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How fast?
How fast is earth travelling through space?
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Firstly, for jake-the-peg, I don't see where anyone asked for or responded with absolute speed, whatever that may mean... however we easily know the individual speeds at which the earth moves relative to various objects, to which Loosehead has alluded. Why is it so difficult to bring these individual sums into a total? Someone, and this speaks to MargeB as well, "standing" at an independent point in space could readily "see" the individual motions of the earth, calculate each speed and total them... Hmmm... I'm repeating myself... What's the big deal?
Absolute speed means the speed at which an object is moving without reference to any other object or position in space, or without reference to absolute rest. Apart from light (a special exception), and even though it was thought to exist for the vast majority of human civilization, it is total guff: totally meaningless. All speeds only make sense with reference to another object or point in space.
Now do we accept this? If not, why not? If so, it becomes clear that to talk of a 'combined speed' (presumably by assuming that there are different 'planes') is pointless: it gives no meaningful information about the object's relative speed. We are talking of speed here, not velocity, which alone could consider reference to multiple objects.
The original question, lest we loose sight of it, asked simply " How fast is earth travelling thru space"... It appears MargeB's answer would be zero... Hmmmm that provides a lot of information to the inquirer. My answer can be shown to be correct when all speeds are considered. Does it provide a great deal of information in and of itself? Probably not, but fact is it still represents all modes of motion and provides an answer to the question. Additionlly, absolute speed, within the realm of Einstein is c (speed of light)... I have no idea of where you obtained your definition. And, finally, velocity =speed unless there is a change in either or a change in vector occurs... BTW, an object can and regularly does travel in different planes of motion simultaneously... consider the simple Yo-Yo childs toy . It certainly has a measurable speed as it rotates around its axis, but it also has a measurable speed as it moves up or down the string. Now do an 'out and back' trick and yet another 'plane of motion' is introduced and it has a measurable speed. All of the speeds can be totaled, but the information provided by that total is interesting, but not much more...
Clanad - you were talking about an observer "at an independent point in space". But there is no such thing. The observer is at a point relative to somewhere.
Anyway, from the point of view of the solar system:
Earth's distance from Sun = 93 million miles
Therefore distance of Earth's orbit around the Sun = 584 million miles
Therefore speed of Earth within orbit = 584million miles per year = 19 miles per second
Or, from the point of view of the galaxy:
Earth's distance from centre of Galaxy = 30,000 light years = 176,000 million million miles
Therefore length of Earth's orbit around the galaxy = 1.1 million million million miles
Speed of rotation of the galaxy = once every 220 million years
Therefore speed of Sun & Earth around the Galaxy = 5000 million miles per year = 158 miles per second
As Loosehead said, the Earth is also on a bigger journey because the galaxy itself is travelling through a large cluster of galaxies, which is moving through the universe.
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I'm somewhat surprised at your lack of imagination... especially you, bernardo. All artistic depictions of space scenes, including those of the spiral arms of our Milky Way galaxy, are done from an independent, yet imagined point in space. No one has ever seen our galaxy except edge on as viewed from earth. The closest yet attained are those magnificent photos from the Hubble Telescope. Therefore, earth, viewed from such an imagined vantage point could be "seen' to be moving in all the planes or modes of motion and the speed of each can be measured and totaled. BTW, bernardo, the examples you presented are part and parcel of the total speed I quoted. MargeB, the expansion, or more accurately, inflation you describe is one of the major proofs of the Big Bang theory of initial creation of the universe. Distant objects are measured to be speeding away from each other in combined speeds that are greater than the speed of light, yet we know the speed of light, c, is inviolable...
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