Re: If a large balloon floated stationary 80km (50m) above the Earth's surface

Dear Roger,
     This is a good question. The first thing that we have to look at any 
time we are talking about things moving about the earth is called the 
Coriolis Effect. While the math can become rigorous in these applications, 
the principle is quite simple. The effect says that anytime you leave the 
surface of the earth, you keep the speed of the ground that you left from. 
It is fairly simple to figure out the velocity of the ground at the 
equator. The earth has a radius of 6380km, multiply that by the distance 
it travels (2 pi) and divide that by the amount of time it takes. So 
(6380km x 2 x 3.14)/24hours = 1670 km/hr. Now down in New Zealand, on the 
40 degree south parallel, your velocity is smaller, because you are 
traveling around a smaller part of the earth. Smaller with respect to the 
axis of the earth, not smaller in general. So the radius about the axis of 
New Zealand is 4255 km (6380 cosine 40) Through the same process as above 
we find that your tangental velocity is only 1114 km/hr. You can see that 
there is nothing magical going on here, we are just figuring different 
velocities for different radii. Okay, now that we know what velocity we 
are moving at on New Zealand, we are to figure out what happens if we go 
80 km into the air. Now looking at the Coriolis principle, we know that we 
will keep the velocity of the ground that we left from (1114 km/hr). But 
now we are increasing our path of travel, we have a new radius 4335 km.
Since our velocity doesn't change how do we find out what the earth below 
us is doing? I have an idea, lets see how long a day to us would be up 
here. So our new radius is 4335 km multiply by 2xpi, now instead of 
dividing by time we will divide by velocity, and that should give us our 
new time. What do you know our new time is 24.5 hours, seems reasonable. 
Now in order to find out how fast the earth "appears" to be moving, we 
will take that time and put it back into our old equation. V= (4255 x 2pi) 
now divide by 24.5 and we find our apparant velocity is 1091 km/hr. Now 
the important thing to remember here is that we are still moving at the 
exact same speed as the earth below us, but because we are on a larger 
radius, it appears as if the earth is moving faster than we are. If we 
take the true velocity and subract our apparent velocity, we see a 
difference of 23 km/hr. This is how much faster the earth appears to be 
moving beneath us. 
     Now we had to do a lot of calculation just to figure out how 
something sitting still in the air behaves to the Coriolis effect, you can 
imagine how much calculation goes into flying a jet around the world! This 
is a fascinating subject that is fun to play with. You can learn a little 
more about the Coriolis effect at stratus.edu/gg101/coriolis/coriolis.html
Happy flying!

Sincerely,
Norman Parker