Final answer:
Without specific data such as the prince's mass or orbital speed, we cannot calculate the radius of asteroid B-612 or the acceleration of the prince. We would normally use universal law of gravitation and circular motion equations for these calculations.
Step-by-step explanation:
To find the radius of asteroid B-612 and the magnitude of the prince's acceleration, we'll use the universal law of gravitation and circular motion concepts. The gravitational force acting on the prince is also providing the centripetal force needed to keep him in orbit on the asteroid's surface. The universal law of gravitation is given by F = G(m1*m2)/r^2, where F is the gravitational force, G is the gravitational constant (6.674 x 10^-11 N(m/kg)^2), m1 and m2 are the masses of the two objects, and r is the distance between their centers of mass. For circular motion, the centripetal force needed to maintain the orbit is given by Fc = m*v^2/r, with m being the mass of the prince, v the orbital speed, and r the radius of the orbit.
Unfortunately, we're not provided with specific values for the prince's mass or his orbital speed; therefore, we can't calculate the radius or the acceleration without additional data. Normally, you'd equate the gravitational force to the centripetal force and solve for the radius and acceleration with the proper numbers. The acceleration can be found by rearranging the equation for centripetal force to a = v^2/r.