A novel method for computing state transition matrices due to the unscented transform.

We present a new method for computing the state transition matrix of a nonlinear dynamical system. The proposed method does not require the implementation of complex partial derivatives or auto-differentiation of the dynamics, while removing the arbitrary choice of a perturbation step for traditional finite difference methods. We tested the new state transition matrices using three different applications: a simple two-body problem, a Mars atmospheric entry flight mechanics problem, and two future close encounters of the asteroid (101955) Bennu with the Earth.

Elliptical ejecta of asteroid Dimorphos is due to its surface curvature.

Kinetic deflection is a planetary defense technique delivering spacecraft momentum to a small body to deviate its course from Earth. The deflection efficiency depends on the impactor and target. Among them, the contribution of global curvature was poorly understood.

Ejecta from the DART-produced active asteroid Dimorphos.

Some active asteroids have been proposed to be formed as a result of impact events. Because active asteroids are generally discovered by chance only after their tails have fully formed, the process of how impact ejecta evolve into a tail has, to our knowledge, not been directly observed. The Double Asteroid Redirection Test (DART) mission of NASA, in addition to having successfully changed the orbital period of Dimorphos, demonstrated the activation process of an asteroid resulting from an impact under precisely known conditions.