Spin State Evolution of 99942 Apophis during its 2029 Earth Encounter Conor J. Benson Daniel J. Scheeres University of Colorado Boulder 3775 Discovery Drive Boulder CO 80303 USA

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Spin State Evolution of (99942) Apophis during its 2029 Earth Encounter

Conor J. Benson, Daniel J. Scheeres

University of Colorado Boulder, 3775 Discovery Drive, Boulder, CO 80303, USA

Marina Brozovi´c, Steven Chesley

Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA

Petr Pravec, Petr Scheirich

Astronomical Institute, Academy of Sciences of the Czech Republic, Friˇcova 1, CZ-25165 Ondˇrejov, Czech Republic

Abstract

We explore the eﬀects of the 2029 Earth encounter on asteroid (99942) Apophis’ non-principal axis

spin state, leveraging reﬁned orbit, spin state, and inertia information provided by more recent optical and

radar observations. Propagating the asteroids’ coupled orbit and rigid body attitude dynamics through the

ﬂyby, we present the range of possible post-ﬂyby spin states. These spin state distributions will be valuable

for planning Apophis observation campaigns and spacecraft missions, most notably OSIRIS-APEX. The

simulations indicate that gravitationally induced changes to the asteroid’s tumbling periods and rotational

angular momentum direction (pole) will likely be signiﬁcant and measurable. For the current spin state

and inertia estimates and their uncertainties, Apophis is likely to remain in a short axis mode (SAM)

tumbling state but its eﬀective spin rate could halve or double. Its pole is likely to shift by 10 degrees or

more and increase in longitude while moving closer to the ecliptic plane. These spin state changes are very

sensitive to the asteroid’s close approach attitude and mass distribution. With ground-based tracking of

the asteroid’s spin state through the encounter, this sensitivity will help reﬁne mass distribution knowledge.

We also discuss the implications of this abrupt spin state alteration for Apophis’ Yarkovsky acceleration

and geophysical properties, identifying possible pathways for surface and internal changes, most notably

if Apophis is a contact binary. Comparison of the pre and post-ﬂyby inertia estimates obtained from the

ground-based observations will help assess the extent of possible geophysical changes.

Keywords: Asteroids, dynamics; Asteroids, rotation; Near-Earth objects

Preprint submitted to Elsevier October 25, 2022

arXiv:2210.13365v1 [astro-ph.EP] 24 Oct 2022

1. Introduction

On April 13, 2029 asteroid (99942) Apophis will make a close approach to the Earth, coming within 6

Earth radii from the geocenter. This unprecedented ﬂyby oﬀers a unique opportunity to learn about small

body evolution and has been highlighted in the Planetary Science Decadal Survey (National Academies

of Sciences, Engineering, and Medicine, 2022). It is an event that will drive much planning and analysis.

Of particular interest is NASA’s OSIRIS-APEX mission, which is set to rendezvous with Apophis several

months after the asteroid’s 2029 Earth encounter (DellaGuistina et al., 2022). The close approach will

have a signiﬁcant impact on two aspects of Apophis’ dynamic state, its orbit and its rotation. In this

paper we revisit an analysis by Scheeres et al. (2005) conducted shortly after Apophis’ discovery in 2004

that studied the range of possible spin states the asteroid could have following its close approach ﬂyby.

Given the limited observations up to that point, this study was subject to large uncertainties in the close

approach distance and asteroid physical properties. From preliminary light curve analysis, the asteroid was

modeled as a triaxial ellipsoid in uniform rotation about its maximum inertia axis. In our current analysis,

we take advantage of Apophis’ greatly constrained orbit, spin state, and shape made possible by extensive

subsequent observations. Speciﬁcally, we draw from much richer knowledge of its non-principal axis rotation

state and shape obtained from optical (Pravec et al., 2014) and radar (Brozovi´c et al., 2018) measurements.

These important reﬁnements greatly improve the modeling of the eﬀects of Apophis’ Earth encounter and

will provide a realistic range of post-ﬂyby spin states that may be expected.

This analysis supports several important scientiﬁc aspects. First, the ﬂyby will provide insight into

the asteroid’s mass distribution and interior based on the observed changes in its spin state. When the

actual moments of inertia are compared to those derived from the constant density asteroid shape model,

the extent of Apophis’ density homogeneity can be explored. Discrepancies between the shape-derived and

actual moments of inertia could indicate density variations across the asteroid’s surface and/or interior. The

convex shape model solution of Pravec et al. (2014) shows some discrepancy between these inertias. But it

is very possible that these diﬀerences are due to surface concavities that cannot be resolved with current

optical observations. The radar observations suggest that Apophis has a bi-lobed shape (Brozovi´c et al.,

2018), supporting this hypothesis. Improvements in shape and spin state provided by future observations,

particularly those around the 2029 encounter, should allow for further reﬁnements to the shape, ﬂyby-

induced evolution, and mass distribution. Detailed knowledge of Apophis’ spin state and mass distribution

will be crucial for planning and operating in-situ missions such as OSIRIS-APEX.

These spin state simulation results will allow also us to predict the range of surface accelerations and

global stresses that will be placed across the body during its closest approach. Previous work by Scheeres

et al. (2005), DeMartini et al. (2019), and Hirabayashi et al. (2021) explored the geophysical implications

of the ﬂyby. All three studies make simplifying assumptions about the pre-encounter spin state and its

uncertainty. Both Scheeres et al. (2005) and DeMartini et al. (2019) do not account for the asteroid’s non-

principal axis rotation. Hirabayashi et al. (2021) consider the full Pravec et al. (2014) spin state solution but

do not account for current uncertainties in Apophis’ tumbling periods and rotational angular momentum

direction (pole) and the resulting increase in possible close encounter attitudes. Souchay et al. (2018)

explore the eﬀects of the encounter on Apophis’ pole direction using the Pravec et al. (2014) solutions and

their uncertainties, but they assume the asteroid is uniformly rotating about its maximum inertia axis.

Furthermore, Souchay et al. (2018) do not explore how the asteroid’s tumbling periods will change due

to the gravitational torques. In this work, we conduct rigid body dynamical modeling that accounts for

both the asteroid’s non-principal axis rotation and initial condition uncertainties. We present post-ﬂyby

distributions for both the pole and tumbling periods, providing a complete picture of possible encounter

outcomes from which to address geophysical implications. These predictions may enable more precise designs

of any measurements that may be performed by visiting spacecraft. Finally, the ﬂyby-induced spin state

change may alter the asteroid’s Yarkovsky acceleration and subsequent Earth encounter predictions.

In this paper, we outline the current Apophis spin state estimates, propagate these states through the

ﬂyby, present the resulting post-ﬂyby spin state distributions, and ﬁnally discuss implications for Apophis’

ﬂyby-induced geophysical evolution and the Yarkovsky eﬀect.

2. Current Spin State Estimates

The Apophis spin state and shape model solutions provided by Pravec et al. (2014) and Brozovi´c et al.

(2018) are both considered in our analysis. From here on, these will be referred to as the “photometric” and

“radar” solutions respectively. Table 1 lists these solutions. Here, P¯

φsis the average precession period of the

asteroid’s maximum inertia (short) axis around the rotational angular momentum vector H(Samarasinha

and Mueller, 2015). This is the short axis period convention assumed in Pravec et al. (2014). Alternatively,

we can use the long axis convention where P¯

φlis the average precession period of the minumum inertia (long)

axis about H(Samarasinha and A’Hearn, 1991). Given Apophis’ elongated shape, it can be more intuitive

to track motion of the long axis. P¯

φlalso tends to have the largest associated amplitude in Apophis light

curves (Pravec et al., 2014). The other tumbling period, Pψ, is the rotation period about the short or long

axis in the corresponding convention. Since Pψis equal to the circulation period of the asteroid’s angular

velocity vector ωin the body-ﬁxed frame, its value is the same for both short and long axis conventions

(Samarasinha and Mueller, 2015). A schematic of the tumbling periods for the long axis convention is shown

in Figure 1 where θis the time-varying nutation angle between the long axis and H.

Figure 1: Long axis tumbling period convention for Apophis

The three tumbling periods are related by the following equation (Samarasinha and Mueller, 2015),

P¯

φs

P¯

φl

Pψ

(1)

In Table 1, λand βare the J2000 ecliptic longitude and latitude of H. Finally, denoting the three

principal moments of inertia as Il≤Ii≤Is, we provide the two inertia ratios Il/Isand Ii/Is. Uncertainties

in the photometric solution quantities are given to the 3σconﬁdence level. For the photometric solution,

the nominal λand βvalues are given while Pravec et al. (2014) provide the range of admissible rotational

angular momentum directions in Figure 4 of their paper. Throughout this work we refer to the angular

momentum direction as the “pole”. Due to the limited resolution of the 2012 - 2013 Apophis radar data

given the relatively large 0.1 AU encounter distance, Brozovi´c et al. (2018) were unable to improve on the

photometric solution uncertainties. So the radar solution is subject to similar uncertainties. See Brozovi´c

et al. (2018) and its supplemental material for more insight on the radar solution uncertainties.

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SpinStateEvolutionof(99942)Apophisduringits2029EarthEncounterConorJ.Benson,DanielJ.ScheeresUniversityofColoradoBoulder,3775DiscoveryDrive,Boulder,CO80303,USAMarinaBrozovic,StevenChesleyJetPropulsionLaboratory,CaliforniaInstituteofTechnology,4800OakGroveDrive,Pasadena,CA91109,USAPetrPravec,PetrSchei...

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Spin State Evolution of 99942 Apophis during its 2029 Earth Encounter Conor J. Benson Daniel J. Scheeres University of Colorado Boulder 3775 Discovery Drive Boulder CO 80303 USA

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