[zipper]

I only read a few paragraphs so far, but already I have issues with some statements:

Mach 1 is the speed of sound at sea level

No, Mach 1 is the speed of sound, regardless of altitude.

When a gyroscope is spinning, it resists being pushed around because it is interacting with the Earth, the stars, and distant galaxies. If those objects didn't exist, the gyroscope would have no inertia.

No, it resists being pushed around because it has mass (inertia). That doesn't require interaction with other objects.

[LibWhacker]

The speed of sound is quite a complicated subject and is dependent upon a number of different variables, some of which one could guess, some of which one would have difficulty guessing. For example, it depends on the density of the material through which it is propagating; it's faster in rock than in air and faster in iron than in rock, etc. It can depend upon the temperature, heat capacity and pressure of a medium. It can even depend upon the frequency of the sound wave. It's enough to drive a physics student mad.

You might think, well then, let's restrict our attention to a gas, since the atmosphere is a gas. But... there are different types of gases, including one called an ideal gas, and the rules are different for each of them. Ideal gases do not exist in nature but physicists like them because the calculations are easier and the speed of sound in an ideal gas does not depend on things like temperature, pressure, density, etc. Air is almost an ideal gas, but not quite. So there is actually a variation in the speed of sound in air with different altitudes... For example, check out the following table (from Wiki):

Given normal atmospheric conditions, the temperature, and thus speed of sound, varies with altitude:

Altitude	Temperature	m·s−1	km·h−1	mph	knots
Sea level	15 °C (59 °F)	340	1225	761	661
11,000 m−20,000 m (Cruising altitude of commercial jets, and first supersonic flight)	−57 °C (−70 °F)	295	1062	660	573
29,000 m (Flight of X-43A)	−48 °C (−53 °F)	301	1083	673	585

One can even say the speed of sound varies with latitude, as in the following graph:

Ignore the information for Titan, Mars and Venus for now, and just concentrate on the graph for the Earth. Notice that the speed of sound is different at various altitudes at the North Pole (dashed line) than at the equator (solid line). I think it has to do with the fact that air is not an ideal gas and that the average temperature at the North Pole is colder (of course) than at the equator, but I'm not sure. Like I said, it's enough to drive a person who is trying to understand this stuff insane!

Regarding your other point. It's a good point and I have a hard time myself believing that my mass sitting here on Earth has anything to do with every little lump of rock clear across the universe. But that is exactly the point of the article. And you have to admit Ernst Mach's point makes you stop and think:

What if there was only one object in the universe? Mach argued that it could not have a velocity, because according to the theory of relativity, you need at least two objects before you can measure their velocity relative to each other... Taking this thought experiment a step further, if an object was alone in the universe, and it had no velocity, it could not have a measurable mass, because mass varies with velocity.

[jpsb]

Re Mach 1, that is what I thought to but just to be certain I looked it up

"Mach number is a common 'ratio' unit of speed when one is talking about aircrafts. By definition, Mach number is a ratio of the speed of a body (aircraft) to the speed of sound in the undisturbed medium through which the body is traveling. It is said that the aircraft is flying at Mach 1 if its speed is equal to the speed of sound in air (which is 332 m/s or 1195 km/hr or 717 miles/hour.) An aircraft flying at Mach 2 is flying at twice the speed of sound in air, etc."

http://www.physlink.com/Education/askExperts/ae58.cfm

Now I am confused Mach is a ratio but Mach 1 is an actual speed?