Final answer:
The radius of satellite B's orbit will be 1/16 that of satellite A's orbit, given that satellite B's velocity is four times that of satellite A because orbital velocity is inversely proportional to the square root of the orbital radius.
Step-by-step explanation:
The question pertains to the relationship between a satellite's orbital velocity and its orbital radius. Using the orbital mechanics principle where orbital velocity is inversely proportional to the square root of the radius (V √ R), we can derive that if satellite B's velocity is four times that of satellite A, then the radius of B's orbit (Rb) would be 1/16 that of satellite A (Ra), given that (Vb/Va) = (Ra/Rb)^0.5.
Therefore, the correct answer to the question 'If satellite velocity of B is four times the distance of satellite A from the Earth, then the circular satellite B is how many times that of satellite A?' is 1/16 times because when the velocity increases by a factor of 4, the radius must decrease by a factor of 4 squared, which is 16.