Speaker
Description
After the success of the NASA/DART mission (Daly et al., 2023; Chabot et al., 2024), attention has turned to demonstrating alternative technologies for mitigation and deflection. The gravity tractor is one such technology that uses its own gravity to slowly ``tow'' an asteroid and alter its trajectory (Lu and Love, 2005). Using the Gauss planetary equations, we derive a simple first-order metric to determine the effectiveness of a gravity tractor for a given asteroid. This metric estimates how quickly a gravity tractor changes the orbital period of a body. The metric can be applied to both heliocentric orbits on single asteroids and to a secondary body's orbit around a primary in a binary asteroid system. By comparing the metric for heliocentric orbits versus those for binary systems, we find that binary systems are better suited for demonstration missions than single objects. The metric can also be used to compare two separate systems and determine which one is more suitable for a gravity tractor demonstration mission. The metric may also be generalized to compare kinetic impactors to gravity tractors in the future.
The metric is
\begin{equation}
\mathcal{C} = \frac{a^2}{\sqrt{1-e^2}}\frac{M_3}{M_1 + M_2} \frac{1}{r_{2/3}^2}
\end{equation}
where $a$ and $e$ are the object's semi-major axis and eccentricity, respectively. $M_3$ is the mass of the gravity tractor while $M_1$ is the mass of the center body and $M_2$ is the mass of the body being perturbed. $r_{2/3}$ is the distance from the center of the gravity tractor to the center of mass of the perturbed body. As it is written, $\dot{P} \propto \mathcal{C}$ (i.e., the rate of change to the period of the perturbed body is proportional to the metric, $\mathcal{C}$). For a single body on a heliocentric orbit, we can define
\begin{equation}
\mathcal{C_\odot} = \frac{a_\odot^2}{\sqrt{1-e_\odot^2}}\frac{M_3}{M_\odot + M_2} \frac{1}{r_{2/3}^2}
\end{equation}
which is identical to the previous metric but with the solar mass, $M_\odot$, heliocentric semi-major axis, $a_\odot$, and heliocentric eccentricity, $e_\odot$, substituted in. For cases where we may directly compare a binary system to a heliocentric orbit, we find that $\mathcal{C} > \mathcal{C}_\odot$. For example, $\mathcal{C}/\mathcal{C}_\odot \approx 76$ for Dimorphos using the most up-to-date values of the Didymos-Dimorphos system (Chabot et al., 2024).