Sorry I wasn’t more succinct in wording my question. I was on my way out the door and didn’t have time to phrase it properly.
54 years ago, the earth occupied a specific point in space. At this moment, it occupies a different point in space. If you could draw a straight line between these two points, how long would it be?
There, how’s that? Is 1,022,444,402,400 km the answer I’m looking for?
Thank you for your indulgence. (This info is for someone’s birthday card.)
Maybe the OP is writing a time travel story, where the time traveler unexpectedly winds up in space, millions of miles from Earth.
To say that a point in space at time T1 is the same as/different from a point in space at time T2 is physically meaningless whenever T1 and T2 are different. If you could meaningfully talk about such things, then you could meaningfully determine which objects were at rest and which were moving, and thus determine a privileged frame of reference, at least so far as absolute rest is concerned, which, in itself, cannot be done.
Let’s illustrate. Pretend there’s nothing in the universe except you and me. If you see me hurtling past you at 5 MPH, and I, correspondingly, see you hurtling past me at 5 MPH, how are we to say which of us, if any, is still and which is moving? Well, as the symmetry of the situation may help illustrate, we can’t, in absolute terms. There’s no principled general means to do so; motion is all relative. If we wanted to, we could adopt the convention that “If your displacement from Indistinguishable remains constant, then you are staying still”, but this is an arbitrary convention, and we could just as well pick some other frame of reference to use. That’s the point people are trying to make; questions of how far something has travelled over time are only meaningful once such conventions regarding the selection of a frame of reference are made.
You’ll not find a larger frame of reference anywhere in the visible universe.
The most relevant distance would be the 54 trips traveled around the sun. As explained up-thread, linear motion is relative. So you need something to compare it to. If you’re looking for an enormous sounding distance, you can find one, but it won’t make much sense to anybody (and doubtfully very humorous) in the context of a birthday card to let them know they’ve traveled blahblah miles relative to M45. Just go with the distance traveled around the sun.
Okay, I understand those explanations. Thing is, I’ve used “trips around the sun” before, and wanted a new spin, so to speak.
Still, though…NASA has sent probes to the outer planets and beyond. They had to know where a celestial body would be in the future, right? Wouldn’t some part of those calculations have to consider the distance the craft was going to travel? I know that wouldn’t be a straight line, but they still need to know how far it is from point A (earth) to Point B (object they wish to land on/fly by), true?
My thread-starting-fu isn’t too good this week. 
I realize we can’t define the center of mass of the universe, but can we define the center of mass of the known universe?
Is it anywhere near Texas?
Worst of all, there’s no answers to the problems at the back of the book.
Skip the arm of the galaxy; the sun is not part of one. Nor is any star, for that matter.
Substitute the motion of the sun around the galaxy. But it’s not a simple circle. The sun does not orbit in the exact plane of the galaxy, but rather oscillates above and below that plane much like a horse on a merry-go-round that goes up and down as it goes around. The exact parameters of this orbit are not very well known, so we can’t really say exactly how far the sun travels in one orbit.
However, in 54 years the sun has only travelled an extremely small fraction of that orbit, so you could just use the relative motion of the sun to a large number of not-so-nearby stars to figure its galactic motion in that time. That, I believe, is how they came up with the figure for the sun’s orbital velocity as quoted by DDG earlier in the thread.
As far as the galaxy’s motion, it’s moving within the Local Cluster, which can be thought of as a three-way orbit with the Andromeda and Triangulum galaxies. In turn, the Local Cluster is moving towards the Great Attractor as mentioned previously in the thread. And as been pointed out, that motion overwhelms all the rest in its magnitude.
If you’re measuring with respect to the Cosmic Microwave Background, the motion caused by the expansion of space-time is zero.
Yes but that wouldn’t really help. If the probe is being launched from Earth, you just have to know how fast and how far it’s going to travel * relative to Earth*. But you want to measure how far the Earth itself is travelling, so the question remains, relative to what?
In any case mankind has only sent probes to intercept other bodies within our solar system. (I’m counting comets in that definition, btw.) Yes, we sent the Voyager probes out into deep space, but those just keep heading on out of the solar system in no particular direction having done their stuff with the planets – and in any case, it would take something like 77,000 years for Voyager I to reach Alpha Centauri, the nearest star to the Sun, even if it was headed that way!
Sending a probe to intercept, say, (because I have to) Uranus is easy, relatively speaking. We know the orbits of the planets relative to the Sun and the Earth, and the solar system can be thought of as one coherent lump moving through space.
Mainly, because everything in the universe is moving away from everything else, on average. The closer you get to us, the less that’s true–many objects on our local group of galaxies are movuing towards us. Your extragalactic markers look stationary with respect to us, but that’s just because they’re so distant. As Stranger and others note, the most stable reference is the cosmic microwave background–at least it’s a reference (nearly) everyone can agree upon; in any science, that’s a pretty impressive achievement.
Our galaxy (and the rest of the Local Group, and indeed, the entire Virgo Supercluster) is in motion with respect to the CMB, or alternatively, the Hubble Flow (the aggregate motion of all objects in the observable universe). Out motion with respect to our own position due to expansion is, by definition, zero, but we are definitely have linear motion with regard to the sum of everything else.
Stranger
Of course it is. I was taught in school that Texas IS the center of the universe. Oddly, it wasn’t in science class though. :dubious:
Perhaps Texas is a black hole? 
Not the OP, but might I suggest the galactic core? That’s relatively stationary as far as things in the galaxy are concerned. Then for movement of the galaxy as a whole the point the universe is expanding away from would be a good reference point as it’s prolly pretty stationary too.
Hijack;
All of the numbers above explain why we have never seen a time traveler.
Because they disappear at this moment, and reappear in the past or future at the exact same position. Which is no longer located anywhere near Earth.
Oops.
oh by “stationary” I mean the common notion of the term where in the larger thing is assumed not moving.
Like for example how when your speedometer reads 60 MPG what it means is your auto is moving 60 MPH relative to the earth, even though from your relative stand point you’re standing still and the earth is moving past you at mph.
In other words when moving around relative to a larger body the larger body is stationary.
The galactic center of the galaxy has no rotation at it’s center point so it’s only motion is the movement of the galaxy as a whole through the local group. So it’s a good benchmark to compare relative speeds of other galactic things (like our sun) with. The point everything in the universe is expanding from shouldn’t be moving if Newton’s third law holds universal truth.
The universe isn’t expanding away from any one point. It’s just expanding. I’ll let the physicists fill you in on the details.
There is no such thing as “the point the universe if expanding away from”. The universe is expanding uniformly at all points in space.
Except, oddly, in Brooklyn. http://www.sciam.com/article.cfm?id=misconceptions-about-the-2005-03&page=5
(My thanks to Stranger on a Train for that interesting link in the “Edge of the Universe” thread: At the Edge of the (theoretically visible) Universe - Factual Questions - Straight Dope Message Board . Interesting link.)