Orbits have several important components, namely the period, the semimajor axis, the inclination and the eccentricity. You can only compute the eccentricity and the inclination from observations of the orbit itself over time, but the semimajor axis and the period are related mathematically. If you know one of these parameters, usually determined originally from observations, you can determine the other. It is possible to find the semimajor axis of many orbits from information tables about astronomical objects. Once you have the semimajor axis, you can find the period of an orbit.
Things You'll Need
 Astronomical information table
 Calculator
Steps to Calculate the Period of an Orbit

Look up the semimajor axis of the orbit you want to use. Astronomical tables for planets usually list the semimajor axis as the distance from the Sun. The semimajor axes for other bodies are their distances from their centers of rotations. The semimajor axis of the Moon, for example, is its distance from Earth.

Convert the units of your semimajor axis to astronomical units. An astronomical unit is equal to the distance of the Earth from the Sun. That distance is 93,000,000 miles or 150,000,000 kilometers.

Use Kepler’s Third Law to calculate the orbit’s period from its semimajor axis. The Law states that the square of the period is equal to the cube of the semimajor axis (P^2 = a^3). In order for the units to be correct, the semimajor axis should be in astronomical units, and the period should be in years.

Convert the period into the most appropriate units. For fastmoving bodies with small orbits (like the planet Mercury or the Moon), the most appropriate unit is usually days, so divide the period in years by 365.25. Larger orbits have longer periods that you should generally measure in years.
Tips & Warnings
 If you can not find the necessary orbital parameters in an astronomical table (this can be the case for artificial satellites and newlydiscovered comets), you can try to determine semimajor axis and period with observation. You will need many observations conducted with precision over time in order to begin. There are computer and calculator programs that can determine the orbital parameters from your observations.
 When checking astronomical tables for semimajor axes, try to find the value for the maximum distance between the object and the orbital center. Using the average or mean distance will only give you an approximation for the semimajor axis, based on the assumption of a circular (rather than elliptical) orbit.
References
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