How do I show that binary systems with small orbits have high orbital speeds? Help me please :(?

Question

How do I show that binary systems with small orbits have high orbital speeds? Help me please :(?

Answer 1

For a given two bodies, the orbital period goes as:

P = 2(pi)sqrt((a^3)/(G(M1 + M2))

where a is maximum distance between the two bodies.

http://en.wikipedia.org/wiki/Orbital_per...

The speed is proportional to a/P and so goes as 1/sqrt(a)