Gravitational keyhole

from Wikipedia, the free encyclopedia

A gravitational keyhole , literally gravitational keyhole is a narrow region in the vicinity of a planet , the potential paths of a passing asteroids or comets comprises at a later re-approach to a impact lead. The word "keyhole" illustrates the tiny size of the area compared to the great uncertainty of the orbit forecast. The term was coined in 1999 by P. W. Chodas and gained public interest in January 2005 when it became clear that the orbit of the asteroid (99942) Apophis , which has only been known for half a year , will not end with an impact on Earth in 2029, but it may could belong to one of several keyholes and lead straight to an impact in 2036 or 2037. This could be ruled out in 2012 by new observations of the asteroid.

Keyholes are similar to the images of gravitational lenses . They are distorted images of the planet from the distant future. The image is not conveyed by light, but by the potential paths of the impactor, which are calculated according to the laws of celestial mechanics . Keyholes are named after the number of orbits the planet or impactor can make between the flyby and the impact around the sun. The "7: 6- resonance keyhole " for the flyby of Apophis 2029 includes those orbits on which Apophis would hit earth within exactly seven years after exactly six further orbits around the sun.

There are more numerous, much smaller, secondary keyholes , the trajectories of which contain another encounter between the first flyby and the impact.

background

Due to inaccuracies in the individual observations of the asteroid, systematic errors in the astrometric reference system and roughly estimated non- gravitational orbital disturbances , especially the Yarkovsky effect , the position of the asteroid relative to the planet is uncertain in all spatial dimensions. Typically, the residence distribution has the shape of a hair, i.e. long, thin and curved, because the visual observations only provide two-dimensional positions in the sky, but no distances. By including observations over a longer period of time, the distribution is reduced to a multi-dimensional normal distribution , which appears in the projection along the relative speed as an ellipse next to the planet. The plane into which it is projected is called the b-plane, after the impact parameter  b . In their origin lies the planet.

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 major semi-axis and the period length of the revolution. If the orbit period after the flyby is in an integer ratio to the orbital period of the planet, there will be another close encounter after a corresponding number of orbits. According to a theory by Ernst Öpik , the tracks with a certain resonance ratio form a circle in the b-plane. The planet and two keyholes lie on this circle (or just next to it due to orbital disruptions). The shape of the keyholes is thin, long ellipses, which curve into the circle. The keyhole that is closer to the planet is shorter and thinner, because the fanning effect of the gravitational field decreases with  b . The above-mentioned “7: 6- resonance keyhole ” for Apophis is about 600 meters wide, the current (2012) estimate for the orbit is almost 2000 km away from this keyhole - and over 38,000 km from the center of the earth .

activities

Since gravitational keyholes are very narrow, you can and should take your time with defensive measures . It is very likely that soon enough - several years before the encounter - it will be found that the probability ellipse is contracting next to the keyhole. If that doesn't happen, a gentle push is enough to shift the track far enough - a kilometer or two - in a relatively short time.

In comparison, after the flight through a keyhole, a much greater effort would have to be made, because then the necessary path shift would be a few earth radii. The difference is based on the same effect of the close flyby to which the keyholes owe their existence: in the forward direction, orbital differences are increased, in the backward direction the image of the planet shrinks to a delicate crescent.

literature

Web links