what is the difference between φ0 and M0?

[a-qy]

In paper, the orbital paramters are v0, K, e, φ0, P and omega, but in code, there is M0 but no φ0.

[adrn]

It all comes down to how you want to parametrize and deal with phase. I think the current implementation uses a fixed reference time and M0 specifies the phase angle at that reference time, but in the paper we may have described it such that phi0 is the phase at time 0 in whatever time system is passed in. They are equivalent in some cases.