100 Years of Relativity + Challenge Winners!

A Newtonian “gravitational tractor” approach could plausibly shift the asteroid Apophis by 25,000 kilometers using a spacecraft that never physically collides with it—requiring only about 1,600 metric tons of spacecraft mass (including fuel) and roughly 16 metric tons of fuel over a seven-year lead time. The key insight is that the needed acceleration is tiny—about 10⁻⁹ m/s²—yet sustained long enough to produce the required positional change before Apophis reaches Earth in 2036.

The calculation starts by moving into Apophis’s 2029 orbital-velocity frame, eliminating the need to track its initial ~30 km/s motion. In that frame, the asteroid’s starting velocity is effectively zero, and the task reduces to adding enough velocity so Apophis ends up displaced by 25,000 km relative to where it would have been. The gravitational pull from the hovering spacecraft provides the acceleration. Using a basic kinematics relation (position change from average acceleration over time), the average acceleration needed over seven years comes out to roughly one ten-billionth of Earth’s surface gravity.

To translate that acceleration into required spacecraft mass, Newton’s law of universal gravitation is applied at a standoff distance of 325 meters from Apophis’s center of mass. In the force-to-acceleration step, Apophis’s mass cancels out, which is why the asteroid’s shape and internal composition don’t matter for this portion of the estimate. The resulting average spacecraft-plus-fuel mass is about 1,600 metric tons—comparable to roughly 80% of a space shuttle’s mass.

Fuel needs are then handled with the rocket equation, but with a crucial mass bookkeeping choice: because the spacecraft is effectively “pulling” the entire asteroid, Apophis’s mass dominates the system. The transcript treats the asteroid’s mass (~30 billion kg) as the “dry” mass and adds fuel to form the “wet” mass. The pulsed fusion drive’s exhaust velocity is taken as 500 km/s, but thruster geometry reduces the effective component that contributes to pulling forward. With thrusters angled about 30 degrees to avoid pushing the asteroid the wrong way (assuming a 325-meter-diameter sphere), the usable reverse component of exhaust velocity is about 427 km/s; sideways components require multi-direction pointing to cancel.

Combining these ingredients yields a fuel-to-asteroid mass ratio of about 5.3×10⁻⁷, corresponding to roughly 16 metric tons of fuel—about 1% of the spacecraft mass. That small fuel fraction is the practical payoff: with a sufficiently capable pulsed fusion drive, the gravitational tractor concept appears feasible given the seven-year warning window.

The segment closes by noting that a less advanced propulsion option could still work in principle, though it would demand far more propellant because conventional rocket exhaust velocities are under 1% of the fusion drive’s. It also announces challenge winners receiving PBS Digital Studios t-shirts and previews upcoming episodes focused on black holes and deeper relativity-era weirdness.