Astronomy - rotation period of planet and wind speeds

[mangoluverin]

Homework Statement

assume that the rotation period of saturn at the equator, very deep in the atmosphere is 10 hrs. higher in the atmosphere, the equatorial winds blow west to east at 250 m/s. What would be the rotation period of this higher level in the atmosphere?
also know - maximum wind speed at equator = 450 m/s (from another source)

Homework Equations

The Attempt at a Solution

I converted the rotation period of 10 hrs into rotation rate using 2pi(saturn's radius)/rotation period to get a value of 10 km/s. Now I am stuck - how do I find the relationship between rotation period/rate and wind speed? And does this relationship stay constant as you go up in the atmosphere? I guess ultimately I want to know is - how do I find the rotation rate/period for the upper level in the atmosphere? Thanks!

 

[Borek]

Imagine a balloon in the Saturn atmosphere. Its speed depends both on the rotation and wind. What is its speed? Once you know the speed and circumference, calculating the time is a breeze.

 

[mangoluverin]

But how on Earth can I start to go figuring the circumference and speed of the balloon? Would it's speed at the equator deep in the atmosphere be the rotation speed and the wind speed? But as I go up in the atmosphere - since it's speed varies with the rotation and wind, how can I figure out it's speed if I don't know the rotation speed? I am very confused. Any help would be really appreciated. Thanks!

 

[Borek]

Circumference of the planet - you have already used it, so you know how to calculate.

Balloon speed is that of surrounding gas - that is in turn sum of wind and linear speed at the 'surface' (I suppose 10 km/s that you calculated is just this value).

If there will be no wind, you will just calculate speed of the surface treating the planet as a rigid body, so period and radius are enough. Now there is completely independent move of the outermost surface - that either adds or subtracts (depending on the direction) to the speed of the rigid body.