... always

This approximation can fail in a catastrophic way if there is a close approach by some of the VAs in between the observations and the prediction.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... orbits

Väisälä's method to compute some "Väisälä'' orbit from two observations should not be confused with Väisälä's method to solve Gauss' problem of the orbit from three observations, although of course the two algorithms are related.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... symmetric

But not necessarily diagonal (Carpino et al. 2003).

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... continuation

Our two impact monitoring systems, CLOMON2 and Sentry, use different conventions for the orientation of the LOV. Thus, in comparing the outputs of CLOMON2 and Sentry, it is necessary to check whether the orientation of the LOV is the same.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... examples

The eigenvalues of the covariance matrix are given with the orbital elements in the NEODyS and AstDyS information systems.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... convergence

In a numerical procedure, convergence is defined as having the last iteration with a small enough correction; in this context, the following properties are satisfied only approximately.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... Runge-Kutta

In fact, we use a second order implicit Runge-Kutta-Gauss.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

...$X(\sigma)$

It would be possible to use an interpolation procedure also with the parameter $\sigma_Q$.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... failed

Unless some other preliminary orbit algorithm is available.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... orbit

In this case, the covariance provides information on the uncertainty but it is not possible to define formally a confidence region because the minimum value of the cost function is not known (and may not exist).

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... service

http://hamilton.dm.unipi.it/astdys/

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... ridiculous

The only one-nighters for which a comparatively accurate orbit can be computed are some Near Earth Asteroids, in particular the ones with very high proper motion.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... successfully

We have so far proposed, by using this algorithm, more than 4000 orbit identifications published by the MPC.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... it

The LOV algorithms are available in the free software OrbFit at http://newton.dm.unipi.it/orbfit/

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.