If you monitor Saturn's atmosphere and you see a storm at a longitude of 0° west on one day and at a longitude of 90° west 3 days later,what is the average wind speed on Saturn at this storm's latitude? Note that these positions are measured on a coordinate system that rotates with the planet's interior.(The radius of Saturn is 6 × 10⁷ meters.)

Question

Quizplus · Accepted Answer

Using the formula for angular speed, we can calculate the rotation rate of Saturn:

ω = θ/t

Where θ is the angle between the two storm positions (90° - 0° = 90°), and t is the time between the two observations (3 days = 259,200 seconds):

ω = 90°/259,200 s 
ω = 0.00035°/s

We can convert this to radians per second by multiplying by π/180:

ω = 0.0000061 rad/s

The wind speed at the latitude of the storm can be found using the formula:

v = rω

Where r is the radius of Saturn (6 × 10⁷ meters):

v = (6 × 10⁷ m)(0.0000061 rad/s) 
v = 366 m/s

Therefore, the average wind speed at the latitude of the storm is approximately 360 m/s, which corresponds to choice C.

If You Monitor Saturn's Atmosphere and You See a Storm