# How long before two sidereal months start on the same lunar phase?

I was reading about the difference between the sidereal and synodic month when I started to wonder how many sidereal months need to pass before you get two that start on the same part of the synodic month or lunar phase.

I've tried looking on Wikipedia and googling around a bit and haven't turned anything up so I'm hoping someone here can help me.

• You may enjoy en.wikipedia.org/wiki/Eclipse_cycle which discusses various eclipse cycles based on the synodic month, anomalistic month and draconic month. Dec 30, 2022 at 6:58

The synodic and sidereal period are not in an exact ratio to each other, so there isn't an exact answer,

After 12 synodic months (354.3 days) about 13 siderial months have passed (355.1 days, only one day out)

After 99 synodic months (2923.6 days) about 107 sidereal months have passed (2923.5, one tenth of a day out)

After 235 synodic months (6939.785 days) about 254 sidereal months have passed (6939.788, about 5 minutes out)

So if you mean "in roughly the same phase" After 13 sidereal months, the synodic month has gone through one cycle and is roughly back to where it started the previous year.

And if you mean almost exactly the same, if you wait for 254 sidereal months, the synodic month will, be back in line, almost perfectly.

• Thank you, that's basically exactly what I was after, if I could ask a follow up question though can it be taken one step further than the 235-245 ratio, with a longer wait period and an even smaller error margin? Dec 29, 2022 at 22:42
• Not for any value less than 10000 months. Dec 29, 2022 at 22:48
• And there was a typo, it was 254 sidereal months. Dec 30, 2022 at 8:18