Uncertainty parameter

"Condition code" redirects here. For the computer architecture meaning, see condition code register.

The uncertainty parameter (U) is a parameter introduced by the Minor Planet Center (MPC) to quantify concisely the uncertainty of a perturbed orbital solution for a minor planet. The parameter is a logarithmic scale from 0 to 9 that measures the anticipated longitudinal uncertainty in the minor planet's mean anomaly after 10 years. The uncertainty parameter is also known as condition code in JPL's Small-Body Database Browser. The U value should not be used as a predictor for the uncertainty in the future motion of near-Earth objects.

Orbital uncertainty

Orbital uncertainty is related to several parameters used in the orbit determination process including the number of observations (measurements), the time spanned by those observations (observation arc), the quality of the observations (e.g. radar vs. optical), and the geometry of the observations. Of these parameters, the time spanned by the observations generally has the greatest effect on the orbital uncertainty.

Objects such as 1995 SN55 with a condition code (Uncertainty Parameter U) of E where the eccentricity is assumed and is lost. 1994 WR12 has an Uncertainty Parameter of 8, and the next good chance to observe the asteroid may not be until November 2044 when the uncertainty allows it to pass somewhere between 0.03–0.19 AU from Earth.

Calculation

The U parameter is calculated as follows:

First the in-orbit longitude runoff in seconds of arc per decade is calculated

RUNOFF = ( dT  • e ⁺ 10/P  • dP )  • ko/P 3600  • 3

𝑑𝜏 = uncertainty in the perihelion time (in days)

𝑒 = eccentricity

P = orbital period (in years)

dP = uncertainty in the orbital period (in days)

ko = 180/π  • 0.01720209895 , the Gaussian constant in degrees 3600 converts to seconds of arc

3 is used as an empirical factor to make the formal errors more closely model reality

In-orbit longitude runoff is then converted to the "uncertainty parameter" denoted U , which is an integer between 0 and is capped at 9.

U = INT(ln(RUNOFF)/CO)+1, (0 ≤ U ≤ 9)

CO = ln(648000)/9

If the U obtained is negative, we take U = 0; if the U obtained is greater than 9, it takes U = 9.

U	Runoff Longitude runoff (arc seconds/per decade)
0	< 1,0
1	1.0 - 4.4
2	4.4 - 19.6
3	19.6 - 86.5
4	86.5 - 382
5	382 - 1692
6	1692 - 7488
7	7488 - 33121
8	33121 - 146502
9	> 146,502