How many miles does the Earth travel in space each day?
The first and simple answer is found by calculating the circumference of the Earth's orbit around the sun and dividing by the number of days in a year.
The average distance from the sun to the Earth is 150 million kilometers or 93.2 million miles. Multiplying by 2 Pi gives 585.6 million miles for the circumference. Dividing this by 365.25 days/year gives 1.603 million miles per day. The actual average orbital velocity is closer to 18.5 miles/second, accounting for the fact that the orbit is slightly elliptical. Using this value gives a more accurate 1.598 million miles per day average.
This seemingly simple question also touches on some fundamental principals of relativity and questions in cosmology. Our solar system is in motion relative to the Milky Way galaxy and our entire galaxy, along with the local cluster of galaxies is in motion relative to the Cosmic Background Radiation. This last motion is measured by observing a motional red-shift in the background radiation. (see: http://csep10.phys.utk.edu/astr162/lect/cosmology/cbr.html )
The entire solar system, including the Earth, moves through the cosmic background at about 370 miles per second for a total of 32 million miles per day. This is much larger than the orbital motion, but it is not yet known what is the cause or meaning of this relative velocity.
Scott Wilber, President, ComScire - Quantum World Corporation
'The mathematician's patterns, like the painter's or the poets, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.'