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7  About the Asteroid Impact Mission (AIM): Determining the mass of Didymos’ secondary by visual imaging

A critical requirement for the Asteroid Impact Mission (AIM) is the ability to determine the mass of Didymos’ secondary with an accuracy of about 10 %. The conventional approach to estimate the mass of a solar system body through its gravitational effect by tracking the spacecraft trajectory is only marginally viable for Didymos’ secondary. Instead, the idea to measure the “wobble” of the primary around the common centre of gravity has been put forward. This wobble with an expected radius of about 10 m can possible be measured either by means of optical or radar ranging devices or by direct observation with the Visual Imaging System (VIS). Here, we investigate the latter approach.

We approach the problem of estimating the wobble in two steps: In the first step, the spacecraft trajectory relative to the primary asteroid is reconstructed from the locations of landmarks in images. This relative trajectory comprises the wobble. In the second step, the magnitude of the wobble is extracted from the reconstructed trajectory.

In this preliminary investigation, we do not deal with the problem of landmark identification and determination of their location in images. We just randomly generate landmark positions in the body fixed frame employing a shape model based on radar observations and simulate observations as inertial viewing directions from the spacecraft (with some error). Then we solve simultaneously for the landmark positions in the body fixed frame, the orientation of the asteroid at each image acquisition time, and the spacecraft trajectory relative to the asteroid. This reconstruction is done without any a priori knowledge or modelling of spacecraft trajectory or asteroid rotation. In order to extract the wobble from the reconstructed trajectory in the second step, we only assume that we know the period and the direction of the wobble from the orbit of the secondary.

We conduct Monte Carlo simulations for various scenarios and assess the accuracy of the determination of the wobble. Under reasonably conservative assumptions, the magnitude of the wobble (and hence the mass of the secondary) can be estimated with an accuracy of 3.5 %.

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