Nano spacecrafts are gram level silicon chips that will be accelerated to 20% of the speed of light to reach Alpha Centauri in 20 years.
I wonder if we can break the weight limitation by shooting multiple spacecraft and connecting them after the acceleration. To test this idea, I need your help with calculating the numbers. Let's assume that we want to connect two spacecraft, $A$ and $B$.
- $A$ is accelerated before $B$.
- $B$ is accelerated to a speed slightly bigger than $A$
- it takes $t$ days for $B$ to catch up $A$
As $B$ will get closer to $A$ it will have better precision aligning on $A$ collision path, but it will also require more energy to navigate $B$
Please calculate what precision is needed to collide with $A$ and what maneuvering speed $B$ needs to do it.
This question doesn't contain all the details for making this calculation. I am looking for a realistic example to understand if such a mission is even possible, so please feel the gaps with realistic assumptions about the problem.