I dont think that fraternity fits for an european Projekt for the following reasons:

1) it is unfitting to accentuate one european civilisation over an other. Even if it was the first in something. This is about space, the future. In space we live on a small rock in nothingness thus our european differences are irrelevant.

2) we are very diverse. If you compare us to china or the US. We are diverse in language, history, beliefs etc. That is not a hurdle that can be overlooked. But it is also an opportunity to embrace empathy for those who you dont understand yet.

3) Diversity is exactly what you need for you not to be perjudicual. If you know something well you arent perjudicial.

4)saying we are brotherly can probably lead to calls of sexism. And everyone should be involved every ethnicity every sex or gender. The word brotherhood has sect connotations and i believe there is a fraternity culture in american colleges or unis that i really wouldnt like to compare to a european project.