Beta Pictoris b was recently found to be the fastest rotating planet known to date. Its 56,000 mph is equal to 2.5 x 106 cm / sec.

Taking the orbit to be 9.0AU and its period to be 20.5 years means its orbiting velocity is 1.3 x 107 cm / sec. Combining the velocities vectorially would result in an overall velocity of 1.3 x 107 cm / sec.

If this total velocity squared is expressed as G x mass / radius , then using the mass as being 3J and the radius 1.65 rJ gives:

v2 = ( 6.67 x 108 cm3 / g sec2 ) ( 1.33 x 1031g ) / 1.18 x 1010 cm

and v = 2.7 x 107 cm / sec

Reuters: The head-spinning speed at which Beta Pictoris b whirls, the scientists said, lends support to the notion that a planet’s rotational velocity is closely related to its size: the bigger, the faster.

“Yes, the relation between mass and spin velocity was already known in our solar system,” said University of Leiden astronomy professor Ignas Snellen, another of the researchers.

“We now extend it to a more massive planet to see that the relation still holds. We need to observe more planets to confirm this is really a universal law,” Snellen added.

This paper suggests that, while mass and radius are factors in determining rotational velocity, also so is the orbital velocity which is determined by the distance of the planet from its sun.