Presets
Playback
Asteroid and orbit
The orbit is built so that, without a push, the asteroid reaches Earth's orbit exactly where Earth is.
Impactor and warning time
A small velocity change early enough becomes a large displacement later.
Model checks
The science
A tiny push, a long lever
An impactor of mass m hitting at speed u delivers momentum β m u (the factor β > 1 accounts for ejecta thrown backwards; the 2022 DART test measured about 3.6 for a rubble-pile moonlet). The asteroid of mass M = ρ π D3/6 changes speed by Δv = β m u / M. By the vis-viva equation v2 = GM☉(2/r - 1/a) this changes the semi-major axis, so by Kepler's third law the orbital period changes, and the asteroid arrives at the crossing point later or earlier by about Δt ≈ (3/2)(Δa/a) tlead. That is why warning time matters more than push size.
Near Earth the impact parameter must beat the gravitational capture radius bc = RE √(1 + vesc2/v∞2), because Earth's gravity bends the path inwards (gravitational focusing). The impact energy is E = ½ M (v∞2 + vesc2) (1 megaton TNT = 4.184e15 J).
What the simulation does
The asteroid and Earth (circular orbit) are propagated exactly with Kepler's equation in the ecliptic plane, in AU and years. The burn changes the velocity along (or against) the direction of motion; the new elements are computed from the state vector. The closest approach is found by a fine scan and golden-section refinement; the Earth-frame panel integrates the encounter in Earth's gravity to draw the bent path.
Honest simplifications
- Planar orbits (no inclination), Earth on a circle, point masses; no planetary perturbations, no Yarkovsky effect, no rotation of the asteroid and no fragmentation.
- The push is a single instantaneous velocity change along the track; real missions steer in three dimensions and measure
βafter the fact. - Impact energy is a kinetic-energy figure, not a damage prediction; this is educational planetary-defence physics with an inanimate rock.
What to try
- Load Short warning: the same impactor that works with 5 years of warning now misses nothing; the graph shows how steeply required delta-v grows as the lead time shrinks.
- Flip the push direction: slowing and speeding the asteroid shift its arrival time in opposite directions.
- Raise beta from 1 to 5 and watch the miss distance scale in proportion.