5. Astrometry and Targeting(From the Journal of the British Interplanetary Society 1997, 50, 93-102. Michael N. Mautner)
Precise astrometry can aim the missions to the targets at their positions in the future when the missions arrive. Large interstellar clouds can be targeted easily. The following passage is an analysis of the vectors involved.
The large size of star-forming regions, compared with individual planetary systems, is a major advantage. Compared with astrometry requirements for targeting a habitable zone about a specific star, on the order of several au (1E11 - 1E12m), the size of the model star-forming Ophiuchus cloud fragment is larger by a factor of 10,000 ie., about 6 ly (6E16 m). In terms of angular resolution, a 1 au planetary target zone at 50 ly distends 1.8E-5 degrees, whereas the 6 ly Ophiuchus fragment at 520 ly distends 0.68 degrees as seen from Earth.
Given the substantial space velocities of interstellar clouds, on the order of 1E4m per sec, the vehicles must be aimed at the expected position of the targets at the time of arrival. The uncertainty in calculating this position arises from the limits of the resolution of the proper motion of the cloud when the vehicles are launched. The positional uncertainty at the time of arrival, dy, is expressed by equation (1), where a is the resolution of proper motion, d is the distance from Earth, d**2 denotes d square, and v the velocity of the vehicle (a in arcsecs/yr, other units in SIU).
Angular proper motion resolutions of 1E-5 arcsecs/yr can be anticipated. The positional uncertainties of thevarious targets considered upon the arrival of fast (v = 0.01 c) or solar sail based (v = 1E-5 c) missions, ie., the L y values, are listed in Table 1. Note that for the large cloud core, and even for individual protostellar condensations, the uncertainty is smaller than the radius of these objects.
Given the uncertainty (d y) in the position of the target when the vehicles arrive, the panspermia objects should be launched with a scatter, to arrive in a circle with radius d y about the calculated position (scatter with a Gaussian distribution may be more effective). The probability that the vehicle will actually arrive in the target region, Ptarget, is then estimated from the ratio of cross-sectional areas of the target region to that of the area of the targeting scatter. Equation (6) in reference  was derived on this basis, and similarly we obtain equation (2) for a spherical target with a radius rcloud with cross-sectional area Atarget = 3.14 r2. For planetary targets within a habitable zone of radius r(hz) and width whz = 0.4hz, the area of the target habitable zone is equal to that of a circle with radius r = 0.89 r(hz).
For cases where the area of the target is larger than of the positional uncertainty, we obtain Ptarget > 1, which may be interpreted as approximately unit probability. Equation (2) yields the Ptarget values as shown in Table 1. Note that most of the microbial packets will arrive in the targeted star-forming cloud region, and even the smaller specific protostellar condensations can be targeted accurately. In fact, even with a reduced resolution of 1E-4 arcsec/yr, the dense core can be targeted reliably. However, even with a p of 1E-5 arcsec/yr, Ptarget for a 100 au radius dust sphere about a dust-embedded star or accretion disk (perpendicular to the Earth-star axis) is 3.6E-3, and for 1 au habitable zone about a star at the same distance of 520 ly is only 3.9E-7. Targeting these smaller specific objects at these distances is inaccurate because of the d**-4 dependence of the P(target) function.
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