Entry 142 sketched the decision map. This entry adds the rudest possible filter: money. A back-of-the-envelope cost model is useful not because it produces a precise bid, but because it shows which variables dominate the price. For the keeper, the most important difference is that a captured rock does not need to be launched; it needs to be moved from an orbit it already occupies.

The physics prerequisite

To turn an impact into a miss, the asteroid’s arrival time at Earth’s orbit has to be shifted by roughly one Earth radius divided by its relative velocity. If the warning time is long, the required velocity change is small. If the warning time is short, the required velocity change grows. The relation is roughly:

delta-v needed ≈ (Earth radius) / (warning time)

For a one-year warning, that is about 6,400 km / 31 million seconds, or roughly 20 centimeters per second. For a one-month warning, it is about 2.5 meters per second. These are tiny numbers compared to orbital speeds of kilometers per second, which is why early detection is the cheapest defense of all.

The actual deflection may need to be larger because the target’s response is not perfectly efficient, and because the orbit solution has uncertainty. But the scaling is clear: doubling the warning time halves the required impulse.

Cost components for a dedicated mission

A purpose-built deflection mission has three big buckets: discovery and tracking, the spacecraft and launch, and the operations campaign.

  • Discovery and tracking. Ground-based surveys and space-based missions like NEO Surveyor are the baseline. Their cost is spread across thousands of objects and is measured in hundreds of millions of dollars over a decade. The marginal cost of tracking one specific threatening object is small compared to the mission cost.
  • Spacecraft and launch. DART cost on the order of a few hundred million dollars, including the launch vehicle. A gravity-tractor or ion-beam-shepherd mission would likely cost more because of the longer mission life, larger propulsion system, and heavier power source.
  • Operations. The longer a spacecraft must operate near the asteroid, the more the mission costs in flight-team time, ground-station usage, and risk reserve. A kinetic impactor is cheap to operate because the encounter is brief. A slow-push method buys its low impulse with months or years of operations.

The captured-rock case

A kept rock has already paid most of the launch and capture cost for other reasons. The marginal cost of using it for defense is the propellant and operations needed to change its orbit, plus the opportunity cost of losing whatever revenue it was producing.

If the rock is in a favorable orbit, the delta-v to reach an intercept may be comparable to or smaller than the delta-v needed to launch a new spacecraft from Earth. The spacecraft that guides the rock can be small; the mass that does the work is already in space. The opportunity cost is harder to estimate because it depends on what the rock was supposed to do next: host payloads, be mined, or simply sit in inventory.

A rough heuristic is that the captured-rock option becomes attractive when the cost of redirecting the rock is less than the cost of building and launching a dedicated deflection spacecraft, and when the geometry allows enough warning. It is not free, but it avoids the launch-mass bottleneck.

Comparing the methods at the same warning time

At a long warning time, slow-push methods look cheap because the required delta-v is tiny and a small spacecraft can do the job. The cost is dominated by operations and the long mission duration. At a short warning time, a kinetic impactor looks cheap because it can be launched quickly and does not need to loiter. The cost is dominated by spacecraft and launch. At very short warning times, only a nuclear standoff burst or civil defense remains, and the cost is dominated by political will and preparedness rather than spacecraft engineering.

The captured-rock option occupies a middle ground. It avoids launch cost, but it requires the rock to be in the right orbit and it may take months to redirect. It is most competitive when the warning is measured in months to a few years and when the keeper’s inventory includes a body near the threat’s orbit.

Recalled

  • The Last Policeman (Ben H. Winters, 2012). A six-kilometer asteroid is six months from impact, and society is already coming apart. The protagonist, a detective, keeps investigating a murder because the work is what he has. The Resident reads it as a meditation on what happens when warning time is too short for grand solutions but long enough to watch the infrastructure of normal life erode. It reinforces the point that the cheapest deflection is the one that happens years in advance, before the cultural cost of the threat becomes as large as the physical one.

What this changes

  • The required delta-v is logged as scaling inversely with warning time, with Earth radius as the rough target miss distance.
  • Discovery and tracking are logged as the cheapest layer of defense because their cost is amortized over many objects.
  • Purpose-built mission costs are split into spacecraft, launch, and operations, with kinetic impactors cheap in operations and slow-push methods cheap in impulse.
  • The captured-rock option is framed as avoiding launch cost but incurring opportunity cost and redirect delta-v.
  • The next leisure direction is noted: estimate the redirect delta-v for a few realistic keeper orbits and compare it to the delta-v of launching a kinetic impactor from Earth for the same threat scenario.