Robotic Scouts for a Human Mission to an Asteroid

How best to use robotic surveyors to reduce risk for a human mission?

Asteroid Itokawa (540 m) shown with the International Space Station for scale.

1. Would the cost of sending one or more robotic surveyors be justified in terms of risk reduction to a human mission?
2. What is the optimal number of asteroids to survey to find one suitable for a human mission?
3. If sending multiple survey spacecraft, should they be sent in parallel or in sequence?

Assumptions

For purposes of this study, we assumed that a fully successful human mission would include a "landing" on an asteroid (actually, more like a docking since the asteroid would be unlikely to have much gravity) and extravehicular activities by the astronauts, who would inspect the asteroid at close range, collect samples to return to Earth, etc.

We also assumed that two parameters would be used to determine whether an asteroid is suitable for a human landing — size and spin rate — but that these parameters have not been determined by Earth-based observation for the asteroids identified as possible targets for this mission. The latter assumption was based on the fact that, of the 1200 Near-Earth Objects (NEOs) of interest from our catalog, diameters and spin rates are known for fewer than 10 percent, and a substantial portion of those are not known with high confidence levels. Asteroids with unknown diameters and/or spin rates include many with desirable orbital characteristics, which suggest that they may be targets of interest.

Acceptable size was defined as between 100 meters and 1.5 km in diameter. Acceptable spin rate was defined as no more than half a revolution per hour. The asteroids under consideration were those classified as Near-Earth Objects (NEOs).

We further assumed that the values of a precursor mission and a human mission would be additive. That is, sending both a robotic and human mission would produce more value than sending either alone.

Value of robotic surveying

We addressed the first question by employing Bayes theorem, which is a means to revise predictions in light of evidence. In this case, the initial predictions were made on the basis of NEOs with diameters and spin rates that have been estimated based on observation from Earth. The revision would come from anticipated data to be provided by the robotic survey missions. We attempted to calculate the risk-reduction value of that revised prediction to a potential human mission.

If only one robotic surveyor is contemplated, prior probability of suitability must be greater than 0.6 to justify preceding a human mission with a precursor. But two surveyors are justified in terms of productivity even at a very low initial probability of suitability.

It was found that the value of preceding a human mission with a robotic survey is far greater than the value of sending a human mission without such a survey. This was due in large part to the vastly greater cost of a human mission compared to a robotic mission, but also to the reduction in risk that the chosen asteroid might actually be unsuitable for landing. Using mass (measured in metric tons) delivered to low-Earth orbit as a proxy for cost, and value based on a human landing mission as the goal, robotic precursors could offer up to a 60% increase in productive value versus sending a human mission without precursors. Robotic precursors offer relatively inexpensive insurance against the risk of an outcome in which the human mission would be unable to approach or land on the asteroid.

How many asteroids to survey?

To calculate the probability of finding a suitable target, we used the law of compound probability. We calculated this for probabilities ranging from 0.1 to 0.9 for individual targets and for surveys of 1 to 6 targets to see which combinations produce at least a 0.90 probability of finding a suitable target. The results are shown in the following table.

Number of asteroids in survey Probability that an asteroid is suitable for human landing 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 2 0.19 0.36 0.51 0.64 0.75 0.84 0.91 0.96 0.99 3 0.27 0.49 0.66 0.78 0.88 0.94 0.97 0.99 0.99 4 0.34 0.59 0.76 0.87 0.94 0.97 0.99 0.99 0.99 5 0.41 0.67 0.83 0.92 0.97 0.99 0.99 0.99 0.99 6 0.47 0.74 0.88 0.95 0.98 0.99 0.99 0.99 0.99

How many asteroids must be surveyed to produce the desired probability of finding at least one that is suitable for human landing.

For example, if looking at one asteroid carries a 0.5 probability of finding it suitable for landing, then looking at four asteroids increases the probability of finding a suitable one to 0.94. If the probability of suitability for one asteroid is 0.6, then only three need to be surveyed to achieve a 0.94 probability of finding one suitable.

To calculate the baseline probability — that is, the probability that any one asteroid is suitable — we consulted two data sets containing over 1200 NEOs and identified a subgroup of 112 for which both diameter and spin rate had been determined by Earth-based observation. Of those 112, we found that about 58% met our criteria for suitability. Extrapolating to the total population, we thus assume that 58% of NEOs are suitable for human landing, and that any given NEO carries a 58% probability that it is suitable.

Using 0.58 as our baseline probability, we found that four asteroids would need to be surveyed to produce the desired probability — which we set at 90% or greater — that at least one of them would be found to be suitable.

Parallel vs. Sequential

Given that four potential targets for a human mission need to be surveyed by robotic spacecraft, is it best to send four robots all at once or to visit the asteroids one at a time?

The probability of finding a suitable target is the same under both scenarios.

With four asteroids in our survey pool, then under the sequential option, if the first asteroid is found to be suitable, we save the cost of the subsequent three missions. If the second asteroid is suitable, we save the cost of two missions, etc. However, there could be a long delay in launching a human mission if we have to wait for each of these surveys in turn to rule out an asteroid as a suitable target. Also, under our assumptions, we would miss out on the additive value each unlaunched surveyor would have provided.

The parallel option could cost more in terms of surveyor missions, but as we've seen, these missions would be comparatively inexpensive relative to the human mission. Further, this option would provide a 94% probability (under the conditions of our study) of locating a suitable target in just the time required for one of the four sequential survey missions, possibly enabling the human mission to begin much sooner than it would under the sequential option. This time savings could translate into cost savings as well. Further, it is possible that our pool of potential targets would be significantly reduced if we need to exclude asteroids that would be out of range of a human mission after the time required for up to four sequential survey missions.

Conclusions

Given the assumptions employed in this study, we found the following answers to the questions posed at the beginning of this paper:

1. Risk reduction to a human mission would justify one robotic surveyor if the initial probability that the targeted asteroid is suitable for human landing were 60 percent or greater. Two or more surveyor missions to separate asteroids would be justified at virtually any initial probability of suitability due to the combined productivity of all three (or more) missions regardless of landing suitability.

2. Four asteroids is the optimal number to plan to survey to achieve at least 90 percent probability that at least one is suitable for a human landing.

3. The likelihood of finding a suitable asteroid is the same for parallel and sequential surveyor missions. However, with the assumption that value is additive, parallel missions would provide greater total value if the sequential series ended before all four surveyors were deployed. Further, the parallel option could provide a savings in time which could translate to a savings in cost.

The relative merits of parallel and sequential surveyor missions can be considered in a future study, along with the probability of identifying a suitable asteroid via Earth-based observation, additional factors that could be included in the criteria for suitability, and the possibility of surveying multiple targets with the same robotic spacecraft.