Solar System
Example 1
Sample of randomly selected orbits

(99942) Apophis (1994 MN4)

Number of original observations: 1000
Arc : 2004 03 15 — 2006 08 16
Nominal rms: 0².31 (1971 residuals)

Figures show the sample of 15000+1 clones (virtual orbits or VAs—virtual asteroids) for orbital solution represented by derived nominal orbit. Orbital clonning procedure was applied at the epoch of 2006 09 22 — close to observational arc.
The derived swarm of VAs follows the normal distribution in the orbital elements space. This is visualized by color coding of points in figures below. Each point represents a single virtual orbit, while the colors indicate the deviation magnitude from the nominal orbit:
red points represent virtual orbits within confidence level of 50%,
magenta: confidence level within 50%—90%,
blue: 90%—99%,
cyan: remaining points.
In the crowded areas points' symbols heavily overlap.

Fig.1 Fig.2
Projection of the 6-dimensional space of possible 15000+1 osculating orbits of Apophis onto the plane of two chosen orbital elements.
LOV's (line of variations) are given by black dotted lines.
Each individual plot is centered on the nominal values of respective pair of orbital elements denoted by the subscript '0' (epoch: 2006 09 22).

Solar System Dynamics & Planetology Group, 2008. All rights reserved