A gravity tractor never touches the asteroid. It hovers at a fixed standoff distance d and uses angled ion thrusters to hold position against the asteroid's own pull on the spacecraft. The reaction to that station-keeping thrust is aimed so its exhaust never hits the rock — but the spacecraft's own gravity keeps tugging the asteroid toward it the entire time, for as long as the mission runs.
a = G·m_sc / d² (continuous acceleration on the asteroid)
Δv = a · t_mission (velocity change after the tractoring period)
miss ≈ Δv · (t_warning − t_mission) (position shift accumulated over the remaining lead time)
Note the asteroid's own mass never appears: the force between spacecraft and asteroid is G·m_sc·m_ast/d², so dividing by the asteroid's mass to get its acceleration cancels m_ast out completely — a heavier rock decelerates the tug by exactly as much as it would strengthen it. Only the spacecraft's mass and the standoff distance set the accel.
- Spacecraft mass — heavier spacecraft pull harder (a scales linearly with m_sc).
- Standoff distance — closer hovering pulls much harder (a scales as 1/d²), but risks the plume disturbing loose surface material.
- Mission duration — longer tractoring accumulates more Δv, but eats into the warning time left to let the deflection compound.
- Warning time — how many years before the asteroid would otherwise reach Earth; the leftover lead time (after the mission ends) is what turns Δv into an actual position shift.
The required miss distance here is set to twice Earth's radius (≈12,742 km) as a safety margin — real deflection campaigns target several Earth radii of clearance to absorb trajectory uncertainty.
Drag inside the orbit view to spin your vantage point around the asteroid (a 2D stand-in for orbiting the camera); scroll/pinch to zoom.