Uncertainty parameter


The uncertainty parameter U is a parameter introduced by the Minor Planet Center 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, the time spanned by those observations, the quality of the observations, and the geometry of the observations. Of these parameters, the time spanned by the observations generally has the greatest effect on the orbital uncertainty.
As an extreme example, has an uncertainty parameter of 9; it could be an Earth threatening asteroid, or may always remain beyond the asteroid belt.
Occasionally, the Minor Planet Center substitutes a letter-code for the uncertainty parameter.
Objects such as with a condition code ‘E’ in the place of a numeric uncertainty parameter denotes orbits for which the listed eccentricity was assumed, rather than determined; these are considered lost. Objects with a ‘D’ have only been observed for a single opposition, and have been assigned two different designations ; objects with an ‘F’ fall in both categories ‘D’ and ‘E’.

Calculation

The U parameter is calculated in two steps. First the in-orbit longitude runoff in seconds of arc per decade is calculated, :
with
uncertainty in the perihelion time in days
eccentricity of the determined orbit
orbital period in years
uncertainty in the orbital period in days
, Gaussian gravitational constant, converted to degrees

Then, the obtained in-orbit longitude runoff is converted to the "uncertainty parameter" U, which is an integer between 0 and 9. The calculated number can be less than 0 or more than 9, but in those cases either 0 or 9 is used instead. For instance: As of 10 September 2016, Ceres technically has an uncertainty of around −2.6, but is instead displayed as the minimal 0. The formula for cutting off the calculated value of U is
648 000 is the number of arc seconds in a half circle, so a value greater than 9 would mean that we would have basically no idea where the object will be in 10 years.