  One of the least understood processes in astrophysics is the formation of
planetesimals from molecules and dust within protoplanetary disks. In fact,
current methods have strong limitations when it comes to model the full
dynamics in this phase of planet formation, where small dust aggregates collide
and grow into bigger clusters. That is why microgravity experiments of the
phenomena involved are important to reveal the underlying physics. Because
previous experiments had some limitations, in particular short durations and
constrained dimensions, a new mission to study the very first stages of planet
formation is proposed here. This mission, called Magrathea, is focused on
creating the best conditions for developing these experiments, using a
satellite with a 6 $m^3$ test chamber. During the mission 28 experiments are
performed using different dust compositions, sizes and shapes, to better
understand under which conditions dust grains stick and aggregate. Each
experiment should last up to one month, with relative collision velocities of
up to 5 mm/s, and initial dust sizes between 1 $\mu$m and 1 mm. At least $10^6$
collisions per experiment should be recorded, to provide statistically
significant results. Based on the scientific objectives and requirements, a
preliminary analysis of the payload instrumentation is performed. From that a
conceptual mission and spacecraft design is developed, together with a first
approach to mission programmatic and risk analysis. The solution reached is a
1000 kg spacecraft, set on a 800 km Sun-synchronous orbit, with a total mission
cost of around 438 MEuros.
