Astronomy - rotation period of planet and wind speeds

In summary, the rotation period of Saturn at the equator, very deep in the atmosphere is 10 hrs which is equivalent to a rotation rate of 10 km/s. The equatorial winds at higher levels in the atmosphere blow at a speed of 250 m/s from west to east. To find the rotation period of the higher level, one can use a balloon in the Saturn atmosphere as a reference point. The balloon's speed is a combination of the rotation and wind speeds of the planet. The circumference and speed of the balloon can be calculated using the known rotation speed and wind speed at the equator. However, as you go up in the atmosphere, the balloon's speed will vary depending on the rotation and wind speeds at that level
  • #1
mangoluverin
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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!
 
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  • #2
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.
 
  • #3
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!
 
  • #4
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.
 

1. What is the significance of a planet's rotation period?

The rotation period of a planet refers to the amount of time it takes for the planet to complete one full rotation on its axis. This is an important factor in understanding a planet's climate, weather patterns, and geological processes.

2. How is a planet's rotation period determined?

A planet's rotation period can be determined through observations using telescopes or spacecraft, as well as through mathematical calculations based on the planet's size and mass.

3. What factors can affect a planet's rotation period?

The rotation period of a planet can be affected by its distance from the sun, its size and mass, and any external forces such as gravitational pull from other objects in its orbit.

4. How does a planet's rotation period impact wind speeds?

The rotation period of a planet can impact wind speeds by creating temperature and pressure differences in the atmosphere, leading to the formation of wind currents. The faster the rotation period, the more likely it is to have strong and consistent winds.

5. Can a planet's rotation period change over time?

Yes, a planet's rotation period can change over time due to factors such as tidal forces from other objects, changes in the planet's internal structure, or collisions with other objects. However, these changes are often very gradual and may not be noticeable in a human lifetime.

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