Final answer:
To find the centripetal acceleration of Io, we can use the formula for centripetal acceleration and calculate the velocity of Io based on the given distance and time. Substituting the values into the formula gives an approximate value of 12.18 m/s^2 for the centripetal acceleration of Io.
Step-by-step explanation:
To find the centripetal acceleration of Io, we can use the equation:
centripetal acceleration = (velocity^2) / radius
First, we need to find the velocity of Io. The distance from Jupiter to Io is given as 4.22 x 10^8 m. Since Io completes one orbit in 1.77 days, we can calculate the velocity using the formula:
velocity = distance / time
Converting 1.77 days to seconds (1 day = 24 hours = 60 minutes = 60 seconds), we have:
velocity = (4.22 x 10^8 m) / (1.77 days x 24 hours x 60 minutes x 60 seconds)
Now, we can substitute the calculated velocity and the given orbital radius into the centripetal acceleration formula:
centripetal acceleration = ((4.22 x 10^8 m / (1.77 days x 24 hours x 60 minutes x 60 seconds))^2) / (4.22 x 10^8 m)
After performing the calculations, we find that the centripetal acceleration of Io is approximately 12.18 m/s^2. Therefore, the correct answer is B. Approximately 12.18 m/s^2.