33 Polyhymnia

Photometric observations of this asteroid at the Organ Mesa Observatory in Las Cruces, New Mexico during 2008 gave a light curve with a period of 18.609 ± 0.002 hours and a brightness variation of 0.15 ± 0.02 in magnitude. This result is in good agreement with a previous study performed during 1980.^[9] These results were re-examined with additional observations in 2011, yielding a refined estimate of 18.608 ± 0.001 hours and a brightness variation of 0.18 ± 0.02 magnitude.^[10] In 2020, an analysis of photometric data of Polyhymnia from 2008 to 2019 determined a more precise rotation period of 18.60888±0.00029 h. Two possible north pole orientations of Polyhymnia were also determined, with both solutions indicating an axial tilt of 151–155° (ecliptic latitudes –61° to –65°) with respect to the ecliptic.^[7]

On its highly eccentric (0.338) orbit around the Sun, Polyhymnia appears brightest (apparent magnitude 10) at its minimum distance from Earth of 0.91 AU.^[11] Its orbit puts it in a 22:9 mean-motion resonance with the planet Jupiter. The computed Lyapunov time for this asteroid is 10,000 years, indicating that it occupies a chaotic orbit that will change randomly over time because of gravitational perturbations of the planets.^[12] Measurements of the position for this asteroid from 1854 to 1969 were used to determine the gravitational influence of Jupiter upon Polyhymnia. This yields an inverse mass ratio of 1047.341±0.011 for Jupiter relative to the Sun.^[13]

In 2012, a study by Benoît Carry gave a meta-estimate of a mass of (6.20±0.74)×10¹⁸ kg for Polyhymnia, based on a single study of its gravitational influence on other Solar System bodies.^[5] However, given Polyhymnia's diameter of 54 km (34 mi), this mass implies an extremely high density of 75.28±9.71 g/cm³. Such a high density is unrealistic, so this mass and density estimate of Polyhymnia was considered unreliable by Carry.^[5] Several other asteroids with diameters similar to Polyhymnia were also measured to have extremely high densities in Carry's study, and were rejected for being unrealistic.^[5] Because of Polyhymnia's small size, its gravitational influence on other bodies is extremely difficult to detect and may lead to highly inaccurate mass and density estimates.^[5] For example, the 68 km (42 mi)-diameter asteroid 675 Ludmilla was originally measured to have a density of 73.99±15.05 g/cm³ in Carry's study,^[5] but improved orbit calculations in 2019 showed that it had a much lower density of 3.99±1.94 g/cm³.^[14]

No other peer-reviewed study has attempted to determine a mass and density for Polyhymnia since Carry's study,^[15] though in 2023, researcher Fan Li performed a preliminary analysis of Polyhymnia's close approaches with other asteroids and determined a lower mass of (1.03±0.40)×10¹⁸ kg.^[16] Depending on the diameter used for Polyhymnia, this mass estimate suggests a density of 7.5±3.6 g/cm³ or 12.4 g/cm³, for an occultation-derived diameter of 64 Â± 6 km (39.8 Â± 3.7 mi) and infrared-derived diameter of 54 km (34 mi), respectively.^[16][17]

Visible light spectroscopy of Polyhymnia from 1995 and 2002 show that it is an S-type asteroid, meaning it is mainly composed of rocky silicates.^[3] In particular, Polyhymnia's spectrum exhibits an absorption band at 0.67 μm wavelengths, which indicates olivine and pyroxene on its surface, similar to Q-type asteroids.^{[8]: 155, 164–165 } Since Polyhymnia shares both characteristics of S- and Q-type asteroids, it is further classified as an Sq-type asteroid according to the SMASS classification.^{[8]: 155, 164–165 } Radio telescopes have studied Polyhymnia by radar in 1985.^[18][19]

In 2023, researchers Evan LaForge, Will Price, and Johann Rafelski speculated the possibility that Polyhymnia could be composed of high-density superheavy elements near atomic number 164, if Polyhymnia's extremely high density were correct and superheavy elements could be sufficiently stable.^[20] However, as noted above, Polyhymnia very likely does not have such a high density.^[16][17]