Illustrative list: the other entries are made-up background objects with tiny odds.
Watch an impact probability rise, peak and collapse as observations shrink the uncertainty ellipse. A calm look at how scientists assess risk.
Circular Gaussian offset from a disc: closed form (Marcum Q) vs the numerical integral vs 1 000 000 Monte-Carlo virtual impactors.
Sweeps the observation count for the current scenario and overlays Monte-Carlo points (100 000 samples each) on the graph above.
Integrates real flyby trajectories (RK4) and bisects for the grazing impact parameter, then compares with R_E√(1+v_esc²/v∞²).
An asteroid's position at a future close approach is not known exactly; the orbit fit leaves a cloud of possible positions. Projected onto the plane through the Earth's centre that is perpendicular to the incoming asymptote (the B-plane, Opik 1976; Valsecchi et al. 2003) the cloud is well described by a 2-D Gaussian whose 1-sigma contour is a long thin ellipse: the long axis follows the "line of variations" (the direction in which the orbit is least constrained, mostly timing along the orbit).
Energy and angular momentum are conserved on the flyby hyperbola: ½v²−μ/r = ½v∞² and L = b v∞. Setting the periapsis equal to the Earth's surface gives the largest impact parameter that still hits:
Slow encounters are focused strongly (the Earth looks much bigger than it is). Experiment 3 checks this formula against numerically integrated trajectories.
The page evaluates this semi-analytically: a 1-D Simpson integral along the long axis of the exact chord probability across the short axis (Gaussian error function), and independently by Monte Carlo with sampled virtual impactors, P ≈ hits/n ± √(P(1−P)/n). For a circular Gaussian a closed form exists, P = 1 − Q₁(d/σ, R/σ) (noncentral chi-square, 2 degrees of freedom); Experiment 1 compares all three.
While the ellipse is much larger than the Earth disc but still covers it, P ≈ A_disc / (2π σa σb) rises as the ellipse area shrinks. Real observation arcs shrink the area roughly like 1/N in this simple model (each semi-axis ∝ q/√N, q = astrometric error). The best-fit centre also moves: it equals the (unknown) truth plus an error that shrinks with the ellipse. If the truth lies off the disc, the ellipse eventually shrinks away from the Earth and P falls to nearly zero; if it lies on the disc, P climbs toward 100 %. The probability is a statement about our knowledge, not about the asteroid, and the fall in P is the good outcome of the same process.
A tiny region of the B-plane (kilometres to hundreds of kilometres across) deflects the asteroid onto an orbit that is in resonance with the Earth and brings it back for a later impact (Chodas 1999; Milani et al. 2005). Its probability is the same Gaussian integral over that small circle; the page uses a single illustrative keyhole and assumes a certain hit if it is threaded.
The Torino scale (0–10; Binzel 2000) combines probability and energy on a chart. This page uses a simplified classifier: energy bands (<1 Mt none, 1–300 Mt local, 300–1e5 Mt regional, above global) and probability thresholds (1e-6, 1e-4, 1 %, 10 %, 50 %, 99 %). It follows the shape of the official chart but is not an official rating. Real energy also depends on density, strength, angle and atmospheric breakup: the order of magnitude is what matters.
Asteroid 2024 YR4 was reported in early 2025 to have briefly reached Torino level 3, the highest rating assigned to any object, with an Earth-impact probability for 2032 reported at about 3 % at its peak. Further observations then reduced the Earth-impact probability to effectively zero; a small chance of a lunar impact was reported afterwards. The preset "Rise then collapse" is a stylised illustration with invented numbers shaped like that story, not the real orbit solution.
Given years of warning, a tiny velocity change of about 1 cm/s moves the B-plane point by thousands of kilometres; see Asteroid Deflection and Asteroid Trajectory Correction. For what an impact does, see Asteroid Impact Simulation: Planetary Effects.
Opik, E. J. (1976) Interplanetary Encounters. Binzel, R. P. (2000) The Torino Impact Hazard Scale, Planet. Space Sci. 48. Chesley, Chodas, Milani, Valsecchi & Yeomans (2002) Quantifying the risk posed by potential Earth impacts, Icarus 159. Valsecchi, Milani, Gronchi & Chesley (2003) Resonant returns to close approaches, A&A 408. Milani et al. (2005) Icarus 173. NASA/ESA planetary-defence reporting on 2024 YR4 (2025). NASA DART mission (2022) for deflection.
As of public reporting, no known asteroid poses a significant impact threat to Earth. This is an educational model of how risk assessment works, not a prediction about any real object.