almost all the way around the Sun and reverses near the planet, the horseshoe signature. 2010 SO16 is a more stable example, good for ~10⁵ years.
• Trojans. Here σ librates about +60° or −60°, around L4 or L5. Earth has just two known: 2010 TK7, found by WISE and announced in 2011, and 2020 XL5, confirmed in 2022.
• Minimoons. These are the genuine article — temporarily captured objects that really do enter the Hill sphere and complete bound revolutions. 2006 RH120, a ~3 m body, orbited Earth from mid-2006 to mid-2007; 2020 CD3 was bound for roughly three years, from around 2017 until 2020; 2024 PT5 made a temporarily captured flyby between September and November 2024 without completing a revolution. Minimoons last months; quasi-satellites last millennia and are never bound at all.

These are not permanent categories but phases of one co-orbital dance, and objects migrate between them as eccentricity and libration amplitude evolve secularly. 2003 YN107 was an Earth quasi-satellite from 1996 to 2006 and is now on a horseshoe, expected back around 2120; 2002 AA29 is on a horseshoe today and should become a quasi-satellite around 2600 for roughly 45 years; Kamo'oalewa itself arrived from a horseshoe about a century ago.

There is even a rough entry criterion. The loop must clear the planet's Hill sphere, which requires the conjunction separation ae to exceed a few R_H — that is, e greater than a few times (m_p/3M_☉)^1/3, or e ≳ 0.03 for Earth. Below that the loop shrinks inside the Hill sphere and the encounter stops being a quasi-satellite pass and becomes real gravitational scattering or capture.

Engineered quasi-satellites, and the open questions

Because quasi-satellite orbits are the far-field continuation of Hénon's retrograde family f, mission designers use them deliberately when a target is too small for a bound orbit. Phobos is the extreme case: with a mass of ~1.1 × 10¹⁶ kg at 9,376 km from Mars, its Hill radius is only about 16 km, barely larger than its own 11 km mean radius, so essentially no stable close orbit exists. JAXA's MMX mission, launching in the 2026 window, will therefore fly a nested sequence of explicit quasi-satellite orbits at roughly 100, 50 and 20 km before sampling. JAXA's earlier Hayabusa spacecraft did the same thing at 25143 Itokawa in 2005 — it never orbited the asteroid, it station-kept alongside it in a heliocentric orbit. And in November 2022 the Artemis I Orion capsule flew a distant retrograde orbit around the Moon, reaching about 64,000 km beyond it: the same dynamical family, sized by engineers instead of by chance.

Several questions remain open. How many are there? The known Earth co-orbital census is a handful of objects, almost certainly a severe undercount for 10–100 m bodies at magnitude 24 and fainter; Rubin's LSST is the test. Where do they come from? If Kamo'oalewa really is Giordano Bruno ejecta, a measurable fraction of small near-Earth objects may be lunar debris rather than main-belt fragments — which Tianwen-2's returned sample can confirm or kill outright by isotope ratios. How long do they last? Century-scale integrations are reliable; million-year ones are not, because the Yarkovsky effect drifts semi-major axes at of order 10⁻³–10⁻² au Myr⁻¹ for decametre bodies and eventually breaks any 1:1 lock. And practically: quasi-satellites stay near Earth in longitude and approach at only a few km s⁻¹, giving frequent windows and making them attractive rendezvous targets — though inclinations like Kamo'oalewa's 7.8° erode much of that advantage in Δv.

Six kinds of planetary companion, and which ones are actually bound

Companion type	Resonant angle λ − λ_planet	Gravitationally bound?	Real example
True moon	Not applicable — orbits the planet	Yes, deep inside the Hill sphere	The Moon, 384,400 km = 0.26 Earth Hill radii
Temporarily captured minimoon	Not applicable during capture	Yes, but only for months to years	2006 RH120, captured mid-2006 to mid-2007
Quasi-satellite	Librates about 0°	No — sits ~10× outside the Hill sphere	469219 Kamo'oalewa; 2023 FW13
Trojan (tadpole)	Librates about +60° or −60°	No	2010 TK7, Earth's first known Trojan
Horseshoe	Large libration enclosing 180°	No	3753 Cruithne; 2010 SO16
Distant retrograde orbit (engineered)	Librates about 0°	No, or only marginally	Orion during Artemis I, November 2022