Gravitational keyhole

A Gravitational keyhole, literally gravitational keyhole, is a narrow region in the vicinity of a planet, including the potential paths of a passing asteroid or comet that result in a subsequent, renewed approximation to an impact. The word "keyhole" explains the smallness of the area in comparison to the large uncertainty in predicting the path. The term was coined by PW Chodas 1999 and received in January 2005, the public interest when it became clear that the path of the well-known only for half a year asteroid ( 99942 ) Apophis in 2029, not ends with an impact on the earth, but may could belong to one of several key holes and would thus lead straight to a strike in 2036 or 2037. This could be eliminated by 2012 new observations of the asteroid.

Keyholes are similar to the image gravitational lenses. There are distorted images of the planets from the distant future. The figure is, however, not mediated by light, but by the potential paths of the impactor, which are calculated according to the laws of celestial mechanics. Keyholes are labeled according to the numbers of rounds that travel the planet and the impactor between the flyby and the turning around the sun. Thus includes the " 7:6 resonance keyhole " for the flyby of Apophis in 2029 those tracks on which Apophis would after just six more rounds hit around the sun within just seven years on the earth.

There are more numerous, much smaller secondary keyholes whose orbits contain another encounter between the first flyby and impact.

Background

Due to inaccuracies of the individual observations of the asteroid, systematic errors in the astrometric reference system as well as roughly estimated non- gravitational perturbations, especially the Yarkovsky effect, the position of the asteroid is relatively uncertain to the planet in all spatial dimensions. Typically, the distribution of residence in the form of a hair, so long, thin and curved because the visual observations provide only two-dimensional positions in the sky, but no distances. By inclusion of observations over a long time period, the distribution is reduced to a multivariate normal distribution, which appears in the projection along the minor elliptic relative speed as the planet. The plane in which is projected, ie b- level, after the impact parameter b. In its origin, the planet is located.

Depending on the position of the orbit in this plane, the direction and the kinetic energy of the asteroid change after the flyby. The orbital energy is directly linked to the length of the semimajor axis and the period length of the circulation. If the orbital period is an integer multiple of the orbital period of the planet after the flyby, it will be another close encounter by a corresponding number of rounds. According to a theory by Ernst Öpik the tracks form with a certain resonance ratio a circle in the b plane. On this circle (or by perturbations close to it ) are the planet and two keyholes. The shape of the keyhole is the thin, long ellipses, the arcuate cling to the circle. The one key hole that is closer to the planet, is shorter and thinner, because the fanning effect of the gravitational field increases with b from. The above-mentioned " 7:6 resonance keyhole " for Apophis has a width of about 600 meters, the current (2012 ) estimate for the slope is located 2000 km from this keyhole away - and over 38,000 km from the Earth's center.

Measures

Since gravitational keyholes are very narrow, and may you should be with defensive measures time. Most likely will be soon enough - several years before the encounter - reveal that the probability ellipse shrinks next to the keyhole. Should not happen, so goes a gentle push to far enough the web in a relatively short time - one or two miles - to relocate.

In comparison, a much greater effort needs to be operated after the flight through a keyhole, because then cheating the necessary trajectory displacement few Earth radii. The difference is due to the same effect of the flyby, which is also the key holes owe their existence: In the forward direction path differences are magnified in the reverse direction shrinks the image of the planet on a petite sickle.