Ephemeris Uncertainties Research Articles

TESS Timings of 31 Hot Jupiters with Ephemeris Uncertainties

A precise transit ephemeris serves as the premise for follow-up exoplanet observations. We compare TESS Object of Interest (TOI) transit timings of 262 hot Jupiters with the archival ephemeris and find 31 of them having TOI timing offsets, among which WASP-161b shows the most significant offset of −203.7 ± 4.1 minutes. The median value of these offsets is 17.8 minutes, equivalent to 3.6σ. We generate TESS timings in each sector for these 31 hot Jupiters, using a self-generated pipeline. The pipeline performs photometric measurements to TESS images and produces transit timings by fitting the light curves. We refine and update the previous ephemeris, based on these TESS timings (uncertainty ∼1 minute) and a long timing baseline (∼10 yr). Our refined ephemeris gives the transit timing at a median precision of 0.82 minutes until 2025 and 1.21 minutes until 2030. We regard the timing offsets to mainly originate from the underestimated ephemeris uncertainty. All the targets with timing offset larger than 10σ present earlier timings than the prediction, which cannot be due to underestimated ephemeris uncertainty, apsidal precision, or Rømer effect as those effects should be unsigned. For some particular targets, timing offsets are likely due to tidal dissipation. Our sample leads to the detection of period-decaying candidates of WASP-161b and XO-3b reported previously.

CubeSat Autonomous Navigation and Guidance for Low-Cost Asteroid Flyby Missions

Recent advancements in CubeSat technology unfold new mission ideas and the opportunity to lower the cost of space exploration. Ground operations costs for interplanetary CubeSats, however, still represent a challenge toward low-cost CubeSat missions: hence, certain levels of autonomy are desirable. The feasibility of autonomous asteroid flyby missions using CubeSats is assessed here, and an effective strategy for autonomous operations is proposed. The navigation strategy is composed of observations of the Sun, visible planets, and the target asteroid, whereas the guidance strategy is composed of two optimally timed trajectory correction maneuvers. A Monte Carlo analysis is performed to understand the flyby accuracies that can be achieved by autonomous CubeSats, in consideration of errors and uncertainties in a) departure conditions, b) propulsive maneuvers, c) observations, and d) asteroid ephemerides. Flyby accuracies better than are found possible, and main limiting factors to autonomous missions are identified, namely a) on-board asteroid visibility time (), b) for correction maneuvers (), c) asteroid ephemeris uncertainty (), and d) short duration of transfer to asteroid. Ultimately, this study assesses the readiness level of current CubeSat technology to autonomously flyby near-Earth asteroids, in consideration of realistic system specifications, errors, and uncertainties.

Original Research by Young Twinkle Students (ORBYTS): ephemeris refinement of transiting exoplanets

ABSTRACT We report follow-up observations of transiting exoplanets that have either large uncertainties (>10 min) in their transit times or have not been observed for over 3 yr. A fully robotic ground-based telescope network, observations from citizen astronomers, and data from TESS have been used to study eight planets, refining their ephemerides and orbital data. Such follow-up observations are key for ensuring accurate transit times for upcoming ground- and space-based telescopes, which may seek to characterize the atmospheres of these planets. We find deviations from the expected transit time for all planets, with transits occurring outside the 1σ uncertainties for seven planets. Using the newly acquired observations, we subsequently refine their periods and reduce the current predicted ephemeris uncertainties to 0.28–4.01 min. A significant portion of this work has been completed by students at two high schools in London as part of the Original Research By Young Twinkle Students (ORBYTS) programme.

Reality measure of the published GPS satellite ephemeris uncertainties

ABSTRACT The international GNSS service (IGS) started publishing the precise ephemeris files in the form of the standard products #3, version C (the sp3c files) in which the GPS satellite orbits and clocks and their uncertainties were available since 2004. Incorporating these uncertainties into the GPS observation equations results in a better stochastic model of the processing system. The reality of these uncertainties is questioned and studied in this paper. Precise point positioning (PPP) model, statistical tests and variance component estimation (VCE) techniques are employed for this study. The results confirm the efficiency of the proposed method in the assessment of reality of the published ephemeris uncertainties.

Modeling the Uncertainties of Solar System Ephemerides for Robust Gravitational-wave Searches with Pulsar-timing Arrays

Abstract The regularity of pulsar emissions becomes apparent once we reference the pulses’ times of arrivals to the inertial rest frame of the solar system. It follows that errors in the determination of Earth's position with respect to the solar system barycenter can appear as a time-correlated bias in pulsar-timing residual time series, affecting the searches for low-frequency gravitational waves performed with pulsar-timing arrays. Indeed, recent array data sets yield different gravitational-wave background upper limits and detection statistics when analyzed with different solar system ephemerides. Crucially, the ephemerides do not generally provide usable error representations. In this article, we describe the motivation, construction, and application of a physical model of solar system ephemeris uncertainties, which focuses on the degrees of freedom (Jupiter's orbital elements) most relevant to gravitational-wave searches with pulsar-timing arrays. This model, BayesEphem, was used to derive ephemeris-robust results in NANOGrav's 11 yr stochastic-background search, and it provides a foundation for future searches by NANOGrav and other consortia. The analysis and simulations reported here suggest that ephemeris modeling reduces the gravitational-wave sensitivity of the 11 yr data set and that this degeneracy will vanish with improved ephemerides and with pulsar-timing data sets that extend well beyond a single Jovian orbital period.

Dual-Satellite Geolocation With Ephemeris Correction and Uncertainty Mapping

In this paper, we demonstrate that the uncertainty of the dual-satellite ephemeris must be included in order for the geolocation covariance to be accurate. Without the inclusion of this additional error source, the covariance is no longer consistent with the true uncertainty and can convey misleading results. The larger the uncertainty associated with the dual-satellite ephemeris the larger the geolocation covariance becomes. Therefore, we first demonstrate a technique for improving the dual-satellite ephemeris knowledge by using calibrator transmitters for orbit determination. Second, we derive a consider batch filter, which computes the best estimate of position of the unknown radio frequency source while taking into account the dual-satellite ephemeris uncertainty. An algorithm is also proposed for adding a probabilistic altitude constraint, which significantly reduces the solution error. Finally, we briefly touch upon a technique that allows for the dual-satellite ephemeris and source position to be estimated simultaneously thereby maintaining the correlations and optimality. All algorithms introduced have since been applied to real-world data and conveys actual capabilities rather than a theoretical approach alone.

Near-Earth asteroid 2012 TC4 observing campaign: Results from a global planetary defense exercise

Impacts due to near-Earth objects (NEOs) are responsible for causing some of the great mass extinctions on Earth. While nearly all NEOs of diameter > 1 km, capable of causing a global climatic disaster, have been discovered and have negligible chance of impacting in the near future, we are far from completion in our effort to detect and characterize smaller objects. In an effort to test our preparedness to respond to a potential NEO impact threat, we conducted a community-led global planetary defense exercise with support from the NASA Planetary Defense Coordination Office. The target of our exercise was 2012 TC4, the ~10 m diameter asteroid that made a close pass by the Earth on 2017 October 12 at a distance of about 50,000 km. The goal of the TC4 observing campaign was to recover, track, and characterize 2012 TC4 as a hypothetical impactor in order to exercise the global planetary defense system involving observations, modeling, prediction, and communication. We made three attempts with the Very Large Telescope (VLT) on 2017 July 27, 31 and on 2017 August 5 and recovered 2012 TC4 within its ephemeris uncertainty at 2.2 arcmin from the nominal prediction. At visual magnitude V = 27, the recovery of 2012 TC4 is the faintest NEA detection thus far. If an impact during the 2017 close approach had been possible based on the 2012 astrometric data, these recovery observations would have been sufficient to confirm or rule out the impact. The first automatic detection by a survey (Pan-STARRS1) was on September 25, which is the earliest that 2012 TC4 would have been discovered in survey mode, if it had not been discovered in 2012. We characterized 2012 TC4 using photometry, spectroscopy and radar techniques. Based on photometric observations, we determined a rotation period of 12.2 min with an amplitude of 0.9 magnitudes. An additional lower amplitude period was detected, indicating that 2012 TC4 was in a state of non-principal axis rotation. The combined visible and near-infrared spectrum puts it in the taxonomic X-class. Radar images at 1.875 m resolution placed only a few range pixels on the asteroid, reveal an angular, asymmetric, and elongated shape, and establish that 2012 TC4 is less than 20 m on its long axis. We estimate a circular polarization ratio of 0.57 + -0.08 that is relatively high among NEAs observed to date by radar. We also performed a probabilistic impact risk assessment exercise for hypothetical impactors based on the 2012 TC4 observing campaign. This exercise was performed as part of ongoing efforts to advance effective impact risk models and assessment processes for planetary defense. The 2012 TC4 close approach provided a valuable opportunity to test the application of these methods using realistically evolving observational data to define the modeling inputs. To this end, risk assessments were calculated at several epochs before and during the close approach, incorporating new information about 2012 TC4 as it became available. Two size ranges were assessed—one smaller size range (H = 26.7) similar to the actual 2012 TC4, and one larger size range (H = 21.9) to produce a greater-damage scenario for risk assessment. Across the epochs, we found that only irons caused significant damage for smaller size. For the larger size case, however, hydrous stones caused the greatest damage, anhydrous stones caused the least damage, and irons caused moderate damage. We note that the extent of damage depends on composition in different size regimes and, after astrometry, size is the most important physical property to determine for an incoming object.

Optimizing asteroid orbit computation forGaiawith normal points

Context.In addition to the systematic observations of known solar-system objects (SSOs), a continuous processing of new discoveries requiring fast responses is implemented as the short-term processing ofGaiaSSO observations, providing alerts for ground-based follow-up observers. The common independent observation approach for the purposes of orbit computation has led to unrealistically large ephemeris prediction uncertainties when processing realGaiadata.Aims.We aim to provide ground-based observers with a cloud of sky positions that is shrunk to a fraction of the previously expected search area by making use of the characteristic features ofGaiaastrometry. This enhances the efficiency ofGaiaSSO follow-up network and leads to an increased rate of asteroid discoveries with reasonably constrained orbits with the help of ground-based follow-up observations ofGaiaasteroids.Methods.We took advantage of the separation of positional errors ofGaiaSSO observations into a random and systematic component. We treated theGaiaobservations in an alternative way by collapsing up to ten observations that correspond to a single transit into a single so-called normal point. We implemented this input procedure in theGaiaSSO short-term processing pipeline and the OpenOrb software.Results.We validate our approach by performing extensive comparisons between the independent observation and normal point input methods and compare them to the observed positions of previously known asteroids. The new approach reduces the ephemeris uncertainty by a factor of between three and ten compared to the situation where each point is treated as a separate observation.Conclusions.Our new data treatment improves the sky prediction for theGaiaSSO observations by removing low-weight orbital solutions. These solutions originate from excessive curvature of observations, introduced by short-term variations ofGaiaattitude on the one hand, and, as a main effect, shrinking of systematic error bars in the independent observation case on the other hand. We anticipate that a similar approach may also be utilized in a situation where observations from a single observatory dominate.

Radio Interferometric Observation of an Asteroid Occultation

Abstract The occultation of the radio galaxy 0141+268 by the asteroid (372) Palma on 2017 May 15 was observed using six antennas of the Very Long Baseline Array (VLBA). The shadow of Palma crossed the VLBA station at Brewster, Washington. Owing to the wavelength used, and the size and the distance of the asteroid, a diffraction pattern in the Fraunhofer regime was observed. The measurement retrieves both the amplitude and the phase of the diffracted electromagnetic wave. This is the first astronomical measurement of the phase shift caused by diffraction. The maximum phase shift is sensitive to the effective diameter of the asteroid. The bright spot at the shadow’s center, the so called Arago–Poisson spot, is clearly detected in the amplitude time-series, and its strength is a good indicator of the closest angular distance between the center of the asteroid and the radio source. A sample of random shapes constructed using a Markov chain Monte Carlo algorithm suggests that the silhouette of Palma deviates from a perfect circle by 26 ± 13%. The best-fitting random shapes resemble each other, and we suggest their average approximates the shape of the silhouette at the time of the occultation. The effective diameter obtained for Palma, 192.1 ± 4.8 km, is in excellent agreement with recent estimates from thermal modeling of mid-infrared photometry. Finally, our computations show that because of the high positional accuracy, a single radio interferometric occultation measurement can reduce the long-term ephemeris uncertainty by an order of magnitude.

Unconfirmed Near-Earth Objects

Abstract We studied the Near-Earth Asteroid (NEA) candidates posted on the Minor Planet Center’s Near-Earth Object Confirmation Page (NEOCP) between years 2013 and 2016. Out of more than 17000 NEA candidates, while the majority became either new discoveries or were associated with previously known objects, about 11% were unable to be followed-up or confirmed. We further demonstrate that of the unconfirmed candidates, 926 ± 50 are likely to be NEAs, representing 18% of discovered NEAs in that period. Only 11% (∼93) of the unconfirmed NEA candidates were large (having absolute magnitude H < 22). To identify the reasons why these NEAs were not recovered, we analyzed those from the most prolific asteroid surveys: Pan-STARRS, the Catalina Sky Survey, the Dark Energy Survey, and the Space Surveillance Telescope. We examined the influence of plane-of-sky positions and rates of motion, brightnesses, submission delays, and computed absolute magnitudes, as well as correlations with the phase of the moon and seasonal effects. We find that delayed submission of newly discovered NEA candidate to the NEOCP drove a large fraction of the unconfirmed NEA candidates. A high rate of motion was another significant contributing factor. We suggest that prompt submission of suspected NEA discoveries and rapid response to fast-moving targets and targets with fast growing ephemeris uncertainty would allow better coordination among dedicated follow-up observers, decrease the number of unconfirmed NEA candidates, and increase the discovery rate of NEAs.

The Ceres gravity field, spin pole, rotation period and orbit from the Dawn radiometric tracking and optical data

Ceres’ gravity field and rotational parameters have been precisely measured using 1.5 years of radiometric Doppler and range data and optical landmark tracking from the Dawn spacecraft in orbit about the dwarf planet. As was the case with Dawn at Vesta, the gravity field, orientation parameters, landmark locations, and Ceres’ orbit are jointly estimated in a global solution. Even though Dawn's radio science investigation at Ceres was complicated by additional thrusting for attitude control, the resulting spherical harmonic gravity field has a half-wavelength resolution of up to 82 km (degree 18) near the equator, which is similar harmonic resolution to that of Vesta. The gravity field is consistent with Airy isostatic compensation, and this model assumption limits Ceres’ crustal density to be between 1200 and 1600 kg/m3 for two-layer and three-layer models with mean crustal thickness between 27 and 43 km. The compensation depth is determined using admittance between gravity and gravity from topography and is superior to admittance between gravity and topography. The gravitational mass of Ceres is determined to better than 0.002% (GMCeres = 62.62736 ± 0.00040 km3/s2), the spin pole location is improved by 10× over previous results with right ascension (α = 291.427°) and declination (δ = 66.760°) uncertainty less than 0.001°, and the rotation rate is improved by ∼100× over previous determinations from Hubble Space Telescope (HST) images. Ceres’ heliocentric orbit has also been improved, with about 17 months of precision range measurements reducing ephemeris uncertainties to about 10 m during the Dawn timeframe.

A Radio/Optical Integrated Navigation Method Based on Ephemeris Correction for an Interplanetary Probe to approach a Target Planet

To obtain accurate navigation results with respect to Earth simultaneously with those with respect to the target for an interplanetary probe to approach the target planet, this paper proposes a Radio/Optical integrated navigation method based on ephemeris correction, which deeply affects the fusion accuracy. In this paper, the model of the ephemeris error is established, and taking the analytical solution of the ephemeris uncertainty as measurement, the target ephemeris error and its covariance are estimated by Kalman filter and fed back to modify the force models. By correcting the target ephemeris and using information fusion, the Radio/Optical integrated navigation prevents the ephemeris uncertainty polluting the fusion accuracy, and efficiently combines the radio and optical navigation results. The results show the influence of the ephemeris error can be removed, and the Radio/Optical integrated navigation is capable of providing accurate navigation results with respect to Earth and the target. The results demonstrate the proposed method yields an accuracy superior to the conventional method, which proves its effectiveness.

Autonomous celestial navigation for a deep space probe approaching a target planet based on ephemeris correction

This article aims to propose an autonomous navigation method to simultaneously obtain precise position and velocity estimation of a deep space probe both with respect to Earth and with respect to the target, and estimate and correct the ephemeris uncertainty of the target that has a great influence on the navigation accuracy with respect to Earth. In this article, based on the analysis of the influences of ephemeris error on the state model, optical measurement, and the navigation accuracy, the ephemeris error is modeled. By taking the differences between the planned image and the actual image of the target as the ephemeris uncertainty measurement, the method is carried out by augmenting ephemeris uncertainty as system states, and is able to estimate and correct the ephemeris uncertainty of the target planet, and the position and velocity of the probe with respect to Earth and with respect to the target planet autonomously. The results show the influence of ephemeris error is removed from the orbital dynamics of the navigation system, and the proposed method can improve the accuracy with respect to Earth. The results demonstrate the proposed method autonomously yields superior performance with respect to Earth and with respect to the target.

The Vesta gravity field, spin pole and rotation period, landmark positions, and ephemeris from the Dawn tracking and optical data

The Vesta gravity field and related physical parameters have been precisely measured using 10-months of radiometric Doppler and range data and optical landmark tracking from the Dawn spacecraft. The gravity field, orientation parameters, landmark locations, and Vesta’s orbit are jointly estimated. The resulting spherical harmonic gravity field has a half-wavelength resolution of 42km (degree 20). The gravitational mass uncertainty is nearly 1 part in 106. The inertial spin pole location is determined to better than 0.0001° and the uncertainty in the rotation period has been reduced by nearly a factor of 100. The combined precession and nutation of the pole of Vesta has been detected with angular rates about 70% of expected values, but not well enough to constrain the moment of inertia. The optical landmark position estimates reduce the uncertainty in the center-of-mass and center-of-figure offset to 10m. The Vesta ephemeris uncertainty during the Dawn stay was reduced from 20km to better than 10m in the Earth–Vesta direction.

Statistical and numerical study of asteroid orbital uncertainty

The knowledge of the orbit or the ephemeris uncertainty of asteroid presents a particular interest for various purposes. These quantities are for instance useful for recovering asteroids, for identifying lost asteroids or for planning stellar occultation campaigns. They are also needed to estimate the close approach of Near-Earth asteroids, and subsequent risk of collision. Ephemeris accuracy can also be used for instrument calibration purposes or for scientific applications. Asteroid databases provide information about the uncertainty of the orbits allowing the measure of the quality of an orbit. The aims of this paper is to analyse these different uncertainty parameters and to estimate the impact of the different measurements on the uncertainty of orbits. We particularly deal with two main databases ASTORB and MPCORB providing uncertainty parameters for asteroid orbits. Statistical methods are used in order to estimate orbital uncertainty and compare with parameters from databases. Simulations are also generated to deal with specific measurements such as future Gaia or present radar measurements. Relations between the uncertainty parameter and the characteristics of the asteroid (orbital arc, absolute magnitude, ...) are highlighted. Moreover, a review of the different measuments are compiled and the impact of these measures on the accuracy of the orbit is also estimated.

Analysis of Orbital Dynamic Equation in Navigation for a Mars Gravity-Assist Mission

Gravity Assist (GA) is a kind of transfer orbit technology widely used in interplanetary missions, which highly depends on navigation performance to succeed. The Orbital Dynamic Equation is an essential component in the navigation system, affected by factors including the numerical integrator, perturbing planets, integration step size, gravitational constant and planet ephemerides. To analyse the impact factors mentioned above and investigate an efficient system model, the propagation and navigation results are carried out in a Mars-assist explorer scenario; a specific case study is also provided in this paper. The results indicate that the planetary ephemeris uncertainty and integration size are the dominant error sources, and the integration step size is the dominant impact factor on the real-time performance. In this specific case, the ‘Orbital Dynamic Equation’ considering Sun and Mars perturbation is suggested for integration by RK4 with 60 s integration step size. The conclusions drawn by this study are particularly useful in the design, construction, and analysis of an autonomous navigation system for a GA explorer.

Observational detection of eclipses of J5 Amalthea by the Galilean satellites

We carried out observations of the small jovian satellite Amalthea (J5) as it was being eclipsed by the Galilean satellites near the 2009 equinox of Jupiter in order to apply the technique of mutual event photometry to the astrometric determination of this satellite's position. The observations were carried out during the period 06/2009-09/2009 from the island of Maui, Hawaii and Siding Spring, Australia with the 2m Faulkes Telescopes North and South respectively. We observed in the near-infrared part of the spectrum using a PanStarrs-Z filter with Jupiter near the edge of the field in order to mitigate against the glare from the planet. Frames were acquired at rates >1/min during eclipse times predicted using recent JPL ephemerides for the satellites. Following subtraction of the sky background from these frames, differential aperture photometry was carried out on Amalthea and a nearby field star. We have obtained three lightcurves which show a clear drop in the flux from Amalthea, indicating that an eclipse took place as predicted. These were model-fitted to yield best estimates of the time of maximum flux drop and the impact parameter. These are consistent with Amalthea's ephemeris but indicate that Amalthea is slightly ahead of, and closer to Jupiter than, its predicted position by approximately half the ephemeris uncertainty in these directions. We argue that a ground-based campaign of higher-cadence photometry accurate at the 5% level or better during the next season of eclipses in 2014-15 should yield positions to within 0".5 and affect a corresponding improvement in Amalthea's ephemeris.

Asteroid identification over apparitions

We present a new method for the linking of scarce asteroid astrometry over apparitions, and apply it both to simulated and real data to prove its feasibility. Up to date, there has not been a robust method available to search for linkages between the approximately 50,000 provisionally designated sets of asteroid astrometry spanning less than two days. Unless such a scarce set of astrometry is linked to another set of astrometry, the underlying object can be considered lost as the ephemeris uncertainties are substantial. The new method, which can tackle the challenges, is based on Ranging, which is a fully nonlinear, statistical orbital inversion method. Ranging properly treats astrometric uncertainties and propagates the uncertainty to the resulting orbital-element probability density, which is sampled by a set of orbits. The new orbital-element-space multiple-address-comparison (oMAC) method uses dimensionality-reduction techniques and tree structures to efficiently search for overlapping probability densities in the orbital-element phase space. Overlapping probability densities indicate a candidate linkage between astrometric observation sets. To accept a candidate linkage, we have to find a many-body orbital solution which reproduces the observed positions within the observational uncertainties. To find the linking orbit, we use a multi-step approach starting from a Monte-Carlo generation of possible orbits in a reduced volume of the orbital-element phase space and ending with a least-squares orbital solution, which, in addition to the Sun's gravitation, also takes into account the gravitational influence of the relevant planets. The new multiple-address-comparison method has a loglinear computational complexity, that is, it scales as O ( n log n ) , where n is the number of included observation sets. It has recently also been implemented for the ephemeris-space multiple-address-comparison (eMAC) method, which is optimized for the short-term linking of scarce astrometry.

Asteroid occultations today and tomorrow: toward the GAIA era

Context. Observation of star occultations is a powerful tool to determine shapes and sizes of asteroids. This is key information necessary for studying the evolution of the asteroid belt and to calibrate indirect methods of size determination, such as the models used to analyze thermal infrared observations. Up to now, the observation of asteroid occultations is an activity essentially secured by amateur astronomers equipped with small, portable equipments. However, the accuracy of the available ephemeris prevents accurate predictions of the occultation events for objects smaller than ∼100 km. Aims. We investigate current limits in predictability and observability of asteroid occultations, and we study their possible evolution in the future, when high accuracy asteroid orbits and star positions (such as those expected from the mission Gaia of the European Space Agency) will be available. Methods. We use a simple model for asteroid ephemeris uncertainties and numerical algorithms for estimating the limits imposed by the instruments, assuming realistic CCD performances and asteroid size distribution, to estimate the expected occultation rate under different conditions. Results. We show that high accuracy ephemerides which will be available in the future will extend toward much smaller asteroids the possibility of observing asteroid occultations, greatly increasing the number of events and objects involved. A complete set of size measurements down to ∼10 km main belt asteroids could be obtained in a few years, provided that a small network of ground-based 1m telescopes are devoted to occultation studies.

Predicting the Earth encounters of (99942) Apophis

Arecibo delay–Doppler measurements of (99942) Apophis in 2005 and 2006 resulted in a five standard-deviation trajectory correction to the optically predicted close approach distance to Earth in 2029. The radar measurements reduced the volume of the statistical uncertainty region entering the encounter to 7.3% of the pre-radar solution, but increased the trajectory uncertainty growth rate across the encounter by 800% due to the closer predicted approach to the Earth. A small estimated Earth impact probability remained for 2036. With standard-deviation plane-of-sky position uncertainties for 2007–2010 already less than 0.2 arcsec, the best near-term ground-based optical astrometry can only weakly affect the trajectory estimate. While the potential for impact in 2036 will likely be excluded in 2013 (if not 2011) using ground-based optical measurements, approximations within the Standard Dynamical Model (SDM) used to estimate and predict the trajectory from the current era are sufficient to obscure the difference between a predicted impact and a miss in 2036 by altering the dynamics leading into the 2029 encounter. Normal impact probability assessments based on the SDM become problematic without knowledge of the object's physical properties; impact could be excluded while the actual dynamics still permit it. Calibrated position uncertainty intervals are developed to compensate for this by characterizing the minimum and maximum effect of physical parameters on the trajectory. Uncertainty in accelerations related to solar radiation can cause between 82 and 4720 Earth-radii of trajectory change relative to the SDM by 2036. If an actionable hazard exists, alteration by 2–10% of Apophis' total absorption of solar radiation in 2018 could be sufficient to produce a six standard-deviation trajectory change by 2036 given physical characterization; even a 0.5% change could produce a trajectory shift of one Earth-radius by 2036 for all possible spin-poles and likely masses. Planetary ephemeris uncertainties are the next greatest source of systematic error, causing up to 23 Earth-radii of uncertainty. The SDM Earth point-mass assumption introduces an additional 2.9 Earth-radii of prediction error by 2036. Unmodeled asteroid perturbations produce as much as 2.3 Earth-radii of error. We find no future small-body encounters likely to yield an Apophis mass determination prior to 2029. However, asteroid (144898) 2004 VD17, itself having a statistical Earth impact in 2102, will probably encounter Apophis at 6.7 lunar distances in 2034, their uncertainty regions coming as close as 1.6 lunar distances near the center of both SDM probability distributions.