The probe masses 500 kg and the asteroid maybe 2 billion kg, so it won't get moved much (maybe 0.4 mm/s), but it should change the orbital period by 10 minutes. That's why they're going to a binary asteroid pair - the period change is the only way to see the effect.
This mission also tries out some other cool tech:
- Solar panels with little mirrors on them to reflect more light onto the cells, called the Transformational Solar Array. 3X less weight for the same power! It actually unrolls in space.
- Electronics built in a radiation-hardened FPGA that can implement any circuits at all. They built a big camera onto it, DRACO, that will guide it right into the middle of the asteroid. They can actually modify the electronics in-flight. This will useful for all space tech.
- An ion rocket that uses xenon as a fuel, that gives you far more thrust for a given weight.
This is what NASA is for - PR for American tech!
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