Uncertainty Parameter U
In order to quantify the uncertainty in a perturbed orbital solution for
a minor planet in a concise fashion, the Minor Planet Center has introduced
the U parameter. This is an integer in the range 0 to 9, where 0 indicates
a very small uncertainty and 9 an extremely large uncertainty. In practice,
U is rarely larger than 6.
The U value is calculated in the following manner. First, calculate:
RUNOFF = (dT * e + 10 / P * dP) * ko / P *
3600 * 3
where dT is the uncertainty in the perihelion time (in days)
e is the eccentricity
P is the orbital period (in years)
dP is the uncertainty in the orbital period
(in days)
ko is the Gaussian constant in degrees
= 180 / pi * 0.01720209895
3600 converts to seconds of arc
3 is a empirical factor to make the formal
errors more
closely model reality
and RUNOFF is the in-orbit longitude runoff in seconds of
arc per decade
RUNOFF is then converted to the "uncertainty parameter" (denoted by 'U')
in the range 0 to 9:
CONS = ln(648000)/9
CONS ~ 1.49
U = INT(ln(RUNOFF)/CONS)+1 (0 <=
U <= 9)
where ln is the natural logarithm
INT is a function that returns the largest
integer
smaller than the argument
(e.g., INT(3.5) = 3,
INT(0.99) = 0, INT(-0.45)
= -1)
As a guide, the values of U correspond to the following values of RUNOFF
(in seconds of arc per decade):
U RUNOFF
U RUNOFF
0 < 1.0
5 < 1692
1 < 4.4
6 < 7488
2 < 19.6
7 < 33121
3 < 86.5
8 < 146502
4 < 382
9 > 146502
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