Areal Velocity Conservation

The areal velocity is the term used to denote the surface area swept out by position vector r per unit time during the planar motion of the particle under a central force. If the vector r changes to r + dr in time dt, the area vector d s swept by the radius vector is given by

d s = ½ r × dr = ½ r (r d θ) n

Hence, the areal velocity is,



That is, the area swept out per unit time (or areal velocity) is constant under a central force motion. This is Kepler’s IInd law for planetary motions in the gravitational force of fixed center, Sun.

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