Uncertainty parameter

Calculation

The U parameter is calculated in two steps. 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):

${\displaystyle r=\left(\mathrm{\Delta }\tau \cdot e+10\cdot \frac{\mathrm{\Delta }P}{P}\right)\cdot 3600\cdot 3\cdot \frac{k_{\text{o}}}{P}}$

with

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. The formula for cutting off the calculated value of U is

${\displaystyle U=min\left\{9,max\{0,\lfloor 9\cdot \frac{\log r}{\log \mathrm{648,000}}\rfloor +1\}\right\}}$

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 result is the same regardless of the choice of base for the logarithm, so long as the same logarithm is used throughout the formula; e.g. for "log" = log₁₀, log_e, ln, or log₂ the calculated value of U remains the same if the logarithm is the same in both places in the formula.

648 000 is the number of arc seconds in a half circle, so a value greater than 9 would be meaningless as we would have no idea where the object will be in 10 years within the orbit.