Things get faster when the get closer, because the gravitational energy is converted to velocity. Its just like wondering why things accellerate towards the floor when you drop them, but on a bigger scale.

Add in the fact that you can get though more degrees of rotation per day at even the same velocity by pure dint of the 'r' being smaller in (theta in radians) = r/v, and you're laughing.

Be careful with your quotes, especially when you don't provide a link to the webpage. Luckily, I'm familiar with that particular Straight Dope column--I'm the one who wrote in asking the question. That entire thing should be in quotes, as the Straight Dope was quoting someone else:

I'll try.
You've taken the analogy a bit too far, some people would say, but I say you haven't taken it far enough! The Earth does follow a straight line in spacetime, basically a geodesic. However, just because a path is closed in space doesn't mean it is closed in spacetime. That may be obvious now that I mention it, but it is crucial to the understanding--part of the confusion is the difficulty in understanding why velocity would make the shape of the path any different, right? Just remember, the path is in spacetime, and it is not a closed path.
MTW (Misner, Thorne, and Wheeler's book Gravitation) provides a very good explanation early on in the book that should clear up the whole thing. They use the two examples of the flight of a bullet and a gently tossed ball, and point out that the curvature of the two paths seem to be very different.

That's a lot like your example, isn't it? If both bullet and ball are following straight lines according to general relativity, how come the curvature of the ball's path is so much greater than the curvature of the bullet's path? That's similar to your question of why velocity would make a difference in the orbit of a planet going around the Sun.

MTW says that the curvatures are the same!

All you have to do is calculate what they are in spacetime, instead of just space. The flight of the bullet is fairly flat, but the bullet takes only a short time to travel the path. The height of its arc is a lot less than the height of the ball's path. However, the ball takes a lot longer--and we have the fourth dimension to deal with in general relativity calculations of curvature, remember. To convert time into a quantity that's compatible with space, we have to multiply by c, the speed of light. Since the flight of the ball takes so much longer than the flight of the bullet, the effect of that fourth dimension is to stretch out the path of the ball greatly.

Once, you do that, the curvatures of the ball and the bullet are the same. And that's why gravity is "constant" for both.

Hope that helps.

Or, as I should have noticed earlier, its spaceTIME. Forgetting about that fourth dimension, means that you forget that an object moving at a different velocity is, by the very definition of even a Euclidean spacetime, describing a different path.

I wouldn't accuse you of trying to mislead anyone. I think you are sincerely seeking knowledge. However, saying that the quote is from straightdope.com is not very helpful--that's a big website. There's probably four million articles and posts there. I just provided a direct link--and it shows that you left off the quotation marks. You only included the quotation marks that were included on the webpage, you didn't include the marks that would have shown what was quoted from the Straight Dope.

Just trying to help.

Come on, I was just trying to give a basic example of what velocity has to do with orbit, it can not go further then that. I was not proposing a dissertation on relativity or Newtonian mechanics.

P.S. Of which I could not

__________________
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the change in velocity (some say ecentricity)
hasa a lot to do whith the concept of time
-------------------------------------------------
my experiance WAS:
that Time itself is not UNIFORMED
======================
that would be something like saying
you I would not expect to measure it?
:::::::::::::::::::::::::::::::::::::::::::::::
in the same way once upon the surface of an electron
as Time would be UP ON the surface of the Earth (Sun) {moon} etc
?????????????????????????????????????????????????? ??????????????
once out beyound the Gravity Wave pod comprising the ?
LOCAL GROUP ? I would expect another mmethod of "Doing It'

Kilopi, thanks for the bullet/ball example. I read where you wrote that elsewhere, and I keep it in mind. Time has to be a factor. And you're right, the path is not closed, it would be a spiral due to motion, in my opinion.

But..... last night I came up with two breakthroughs, at least in terms of explaining this in a manner I can understand. However it was 11:30pm and time for bed (cigar time in my backyard is my thinking time) so I only got a hour or two to think it through before conking out. In both, there really is no force of attraction involved. Now remember, I'm not a scientist, so please excuse and/or correct any errors I make. Let me start with the first, since it directly relates to your bullet/ball example, and it leads into the second example that has to do with the apparent attraction of gravity. I'm still writing up the second one and hope to post it today for your opinions. For all I know, these are the accepted theories. I'm sure much greater minds than mine have tackled this issue. But I have never seen it explained quite this way so that a layman can understand. And it brings up some interesting implications.

So on to analogy #1. The analogy again involves a paper cone, and I'll assume the path through space-time is closed to simplify. But this time we must add time to the example.

Previously, I compared our motion through space-time to a straight line drawn on a piece of paper. Mass warps space-time, and sufficient mass will result in a circular path in space-time for an object traveling through it (really a spiral, but that complicates it a bit and I don't see it as necessary for the example). The result would be like bending the paper into a cone so that both ends of the line meet, with the source of the gravity well existing at the closed point of the cone. Really, the better comparison would be to a curved funnel instead of a straight cone, but that's hard to do with paper. Either way, an object on the line still thinks it is traveling in a straight line, and in reality there is no attraction to the source of the gravity well. But to an observer, the object "orbits" the source.

Now, if you add time and the ball/bullet example to this, a faster object would be a line higher up the inside of the cone (farther away from the source), and a slower object would be a line lower inside the cone (closer to the source). Once you go slow enough to make contact with the source of the well, friction from that contact will keep you there unless you can increase your velocity again. And if you travel fast enough, your line won't be in the cone at all and you will not be caught in the gravity well.

So there has to be a relationship between the amount of space-time distance that an object travels in a given amount of time, and where that object's orbit exists in the gravity well. Therefore, Pluto should be traveling much faster than Mercury. The farther out you orbit, the faster you should be going. The closer objects may seem to be faster, but that is because they are deeper in the gravity well, and actually traveling through more and more stretched-out space-time the closer they get, making them appear faster. Likewise, an object traveling towards the sun appears to accelerate, but actually its velocity does not change in relation to space-time as it is still covering the same amount of space-time per second, but the space-time is being stretched more and more the closer it gets. But if the sun were removed from the picture and everything traveled in a flat space-time, Mercury should be much slower than Pluto. Is this true?

If it isn't true, then that obviously flaws the example. That's my first problem with this, since despite the logic of the example, it seems to me that a fast Pluto would exceed the sun's escape velocity at that distance, and a slow Mercury would crash into the sun. But that's answered in analogy #2 which I'm working on.

Then there's my second problem with this example. There is a need for some sort of time/distance (ie speed) relationship with the gravity well, where a faster object orbits farther away than a slower object. Why does this relationship exist? I don't know, but this relationship is further illustrated in my analogy #2.

Lastly, if we take a motionless object (relative to the sun) that enters the sun's gravity well due to the fact that the sun is moving closer to it, it should never gain any motion due to the sun, and once the sun's gravity well leaves the area, the object should still remain motionless in its original spot. Like something floating motionless on the water would appear to move up and down as a wave passes, but it remains in its original spot after the wave passes. (again, #2)

So that brings me to my second analogy which also involves ocean waves... but I don't think I'll have time today. Gotta go. Basically, objects in motion "surf" gravity and space-time, and this is the cause of the apparent attraction and repulsion (which determines orbital distance). I bet you can guess that I was at the beach yesterday . And motionless objects (motionless relative to the center of the universe) have no attractive properties, and cannot be moved from their stationary spot by gravity. Maybe I’ll paste what I’ve written so far into another post, since otherwise I won’t be back until Monday.

But... how does #1 sound so far?

Here's #2. I'm still working on it. But here's what I have so far.

The earth is constantly in motion with regard to space-time. Therefore the earth's gravity well is also constantly moving through a new region of space-time. Looking at the gravity well upside-down, it almost resembles a wave travelling through the water. The water that makes up the specific wave does not travel along with the wave, the wave is continuously moving through new water molecules. That brings me to why an object would be attracted to the top of this wave.

A surfer riding on a water wave requires the wave to be in constant motion. Because the surfer is on the forward side of this wave, he/she will constantly encounter new resistance from new water underneath as the wave travels through the ocean. At the same time, gravity acts on this surfer, pulling him/her down to offset the upward push of the new water entering the wave. The velocity this surfer maintains relative to the earth indicates whether the surfer falls behind, lurches forward, or remains stable with respect to the wave. The amplitude of the wave and its velocity indicate what velocity is necessary by the surfer to "ride the wave", surge ahead, or fall behind. A slower surfer will be pushed toward the top of the wave (and then fall behind it, unless it “wipes out” as I’ll explain later), while a faster surfer can escape the wave and move freely in front of it, without getting pulled to the top (unless the wave catches up again of course).

In this upside-down example, the water is space-time, the wave is a gravity well in motion through space-time, the cause of the well is the Earth (which would exist at the zenith of the wave and is in constant linear motion, and if the surfer hits it, he'll be dragged along by it), and the surfer is you.

I'll get back to this on Monday. But you probably get the picture.

Oh yeah! You asked that question before.
You have to be careful with phrases like "space-time per second." It's a good joke to talk about our journey into the future at a rate of one second per second, but that's kinda like saying I'm walking one mile per mile. What else would you be doing--what possible sense would there be to a "rate" of two miles per mile? (I'm going to think about that.)

If mass curves space, it is curved more the closer to the mass. That's why Mercury can go faster in a circular orbit than Pluto and not fall into the Sun. If Pluto were to go faster, it would speed out of orbit. Just like a golf ball on a green--the faster it rolls, the less it is affected by the undulations of the grass.

In two dimensions I can think of some, but I'm not sure they'd be particularly usefull.

Hey, if you're a frequent flyer and you travel first class, you get two miles per mile all the time.

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Got a quick minute to add to example #2.

So the apparent attraction to the source of the gravity well is only due to the fact that the gravity well is moving through space-time. You are constantly encountering a new spot in space-time that is being warped towards the source of the gravity well, just like the surfer is constantly encountering new water that pushes her up the wave. Should the source (let's say Earth) stop moving in relation to space-time, the attractive force of gravity should no longer apply. Just as if the ocean wave somehow froze in place and stopped moving forward, a surfer on the surface of this wave would be able to move freely with no attractive or repulsive force to worry about. So in effect, we surf the gravity well. We are constantly moving into new space-time that is being stretched toward the center of the earth, but the physical mass of the earth (friction) repels us and keeps us on the surface. The faster we surf, the further away from the source we can get. And if we surf fast enough, we can reach escape velocity and free ourselves from the wave altogether.

So motion keeps us bound to the Earth, and the Earth bound to the sun, etc... This means that the attractive force of gravity should not exist at the center of the universe (the point of the big bang?), since that point is motionless with respect to space-time. Any mass that exists there would simply warp space-time, but there would be no attraction to that point since the gravity well does not move.

So is any of this feasible, or am I completely off?

You are way off, there is no centre to the universe in any cosmological model that I have encountered.

__________________
I am so excited about Canadians ruling the world.
- John Diefenbaker

listyen?
if its simply a matter of gravity
and the Sun really is headed off in the direction of Herculese
then could there be present a lag
{ say of Jupiter } so that when
Jup o .... O was on the Lee side of Herc ------> over there
that Jup would be below(above) the plane of the Ecliptic?
{oh never mind } I forget this is B A asTRon not AS TROL o_g

Ah, yet another chance to paraphrase Kip Thorne. Sorry, you guys who have read it before can skip this:

Thorne says that gravity is not necessarily "really" spacetime curvature nor is it necessarily "really" a field in flat spacetime--not if "really" indicates an ultimate, unambiguous reality of the universe. The spacetime curvature idea is Einstein's wonderful way to model gravity mathematically; a gravitational field in flat spacetime, an odd field which distorts rulers and the timekeeping of clocks, is another equally valid way to model spacetime. According to Thorne the flat-field model gives greater insight when a physicist is working with gravitational waves, and the curvature model is more useful when working with black hole theories, for instance. But if you take them far enough, you find that the two models are exactly equivalent, mathematically speaking.

The question of "ultimate reality: spacetime curvature or field?" is left hanging, and is in Thorne's opinion "uninteresting" because it is mathematically indistinguishable. So I think HankSolo is absolutely right in looking at different ways to think about gravitation...but for me I'll continue to suspect that none of them are "really" gravity, and at the same time all of them are.

(And I also suspect that any description of gravitation except pure mathematics is an analogy, with all the pitfalls and misconceptions that go with analogous thinking.)

OK. That's only a terminology I'm trying to use to find a spot that is motionless with regard to space-time, if that is possible. I figure if the big bang did occur, the point where the universe expanded from should be motionless with regard to space-time. But it doesn't have to be there. The main point I'm trying to find out is if an object can remain motionless with regard to space-time, so it's gravity well does not move through space-time, would another object encounter any attraction to the source of this gravity well? My wave analogy would indicate that a motionless wave can be freely travelled through with no attraction/repulsion, and I'm curious if that would be true.