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.^{[1]}^{[2]} The parameter is a logarithmic scale from 0 to 9 that measures the anticipated longitudinal uncertainty^{[3]} in the minor planet's mean anomaly after 10 years.^{[1]}^{[2]}^{[4]} The uncertainty parameter is also known as condition code in JPL's Small-Body Database Browser.^{[2]}^{[4]}^{[5]} The U value should not be used as a predictor for the uncertainty in the future motion of near-Earth objects.^{[1]}
Object | JPL SBDB Uncertainty parameter |
Horizons January 2018 Uncertainty in distance from the Sun |
Refs |
---|---|---|---|
2013 BL76 | 1 | ±40 thousand km | JPL |
20000 Varuna | 2 | ±140 thousand km | JPL |
19521 Chaos | 3 | ±840 thousand km | JPL |
(15807) 1994 GV9 | 4 | ±1.4 million km | JPL |
(160256) 2002 PD_{149} | 5 | ±8.2 million km | JPL |
1999 DH_{8} | 6 | ±70 million km | JPL |
1999 CQ_{153} | 7 | ±190 million km | JPL |
1995 KJ_{1} | 9 | ±590 million km | JPL |
1995 GJ | 9 | ±160 trillion km | JPL |
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.^{[6]}
As an extreme example, 2010 GZ60 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 (‘D’, ‘E’, ‘F’) for the uncertainty parameter. Objects such as 1995 SN55 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;^{[7]} these are considered lost.^{[citation needed]} Objects with a ‘D’ have only been observed for a single opposition, and have been assigned two (or more) different designations ("double"); objects with an ‘F’ fall in both categories ‘D’ and ‘E’.^{[7]}
The U parameter is calculated in two steps.^{[1]}^{[8]} First the in-orbit longitude runoff \({\displaystyle r}\) in seconds of arc per decade is calculated, (i.e. the discrepancy between the observed and calculated position extrapolated over ten years):
with
\({\displaystyle \Delta \tau }\) | uncertainty in the perihelion time in days |
\({\displaystyle e}\) | eccentricity of the determined orbit |
\({\displaystyle P}\) | orbital period in years |
\({\displaystyle \Delta P}\) | uncertainty in the orbital period in days |
\({\displaystyle k_{o}}\) | \({\displaystyle 0.01720209895\cdot {\frac {180^{\circ }}{\pi }}}\), 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.
U | Runoff Longitude runoff per decade |
---|---|
0 | < 1.0 arc second |
1 | 1.0–4.4 arc seconds |
2 | 4.4–19.6 arc seconds |
3 | 19.6 arc seconds – 1.4 arc minutes |
4 | 1.4–6.4 arc minutes |
5 | 6.4–28 arc minutes |
6 | 28 arc minutes – 2.1° |
7 | 2.1°–9.2° |
8 | 9.2°–41° |
9 | > 41° |
Categories: Orbits | Measurement