Libration-induced Orbit Period Variations Following the DART Impact

Abstract

The Double Asteroid Redirection Test (DART) mission will be the first test of a kinetic impactor as a means of planetary defense. In late 2022, DART will collide with Dimorphos, the secondary in the Didymos binary asteroid system. The impact will cause a momentum transfer from the spacecraft to the binary asteroid, changing the orbit period of Dimorphos and forcing it to librate in its orbit. Owing to the coupled dynamics in binary asteroid systems, the orbit and libration state of Dimorphos are intertwined. Thus, as the secondary librates, it also experiences fluctuations in its orbit period. These variations in the orbit period are dependent on the magnitude of the impact perturbation, as well as the system’s state at impact and the moments of inertia of the secondary. In general, any binary asteroid system whose secondary is librating will have a nonconstant orbit period on account of the secondary’s fluctuating spin rate. The orbit period variations are typically driven by two modes: a long period and a short period, each with significant amplitudes on the order of tens of seconds to several minutes. The fluctuating orbit period offers both a challenge and an opportunity in the context of the DART mission. Orbit period oscillations will make determining the post-impact orbit period more difficult but can also provide information about the system’s libration state and the DART impact.

Energy dissipation in synchronous binary asteroids

“…The binary asteroid cannot settle into an equilibrium while the libration amplitude is nonzero, or equivalently the eccentricity is not equal to its equilibrium value. This is consistent with the findings of Meyer et al (2021), who point out the relationship between the secondary spin and the orbit oscillations.…”

“…This approach means we have developed our own independent estimate of the system density rather than using values derived from observations, although our density lies within the error bars of the observed value (Naidu et al, 2020;Scheirich and Pravec, 2022). We calculate the stroboscopic orbit period using the method outlined in Meyer et al (2021). The resulting equilibrium system has the parameters outlined in Table 1.…”

“…The DART impact will push Dimorphos out of the equilibrium state (Meyer et al, 2021;Agrusa et al, 2021). The impact can be quantified by the momentum enhancement factor known as , which is defined as the ratio of the true system momentum change to the momentum carried by the impactor.…”

NASA’s Double Asteroid Redirection Test (DART): Mutual Orbital Period Change Due to Reshaping in the Near-Earth Binary Asteroid System (65803) Didymos

“…For comparison, we also conduct simulations by using GUBAS with fourth-and eighth-order gravity truncation settings with the same initial conditions, physical parameters, and integrator settings (RK4 with a fixed time step of 60 s). Note that GUBAS has been extensively used for DART-related mutual dynamics studies (e.g., Agrusa et al 2020Agrusa et al , 2021Meyer et al 2021), and GUBAS with a fourth-order gravity truncation setting was determined as sufficient for accurate dynamics modeling (Agrusa et al 2020).…”

“…Not only does the DART impact change the mutual dynamics (i.e., orbital period change, attitude excitation, etc. ; Rivkin et al 2021;Agrusa et al 2020Agrusa et al , 2021Meyer et al 2021), it also modifies the geophysical conditions of the bodies. The impact excavates Dimorphos's surface/subsurface materials and develops a crater (e.g., Stickle et al 2017Stickle et al , 2022Rainey et al 2020;Raducan et al 2019Raducan et al , 2020.…”