Question

Lo completes one (circular) orbit of Jupiter in 1.77 days. The distance from Jupiter to Io is 4.22 x 10^8 m. What is the centripetal acceleration of Io?

Answer 1

To find the centripetal acceleration of Io, we can use the formula centripetal acceleration = (velocity)^2 / radius. By calculating the velocity of Io and plugging it into the formula, the centripetal acceleration is found to be approximately 1.814 m/s^2.

Step-by-step explanation:

To find the centripetal acceleration of Io, we can use the formula:

centripetal acceleration = (velocity)^2 / radius

1. First, let's find the velocity of Io. Since it completes one orbit in 1.77 days, we can convert this to seconds by multiplying by 24 and 60 (since there are 24 hours in a day and 60 minutes in an hour). So the orbital period is 1523.2 seconds.
2. To find the velocity, we divide the distance traveled in one orbit by the orbital period. The distance from Jupiter to Io is given as 4.22 x 10^8 m. So the velocity is 4.22 x 10^8 m / 1523.2 s = 2.768 x 10^5 m/s.
3. Now we can calculate the centripetal acceleration. Plugging in the values, we get centripetal acceleration = (2.768 x 10^5 m/s)^2 / 4.22 x 10^8 m = 1.814 m/s^2.

Therefore, the centripetal acceleration of Io is approximately 1.814 m/s^2.