Orbital measures

It is impossible, from a single observation, to evaluate the orbit of an object. To do so, many observations, made at different instants, are needed. For this reason, when a NEO is discovered for the first time, scientists look for it on old photograph plates, since there are many objects that have been observed in the past only once, for a period that wasn't long enough to determine their future orbits, consequently becoming lost.

Why isn't a single observation enough?
The answer to this question is very intuitive, and can be understood with a very simple, schematic animation .

In fact let's imagine that at a certain time, when planet Earth is in a certain position (initial position on white orbit) an observation of a NEO is made. The object distance from Earth cannot be determined from this single observation: the NEO's orbit can either be the yellow or the blue one (only two possible orbits are indicated to simplify the problem). Only making successive observations, when the Earth has moved along its orbit (and so, after months have passed) the two orbits will be differentiated, and the real NEO's orbit can be determined.

 

Orbital determination

A simple method of determination of the orbit of a NEO consists in making many different observations of the position of the object. In fact, as shown in the animation (wait for the START to see the animation), a single observation only allows to determine a region where the object COULD be and not the real position (using a statistical vision of orbits). This region, when derived from a single observation is a cone with an angular dimension of the instrument error: every point inside this cone is a virtual asteroid. When time passes by, both the observer and the object move along their trajectory. Furthermore, each of the virtual asteroids that initially were inside the cone, moves along its orbit with a different speed (this is a direct consequence of Kepler's third law, since all of the virtual asteroids have different semiaxis, all of them will have different speed). The initial cone will then move in space and begin to be deformed. Making a second observation after some months, means to determine a new cone of virtual positions that will intersect the first one. In this way the asteroid orbit must lie at the interesection of the two regions of space corresponding to the two measurements.