The speed of each particle in mutual gravitational orbit can be found using the formula for gravitational force and centripetal force, with the speed given by v = sqrt(Gm/r).
To find the speed of each particle moving in a circle due to their mutual gravitational attraction, we can use Newton's law of universal gravitation and the formula for centripetal acceleration. For two particles of mass m attracting each other at a distance r, the gravitational force can be given as F = Gm2/r2 where G is the gravitational constant. This force acts as the centripetal force necessary for circular motion, which is also described by F = mv2/r. Equating the two expressions, we have Gm2/r2 = mv2/r. Mass m cancels out from both sides, allowing us to solve for speed v as v = sqrt(Gm/r). Each particle would have the same speed due to symmetry and equal mass.