Question

Ganymede completes one (circular) orbit of Jupiter in 7.16 days. The distance from Jupiter to Ganymede is 1.07×109m . What is the centripetal acceleration of Ganymede?

Answer 1

The centripetal acceleration of Ganymede can be calculated using the provided orbital period and radius by first determining the orbital speed and then applying the centripetal acceleration formula.

Step-by-step explanation:

The student asked about the centripetal acceleration of Ganymede, which is the largest moon of Jupiter, and completes one orbit around Jupiter in 7.16 days. To calculate the centripetal acceleration, we use the formula a = v^2 / r, where v is the orbital speed and r is the radius of the orbit. Since the question provides the orbital period (T = 7.16 days) and the radius of the orbit (r = 1.07 x 10^9 m), we can first find the speed by using v = 2πr / T, and then plug that into the centripetal acceleration formula.

First, we convert the period from days to seconds (7.16 days * 24 hours/day * 3600 seconds/hour), then calculate the speed, and finally the centripetal acceleration. Remember, the speed must be in meters per second (m/s) since we are using meters for the radius as well.

Answer 2

The centripetal acceleration of Ganymede is approximately 112.64 m/s².

Step-by-step explanation:

To calculate the centripetal acceleration of Ganymede, we can use the formula:

ac = v² / r

Where

ac is the centripetal acceleration

v is the velocity

r is the radius or distance from the center of rotation.

In this case, the distance from Jupiter to Ganymede is given as 1.07×10^9m, and we need to find the centripetal acceleration.

Ganymede completes one orbit in 7.16 days.

To calculate the velocity, we need to find the distance Ganymede covers in one day and then convert it to meters per second (m/s).

Distance covered in 1 day = 2πr

V = (2πr) / (24 * 60 * 60)

Substituting the given values, we get:

V ≈ 10,871 m/s

Now we can calculate the centripetal acceleration:

ac = (V²) / r

Substituting the given values, we get:

ac ≈ 112.64 m/s²

So therefore the centripetal acceleration is 112.64 m/s²