Question: What does following of close Earth objects help with anticipating?
About the article "Astronomy", section "Astrometry and celestial mechanics".

Candidate passages:
Near-Earth objects (NEOs) are asteroids, comets and large meteoroids that come close to or collide with Earth.
Spaceguard is the collective name for some of the efforts to discover and study NEOs, though these efforts are not highly funded. 
The asteroid 1981 Midas was discovered on March 6, 1973 by Charles T. Kowal at Palomar Observatory.
It is named after Midas, the king of Phrygia in Greek mythology who turned objects to gold when he touched them.
Midas is an Apollo asteroid, a Venus and Mars-crosser asteroid with an orbital period of 2 years, 134 days.
Midas is about in diameter.
Its last notable close approach to Earth was on 11 March 1992 passing from Earth.
The next notable close approach will be on 21 March 2018 passing from Earth and shining at an apparent magnitude of +12.4.
Even though Midas has an Earth-MOID of , the orbit is well determined and Midas does not pose an impact risk.
In 1987, this object was detected with radar from Goldstone at a distance of 0.08 AU.
The measured radar cross-section was 0.1 km2 or less. 
2002 AY1 is a near-Earth object that is expected to make a close approach to Earth on January 8, 2035.
There are many Near-Earth unusual objects that may gather a higher relevance.
Nevertheless, the ability of today's observatories constant analyses is giving away all possible information so far intelligible for what is really relevant or not - and so far - accessible to public (as the data provided by their databases  
Objects with distances greater than 100 km are listed here, although there is no discrete beginning of space.
The lists do not pretend to completeness. 
A planet orbiting the Sun, the same distance from the Sun and with the same mass as Earth could (according to the theory) be both habitable to beings at least similar to humans, while being undetectable to astronomers (or any other human beings) on Earth.
With the same size and distance from the Sun as Earth, it could have the same (or very similar) surface environment—gravity, atmospheric pressure, and surface temperature range.
At the same time such a planet could have the same orbiting velocity and path as Earth, so that if it was positioned 180 degrees from Earth, it would remain behind the Sun being blocked from view from Earth indefinitely.
The 1968 "Scientific Study of Unidentified Flying Objects" headed by Edward Condon at the University of Colorado even included an a "Numerical Experiment on the Possible Existence of an `Anti-Earth`" as an appendix.
However, if such a planet actually existed, the laws of physics and cosmology would make it detectable from Earth for a number of reasons.
A Counter-Earth would have gravitational influence (perturbation) upon the other planets, comets and man-made probes of the Solar System.
No such influence has been detected, and indeed space probes sent to Venus, Mars and other places could not have successfully flown by or landed on their targets if a Counter-Earth existed, as it was not accounted for in navigational calculation.
The gravitational forces of the other planets on a Counter-Earth would make "its" orbit unstable.
Venus has 82% of the mass of Earth and would come within 0.3 Astronomical unit of the location of a Counter Earth every 20 months, providing considerable gravitational pull that over the years would move its orbit into sight of observers on Earth.
If a Counter-Earth was much smaller than Earth, its location at the "Sun–Earth L3" Lagrangian point (see diagram), would mean the combined gravitational pull of the two large masses of Earth and Sun would provide "precisely the centripetal force required to orbit with them".
But a small planet would be even more influenced by the orbit of Venus, Mars and Jupiter, making it even more unstable.
Any planetary sized body 180 degrees from Earth should also have been visible to some space probes, such as NASA's STEREO coronagraph probes (two spacecraft launched into orbits around the Sun in 2006, one farther ahead of and one behind the Earth's orbit) which would have seen the Counter-Earth during the first half of 2007.
The separation of the STEREO spacecraft from Earth would give them a view of the L3 point during the early phase of the mission.
Given the sensitivity of STEREO's COR2 coronagraph, anything larger than in diameter should have been detected.
Also, if a Counter-Earth had an electromagnetic energy signature similar to that of Earth's, it would be able to be detected by astronomers since the signature would extend well beyond the surface of an Earth-like planet.
The Sun's "wobbling" motion around its "barycenter" would prevent it from blocking all signs of that energy from Earth, at least for part of the year.
The Sun does not remain stationary—relative to its planets—at the center of the solar system because of the gravitational pull of the most massive planet—Jupiter.
The Sun wobbles around the "true" center known as a barycenter, which lies just inside the Sun.
When the Sun's position is 90 degree from the barycenter relative to Earth, it would come close to "unblocking" from view a planet 180 degrees from Earth, enough to reveal the aforementioned hypothetical signature.
For a Counter-Earth orbiting the same path as Earth to always stay 180 degrees from Earth, the two planets would have to have circular orbits, but Earth's orbit is elliptical.
Following Kepler's second law, a planet revolves faster when it is close to the star, so a Counter-Earth following the Earth on the same orbit with half a year of delay would sometimes not be exactly 180 degrees from Earth.
To be hidden from Earth, the Counter-Earth would have an orbit symmetrical to Earth's, not sharing the second focus or orbit path.