Asteroid Deflection Mission - 2D Heliocentric Orbit and B-Plane Miss Distance

Presets

Speed

Live readouts

Graphs

Numerical checks

running...

How to use

The grey orbit is the unperturbed asteroid that would reach Earth at the encounter time; a spacecraft hits it at the white flash and the gold orbit is the result. Try: (1) Small rock, long warning - a 600 kg impactor needs years to move the miss distance by more than one Earth radius; (2) Short warning - months are not enough; (3) Retrograde push - the sign of the effect flips; (4) Sideways push - a push across the velocity changes the orbit shape far less than along it; (5) read the green graph for the impulse needed at each warning time. Planetary-defense science only, no real target. Space pauses, R restarts.

The science

Momentum transfer. A kinetic impactor of mass m at speed v changes the asteroid's velocity (mass M) by

dv = beta m v / M

where beta ≥ 1 is the momentum-enhancement factor from ejecta thrown backwards (beta > 1 means the crater recoil adds to the push; measured near 3.6 for the DART impact on Dimorphos, a different, binary system).

Orbit change. The page works with exact two-body Kepler motion (mu = 4 pi^2 AU^3/yr^2). The kick is added to the position-velocity state at the impact time; orbital elements are recomputed (vis-viva, eccentricity vector, Kepler's equation) and both orbits are evaluated at the encounter time. A prograde push raises the energy and period; the body then arrives late by about

along-track shift ~ 3 dv t (circular orbit, Hill): y(t) = (dv/n)(4 sin nt - 3 n t)

so the effect grows linearly with warning time, which is why early deflection wins. The miss distance is measured in the B-plane, perpendicular to the Earth-relative velocity; Earth's gravity enlarges the target to b = R_E sqrt(1 + v_esc^2 / v_inf^2) (gravitational focusing).

Checks. (1) the numerical along-track drift equals the Clohessy-Wiltshire (Hill) formula; (2) state to elements to state round trip; (3) Kepler's third law; (4) vis-viva on the deflected orbit.

Simplifications. Coplanar orbits, Sun-only gravity (no planetary perturbations, no Yarkovsky), a point asteroid, instantaneous impulse, the Earth moves on a circle, the close encounter is treated by a B-plane radius not integrated. Not a mission-design tool.