We have two objects - one massive star, and one planet which has a considerably smaller, but non-negligible mass, in a circular orbit about a common centre of mass. Using equation
$F$=$GMm$/$r^2$ where M is the mass of the star, m is the mass of the planet, and r is distance from the centre of mass of the two objects.
We can work out the velocity of the star about the centre of mass of the two objects by equating F to the centripetal force. This will give us
This seems to indicate that the tangential velocity of the star is much greater than that of the planet, because as r gets smaller v becomes greater, and r is so much smaller than the star. What I understand is that the period of the two objects is equal, and so the star travels much slower to complete a orbit which has a far smaller distance travelled. This makes sense to me, however I want to know what's wrong with my maths, or perhaps my notation.