planet - Years, Months, Day, and Weeks?

The synodic period of the moon is $29.53$ days, a little shorter than a calendar month, which is on average about $30.4$ days. This is slightly longer than its orbital period, but corresponds to the periodic visual appearance of the moon as viewed from Earth. I mention this to make it clear that we should be forgiving of a little imprecision.

Conventionally, the moon's appearance is divided into four phases: first quarter, full, last quarter, new. That means that on average, each phase lasts about $7.4$ days. Since calendars count days in integer amounts, a $7$-day period seems to be a natural choice.

The social importance of the seven-day period in Western cultural probably has much more to do with its religious significance in Abrahamic religions than astronomy per se (although certainly not unique to it). But its ultimate origin probably does lie in the natural division of the moon's appearance into four phases, which correspond to an apparent geocentric celestial latitude difference between the Moon and Sun of $0^circ$, $90^circ$, $180^circ$, and $270^circ$.

That, the explicit answer to your question is

• 1 week = 7 days = one lunar phase.