Astronomy & Celestial Mechanics
the sky, computed
Concept

Kinetic impactor — where it appears

A spacecraft deliberately crashed into an asteroid to change its velocity. The change is larger than the spacecraft's momentum alone by the factor β, because the ejecta thrown out carry momentum away in the opposite direction.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

A rubble pile that splits below a mass ratio of 0.204 can lose its piece; above it, the piece stays. The total energy of two spherical components of equal density in contact, spinning together at the rate at which their mutual gravity just holds them against the spin, against the mass ratio of the smaller to the larger, in units of G m₁²/R₁. The energy is the kinetic energy of the rotating pair minus their mutual gravitational binding. When the smaller piece is a small fraction of the whole, the spin carries more energy than the binding and the total is positive: a body spun to breakup that sheds a fragment of that size has enough energy for the fragment to escape entirely, becoming a separate asteroid on a nearly identical orbit. The total changes sign at q = 0.204. Above that ratio the pair cannot separate without an energy source; it stays as a binary, orbiting and eventually synchronising, or re-accretes. As q goes to zero the energy tends to 0.2 G m₁²/R₁, the rotational energy of the primary alone at its breakup rate. Nothing in the threshold depends on the size or the density of the body — it is a pure number from the geometry of two touching spheres — and asteroid pairs sharing an orbit have been found overwhelmingly with estimated mass ratios below it.

A split that decides whether the piece can leave

A rubble pile spun past its limit splits in two, and whether the smaller piece escapes or stays in orbit is not a matter of luck. Two touching spheres spinning at their shared limit have positive total energy only when the smaller is less than 0.204 of the larger's mass — a number with no size and no density in it. Below it the pieces can become a pair of asteroids on nearly identical orbits; above it, a binary. And the larger the piece that leaves, the slower the body left behind.

orbits · Rubble piles How hard a hovering spacecraft pulls an asteroid. The velocity change a spacecraft hovering beside a 200-m asteroid gives it in a year by gravity alone, in millimetres per second, against the hovering distance from the asteroid's centre in asteroid radii, for spacecraft of 5 t, 20 t, 50 t. The pull depends on the spacecraft's mass and the distance, not on the asteroid's mass. A 20-tonne tractor at 1.5 radii gives 1.9 mm/s a year; at 3 radii, a quarter of that. Closer is better, and the limit on how close is set by the exhaust: inside the shaded region the engines would have to point so steeply outward to keep their 20° plumes off the surface that holding station costs more than the pull is worth.

A tow with no rope

A spacecraft parked beside an asteroid pulls it by gravity alone, with a force set by the spacecraft's mass and its distance and nothing else. Twenty tonnes hovering a hundred and fifty metres from the centre of a two-hundred-metre asteroid moves it by two millimetres a second in a year. That is the gentlest engine there is, and its limit is not the pull but the exhaust: the spacecraft must thrust away from the rock to stay put without blasting it, and the angle that takes decides how close it can hover.

spaceflight · Low-thrust transfer

Named alongside it

The objects these essays reach for when they reach for this one.

Along-track driftAngular momentumAsteroid pairBinary asteroidContact binaryFree energyGravity tractorKeyholeLow-thrust transferMass ratioMomentum enhancementPlanetary defence

All concepts