3.3 Observing conditions and tradeoffs

The main problem in devising a strategy for negative observations of VIs is the expected apparent magnitude; lesser problems are the proper motion, the lunar phase and the galactic latitude.

The absolute magnitude of 1998 OX₄ is estimated, by a fit to all available photometric measurements, at $H=21.3\pm 0.23$; however, this value is estimated for the nominal orbit, further changes by $\pm 0.2$occur between the different virtual asteroids spanning the confidence region; this is taken into account in the predicted magnitudes listed in Tables 2-4. The photometric data of Spacewatch are generally quite good (P. Pravec, private communication, 1999), although an absolute calibration is difficult for such faint objects, for which there are in most cases no multi-opposition orbits.

So, in this case the main source of uncertainty in the prediction of the apparent magnitude at some later apparition is not the photometric uncertainty, but the change of the luminosity with rotational phase and aspect angle. From known lightcurves the changes can be up to $\pm 1$ magnitude, although such extreme values are unusual. Phase effects are also difficult to model reliably, if there is no available information on the physical properties of the asteroid [Bowell 1989], as in this case.

The conclusion is that in this case the uncertainty of the predicted apparent magnitude is large, and to be reasonably confident in a negative observation it is necessary that the given telescopes, exposures and detection techniques be validated for about two magnitudes fainter than the predicted values given in Tables 2-4.

The dates we have selected for the January-February 2001 and for the February 2003 opportunities have also taken into account the need to have a moderate proper motion (too high could result in too large trailing losses and/or pointing problems, too low could result in the VI hiding in the glare of a bright star), a large enough galactic latitude and an appropriate lunar phase, especially for the dimmer case. These dates can be changed for the convenience of the observers, but the observing time windows are short (a few days only) in the cases in which very close approaches are used, as in the case of the 2014 VI; thus it is advisable to have telescope and observer time reserved at different sites, to be safe against the possibility of bad weather. There is, in fact, another observing opportunity in July 2000 for all four VIs, but observing conditions would be significantly worse, because of fainter apparent magnitudes, the lunar phase and the proximity of the galactic disk.

For the 2038, 2044 and 2046 VIs we have presented two opportunities for negative observations; the choice among the two amounts to a tradeoff between the size of the telescopes required and the difficulty of the observation; also the time we have to wait to know is an issue. The February 2001 opportunity would allow us to guarantee safety from these possible impact two years earlier. However, the telescopes needed to guarantee detection up to apparent magnitude 22.5 are not available as a matter of routine for asteroid observations: the observing nights have to be requested in advance, keeping margins for possible bad weather, and experienced asteroid observers need to be available at observatories where they may not be normally working. On the other hand the total telescope time could be small, given that the size of the regions to be scanned are small (see Figure 3 and Table 3).

Since 2038, 2044 and 2046 are far in the future, we may decide that we can wait two years longer to know if these impacts are indeed possible. The February 2003 opportunity would allow the use of telescopes of a size which is normally available for asteroid discovery and follow-up, including some good amateur sites. But, in this case the time window is more restricted and the observing conditions change rapidly, thus several observatories should be invited to join as a safeguard against bad weather at some site. Moreover most small telescopes would have to scan several frames to cover the three skyprints, which are somewhat larger than in the other case. Thus coordination is more an issue than telescope size. At this encounter it is in fact possible that 1998 OX₄ would be recovered anyway, even if it is not going to have close approaches either in 2038, on in 2044, or in 2046.

For the 2014 VI there is no other opportunity with good observing conditions (say apparent magnitude <22) until the possible impact. Although this is the VI with lowest impact probability of the four, the earlier time of possible impact and the lack of a later opportunity, in our opinion, suggest that the opportunity given in this paper for negative observation should not be missed.