What orbital period would produce one New Moon (and one Full Moon) each year? What other effects would this produce? I am interested to know whether it's possible for the moon to orbit the earth at such a rate that we would see only one New Moon and one Full Moon a year. If so, what other effects would we experience?
I at first assumed this would be a one-year period, and technically I think that would produce one New Moon, but that single New Moon would last all year (i.e., you would never see the moon). So I'm interested to know if there is an orbital period that would give us one New Moon and one Full Moon, as seen from our earth, each year.
As I hold my hands up in front of my face and experimentally rotate them around each other, I want to say a six-month period would produce this effect, but I'm not sure that's correct, so I'd appreciate a word from anyone who actually knows what they're talking about. Thanks!
(Apologies if this has been asked before; I wasn't able to find it.)
This would naturally be achieved by a quasi-satellite. These are objects with a 1:1 orbital resonance with a different eccentricity to the planet. From the perspective of the planet, this leads to the quasi-satellite appearing to travel around the planet once a year in a retrograde direction. Starting with the quasi-satellite at its maximum distance from the Sun, this would be at full phase. Six months later, the quasi-satellite would be between Earth and the Sun, so would be at new phase. The diagrams below show an idealised version of the configuration based on Keplerian orbits in a non-rotating frame and in a frame where the Earth and the Sun are kept in a fixed position.


Real systems will evolve dynamically due to the gravitational interaction between the planet and the quasi-satellite, leading to precession and oscillations of the alignment of the orbits.
Earth currently has several known quasi-satellites, the closest of which is (469219) Kamoʻoalewa. The known quasi-satellites in our Solar System do not have long lifetimes: they are relatively recent captures into the quasi-satellite orbit that will eventually escape. Nevertheless, there are some conditions under which quasi-satellites can be stable over long periods, and perhaps some exoplanetary systems have more favourable conditions for quasi-satellites than ours does.