On maps and globes of the Earth, the locations of the equator, the Arctic and Antarctic circles, and the tropics of Cancer and Capricorn are clearly shown. These circles indicate certain characteristics of the apparent journey that the sun makes over the Earth's surface each year.
There are two other conjured circles on the Earth's
surface that few people know about. They are called "sonic
boom lines," and they indicate the latitudes where the
Earth's surface velocity is equal to the speed of sound.
However, despite federal regulations and public desires, the rotation of the Earth causes many parts of the surface to spin at velocities that exceed the speed of sound. Since the circumference of the Earth is roughly 24,000 miles, the surface speed at the equator due to the rotation of the Earth is about 1,000 miles per hour (well above the speed of sound).
Using simple trigonometry, it is easy to compute the latitude where the Earth's surface is moving at precisely the speed of sound (computational details appear below). At sea level and zero degrees Celsius, that latitude is 44 degrees 21 minutes, and a circle drawn around the Earth at that latitude is a sonic boom line. Of course, there are two such lines; one in the Northern Hemisphere, the other in the Southern Hemisphere.
Unlike the equator and tropics, the exact locations of the sonic boom lines vary according to local altitude and air temperature. For example, using my altitude at Madison, WI (978 feet above sea level) and average atmospheric conditions (11.83 degrees C), the sonic boom line moves to 43 degrees 04' 55" north latitude. Although these effects are very small, they are enough to make the exact locations of the boom lines laborious to determine and in continuous flux. That is why cartographers refuse to put these lines on their maps.
The Earth's motion around the sun and the sun's motion through the cosmos do not affect the sonic boom phenomenon nor produce one of their own. This is because sound waves cannot travel through the vacuum of outer space.
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This article was originally published in the Heurikon Horizon (Heurikon Corporation's employee newsletter), February 1992.
r = R * cos ø Vø = (2 * pi * r) / t Vø = (2 * pi * R * cos ø ) / (24 hours) S = 44.856 * sqrt(273 + T) mph where: ø = degrees of latitude R = radius of the Earth (3958.89 miles) r = radius of rotation at latitude ø t = period of Earth's rotation (24 hours) Vø = velocity at latitude ø due to rotation T = air temperature in degrees Celsius S = speed of sound at temperature T Solving for ø and setting Vø = S gives: ø = arccos [ (24 hours * S) / (2 * pi * R) ] ø = arccos [0.715] (at 0 degrees C) ø = +/- 44.35 degrees