How do you calculate the period of a planet from its speed and distance from the Sun?

The velocity of a planet in a circular orbit is just the circumference of the orbit, 2 x pi x radius, divided by the time it takes to go once around in its 'year'. So, that means that since

                2 x Pi x Radius
  Velocity =   -------------------
                    Period


that
                   2 x Pi x Radius
    Period   =   -------------------
                      Velocity

Just make certain you use the same units in velocity as you do in the radius of the orbit, example, Radius in kilometers, Velocity in kilometers/second gives period in seconds. For planets in highly elliptical orbits, the formula is more complex, but is still useful to get the order of magnitude right!
Copyright 1997 Dr. Sten Odenwald
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