The analysis of Apophis previews situations likely to be encountered with NEAs yet to be discovered: a close approach that is not dangerous (like Apophis in 2029) nonetheless close enough to obscure the proximity and the danger of a later approach (like Apophis in 2036) by amplifying trajectory prediction uncertainties caused by difficult-to-observe physical characteristics interacting with solar radiation as well as other factors.

BACKGROUND
Upon its discovery in 2004, Apophis was briefly estimated to have a 2.7% chance of impacting the Earth in 2029. Additional measurements later showed there was no impact risk at that time from the 210-330 meter (690-1080 foot) diameter object, identified spectroscopically as an Sq type similar to LL chondritic meteorites. However, there will be a historically close approach to the Earth, estimated to be a 1 in 800 year event.

The Arecibo planetary radar telescope subsequently detected the asteroid at distances of 27-40 million km (17-25 million miles; 0.192-0.268 AU) in 2005 and 2006. Polarization ratios indicate Apophis appears to be smoother than most NEAs at 13-cm scales. Including the high precision radar measurements in a new orbit solution reduced the uncertainty in Apophis' predicted location in 2029 by 98%.

While trajectory knowledge was substantially corrected by the Arecibo data, a small chance of impact (less than 1 in 45,000) remained for April 13, 2036. With Apophis probably too close to the Sun to be measured by optical telescopes until 2011, and too distant for useful radar measurement until 2013, the underlying physics of Apophis' motion were considered to better understand the hazard.

RESULTS OF THE STUDY
(1) Extending the "Standard Dynamical Model"

Trajectory predictions for asteroids are normally based on a standard model of the solar system that includes the gravity of the Sun, Moon, other planets, and the three largest asteroids.

However, additional factors can influence the predicted motion in ways that depend on rarely known details, such as the spin of the asteroid, its mass, the way it reflects and absorbs sun-light, radiates heat, and the gravitational pull of other asteroids passing nearby. These were examined, along with the effect of Earth's non-uniform gravity field during encounters, and limitations of the computer hardware performing the calculations.

One would normally look for the influence of such factors as they gradually alter the trajectory over years. But, for Apophis, the changes remain small until amplified by passage through Earth's gravity field during the historically close approach in 2029.

For example, the team found solar energy can cause between 20 and 740 km (12 and 460 miles) of position change over the next 22 years leading into the 2029 Earth encounter. But, only 7 years later, the effect on Apophis' predicted position can grow to between 520,000 and 30 million km (323,000 and 18.6 million miles; 0.0035-0.2 AU). This range makes it difficult to predict if Apophis will even have a close encounter with Earth in 2036 when the orbital paths intersect.

It was found that small uncertainties in the masses and positions of the planets and Sun can cause up to 23 Earth radii of prediction error for Apophis by 2036.

The standard model of the Earth as a point mass can introduce up to 2.9 Earth radii of prediction error by 2036; at least the Earth's oblateness must be considered to predict an impact.

The gravity of other asteroids can cause up to 2.3 Earth radii of prediction uncertainty for Apophis.

By considering the range of Apophis' physical characteristics and these error sources, it was determined what observations prior to 2029 will most effectively reduce prediction uncertainties. Observing criteria were developed that, if satisfied, could permit eliminating the 2036 impact possibility without further physical characterization of Apophis.

Such observations could reduce the need for a visit by an expensive spacecraft and reduce the risk of Apophis being prematurely eliminated as a hazard under the standard model, only to drift back into the hazard classification system years later as the smaller, unmodeled forces act upon it.

(2) Mitigation

Mitigation was not specifically studied, but the team found small variations in the surface properties of Apophis are sufficient to cause enough trajectory change to obscure the difference between an impact and a miss in 2036. Changing the amount of energy Apophis absorbs by half a percent as late as 2018 - for example by covering a 40 x 40 meter (130 x 130 foot) patch with lightweight reflective materials - can change its position in 2036 by at least one Earth radius.

For Apophis, distributing as little as 250 kg (550 pounds) of material (such as carbon fiber mesh) across the surface could produce a 6-sigma trajectory change, moving at least "99.9999998" percent of the statistically possible trajectories away from the Earth in just 18 years.

While no deflection is expected to be necessary, the team's research demonstrates that any deflection method must produce a result known in advance to be greater than all the error sources in the prediction, including some greater than those considered with the standard model.

(3) Impact probability

The study did NOT compute new impact probabilities. This is because key physical parameters (such as mass and spin pole) that affect its trajectory have not yet been measured and hence there are no associated probability distributions.

The situation is similar to having 6 apples (the measured Apophis parameters) and 6 boxes whose contents are unknown (the unmeasured Apophis parameters), then trying to compute the probability one has a total of 12 apples (impact probability). The result reflects back what is assumed about the unknown contents of the boxes, but doesn't reveal new information. The contents of the boxes must be observed (measured) to learn something new.

For similar reasons, the Apophis study instead uses the minimum and maximum range-of-effect in place of computing impact probabilities to provide reasonable criteria for excluding impact in the absence of detailed physical knowledge, once new position measurements are obtained at six key times.

(4) Non-Apophis Conclusions

Aspects of the study relevant to asteroids other than Apophis:

The Standard Dynamical Model can misestimate impact risk for the more numerous sub-km objects preceded by close planetary encounter(s). This problem might be addressed by reassessing impact potential after planetary encounters, given new measurements. The minimum-maximum effect of unmeasured parameters can provide enough information to exclude threats in certain cases. Amplification of small trajectory offsets makes valid prediction across a close-encounter difficult without physical knowledge, but offers the potential to redirect the entire uncertainty region and has significant implications for costly spacecraft missions.

A deflection effort must be known in advance to produce change greater than predicted uncertainties due to ALL parameters, not only the Standard Dynamical Model. For example, if a method produces 10 Earth-radii of change, but prediction uncertainties from all sources are 20 Earth-radii, the deflection would move the asteroid around within the noise, producing an unpredicted result or even a new hazard.

FUTURE
The future for Apophis on Friday, April 13 of 2029 includes an approach to Earth no closer than 29,470 km (18,300 miles, or 5.6 Earth radii from the center, or 4.6 Earth-radii from the surface) over the mid-Atlantic, appearing to the naked eye as a moderately bright point of light moving rapidly across the sky. Depending on its mechanical nature, it could experience shape or spin-state alteration due to tidal forces caused by Earth's gravity field.

This is within the distance of Earth's geosynchronous satellites. However, because Apophis will pass interior to the positions of these satellites at closest approach, in a plane inclined at 40 degrees to the Earth's equator and passing outside the equatorial geosynchronous zone when crossing the equatorial plane, it does not threaten the satellites in that heavily populated region.

Using criteria developed in this research, new measurements possible in 2013 (if not 2011) will likely confirm that in 2036 Apophis will quietly pass more than 49 million km (30.5 million miles; 0.32 AU) from Earth on Easter Sunday of that year (April 13).

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