Roaming the Relativistic Realm: Short-term Dynamical Evolution of Atira 2021 PH₂₇

Sekhar et al. (2017) confirmed that effects from the theory of general relativity (Einstein 1915) and from the von Zeipel–Lidov–Kozai mechanism (von Zeipel 1910; Kozai 1962; Lidov 1962; Ito & Ohtsuka 2019) can coexist for Solar system objects with low perihelion distances, q. One such object is comet 96P/Machholz 1 (de la Fuente Marcos et al. 2015; Sekhar et al. 2017), although they are also expected to exist among the so-called relativistic asteroids (see Table 2 in Benitez & Gallardo 2008). The anti-correlated eccentricity-inclination oscillations characteristic of the von Zeipel–Lidov–Kozai mechanism may be preserved or suppressed when relativistic effects are at work as the evolution of the argument of perihelion is subjected to relativistic precession (see e.g., the analysis of the particular case of hierarchical triple systems in Naoz et al. 2013). Objects relevant to testing ideas on this subject may populate the low end of the perihelion distance distribution of minor bodies that follow paths contained entirely within the orbit of Earth—i.e., with aphelion distances, Q, <0.983 au, the Atiras or Interior Earth Objects with 26 known members. Within the Atiras there is an even more extreme population, that of the Venus Atiras or Vatiras with Q < 0.718 au (Greenstreet et al. 2012). The first Vatira, 2020 AV₂, was recently characterized, both dynamically (de la Fuente Marcos & de la Fuente Marcos 2020a; Greenstreet 2020) and physically (Popescu et al. 2020).

A potential game changer was found on 2021 August 13, when asteroid 2021 PH₂₇ was discovered by Scott S. Sheppard in images acquired by Ian Dell'Antonio and Shenming Fu with the Dark Energy Camera (DECam) installed on Cerro Tololo Inter-American Observatory's (CTIO) 4 m Blanco telescope in Chile. ³ Among Solar system bodies, 2021 PH₂₇ is a clear statistical outlier, second only to planet Mercury in terms of sidereal orbital period, 114.57 ± 0.02 days. As of 2021 September 3, its heliocentric orbit determination (based on 54 observations spanning 17 days) is: semimajor axis, a = 0.46166 ± 0.00005 au, eccentricity, e = 0.7118 ± 0.0005, inclination, i = 3193 ± 004, Ω = 39417 ± 0005, and ω = 858 ± 002. ⁴ Currently, this object experiences regular close encounters with Venus, sometimes as close as 0.015 au from a planet that has a Hill radius of 0.0067 au. Here, we use numerical simulations to perform a preliminary assessment of the short-term orbital evolution of 2021 PH₂₇. Our N-body calculations were performed as described by de la Fuente Marcos & de la Fuente Marcos (2012) using publicly available input data from Jet Propulsion Laboratory's (JPL) Small-Body Database (SBDB) ⁵ and HORIZONS ⁶ on-line solar system data and ephemeris computation service (Giorgini 2015). Our relativistic calculations were carried out within the framework of the post-Newtonian approximation (see e.g., Aarseth 2007)based on first-order expansion (de la Fuente Marcos et al. 2015).

Figure 1, left-hand side panels, shows the short-term evolution of relevant orbital parameters for the nominal orbit of 2021 PH₂₇ integrated both under the Newtonian (in blue) and the post-Newtonian (in black) approximations. After a few thousand years, the evolution diverges noticeably. The asymmetry between past and future dynamics is driven by close encounters with Venus, the only planet that 2021 PH₂₇ approaches at sufficiently close range (well inside the Hill radius). Figure 1, right-hand side panels, shows the impact of the uncertainties in the current orbit determination on the computed evolution when integrating under the post-Newtonian approximation. The top panel shows that 2021 PH₂₇ is well within the Atira orbital realm and relatively close to the edge of the Vatira orbital parameter space. Even control orbits with Cartesian vectors separated ±9σ from the nominal values (in red) show that the Atira classification is robust. In addition to its robust Atira dynamical status, Figure 1 shows the anti-correlated e-i oscillations characteristic of the von Zeipel–Lidov–Kozai mechanism. This behavior is shared by many of the known Atiras (see e.g., de la Fuente Marcos & de la Fuente Marcos 2018, 2019a, 2019b, 2020a, 2020b). On the other hand, in general relativity, the perihelion shift is given by $\delta {\phi }_{0}\propto {a}^{-1}\,{(1-{e}^{2})}^{-1}$—see e.g., Equation (40.18) in Misner et al. (1973). Therefore, considering the orbital elements of 2021 PH₂₇ pointed out above and those of Mercury, the perihelion shift of this object is 1.6 times that of Mercury that is 429 per century.

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Atira 2021 PH₂₇ has the potential to become a key player in our understanding of how effects from the theory of general relativity and from the von Zeipel–Lidov–Kozai mechanism work together (it has q = 0.1330 ± 0.0002 au, 96P has 0.1237 au). It may also be used to probe general relativity with radar astrometry as discussed by Margot & Giorgini (2009, 2010). However, Figure 1 shows that the current orbit determination of 2021 PH₂₇ is not good enough to make detailed dynamical predictions for this object beyond about 1000 yr forward in time and prior to 11,000 yr into the past. More observations are needed to understand the orbital evolution of this interesting object better.