Author order when listing co-first authors

Hi all!

I’m looking for some guidance and hope I’ve reached the right sub.

As an extension to a project (tied to the university I’m attending), a classmate and I were asked if we’d like to turn the project into an actual publication. Now, the problem is that since we both are seen as co-first authors, it is a bit unclear who will be listed first on the paper (we will make sure to signal equal contribution independently of who is first).

We have had some discussions about this. I’ve presented that I have spent more time on the project than he has in the last months. He countered stating that hours aren’t the same as contributions and that he feels that the only fair way to determine this is to flip a coin.

Now to the question: how important is the order amongst co-first authors really? Especially given that we will explicitly claim equal contribution, does the order matter?

On one hand, I’d appreciate recognition for my hours spent on the project. But on the other hand, we are in the same class (which is quite small) and hence, I might just let him flip his coin in order to keep the group dynamic intact.

The way I see it is that I either continue to argue that my time should be worth something or that I now take a step back (which also would be really nice, not gonna lie), let him catch up with his working hours and then agree to flip for it.

Additional information:

Neither of us has published a paper before and since we are still studying to get our master’s degrees, I think both are a bit nervous about missing out on potential benefits when applying for jobs or PhD positions (which both of us are interested in).

We have not reached a decision with our supervisors regarding which journal to publish in. However, the work is related to astronomy/astrophysics (more specifically, atmospheric composition on distant objects).

Thanks in advance!