Initially, four birds, labeled $A$, $B$, $C$, and $D$ are positioned at the vertices of a regular tetrahedron with side length $a$. At time $t=0$ all birds begin flying. For all $t>0$, each bird flies directly toward another bird in the following pattern: $A$ flies toward $B$, $B$ flies toward $C$, $C$ flies toward $D$, and $D$ flies toward $A$. For any $t>0$, the speeds of all the birds are equal.