What is the relationship between centripital force and period?

Centripetal force is that force which applied to a moving object causes it to travel in a curved path as opposed to a straight path that it would follow without it. Think a string and a rock here. If I let go of the string to remove the centripetal force, the rock then moves in a straight line, carried by momentum. Period is something like a pendulum swinging. Period for a pendulum, is the time it takes to return to the end of a swing, out and back. Period applies to any repeating motion. For the Earth, the time it takes to return to the same place relative to the stars (sidereal time) is the period of the orbit, in our case, 365.25 days. The sidereal day is actually about 4 clock minutes shorter than the rotation of the planet which we call a day. This is because we move in our orbit as well as rotate about the axis each "day". Sidereal time is used by astronomers to locate stars. Leap years is how we correct the solar calendar to match the sidereal calendar to keep track of seasonal religious holidays like Easter. Centripetal force depends directly on motion. No motion = no centripetal force. At the end of each swing of a pendulum, the centripetal force from motion drops to zero when the pendulum stops. It rises to a maximum at the very bottom of the swing and drops to zero at the other end of the swing. The centripetal force trades places with potential energy on a 1 to 1 ratio, but other than the ratio, there is no way to quantify the relationship with numbers without knowing more, such as the weight of the pendulum, the length, and the acceleration of local gravity.

Trivia: In 1582, the then Pope, Gregory decreed a change to the calendar, by dropping 10 days. The next day after October 5th, was the 16th. NOBODY had a birthday of October 6th, 1582 through October 15th because those days ceased to exist. We went from the Julian Calendar to the Gregorian Calendar with the loss of 10 days which got Easter back in sync with the seasons, and the addition of the present system of adding leap years meant Easter would STAY in sync in the future, for the next 3000 years or so anyway...

If U mean "centripetal force" than not necessary anything and here's why:

To have a relationship in physics means to have a mathematical one.

A period refers to a repeating time interval, encountered in motions such as:

pendulum motion

or

circular motion

motions associated with Simple Harmonic Motion (SHM).

Although centripetal force is introduced as a topic in the study of circular motion, it is present in any motion that is curvilinear (that is a curved motion path that has an instantaneous radius = R). In short, a repeating motion time (period) does not have to exist in order to have a centripetal force.

So a relationship between centripetal force and something that may not exist can't either.

Centripital force is the force between an orbiting body, and an anchored point. Think of a tetherball rope. A period is at the end of every sentence, sometimes there is more than one...