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No such thing as a stupid question, just stupid..

by K.J.Healey
Tags: stupid, thing
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K.J.Healey
#1
Jun29-07, 11:24 AM
P: 641
grad students that should know things by now (like me!):
[though in my defense, I have not had any GR yet, only what I've picked up in some books]

My 2 questions:

The effect of our time distortion from being near the earth is cool and all, can I assume we have a similar GR effect from being "near" the Sun?

Is the effect any different because on the earth we are held at a potential by a normal force(ground) while around the Sun we're "held" equipotential by our elliptical orbit (which is moving, and thus constantly accelerating)? If the earth stopped rotating, it would change some correct? Because we lose some acceleration?

I care not about magnitudes, I know it may be very small.
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pervect
#2
Jun29-07, 12:05 PM
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P: 7,634
I think the information in this article may be what you are looking for:

http://en.wikipedia.org/w/index.php?...ldid=110624445

I'll give a short quote
Since ancient times, planetary ephemerides were calculated using a time scale based on the Earth's rotation: Universal Time (UT). In the late nineteenth century it was realised that this time scale was not uniform: the observed timing of planetary positions did not match up correctly with UT. After atomic clocks were invented, they were used from 1960 to realise a new uniform time scale, Ephemeris Time (ET). ET was henceforth used for the time variable in planetary ephemeris calculations.

ET itself was not entirely satisfactory either. Although it was a uniform time scale within its reference frame, it was subject to time dilation when compared with the proper time experienced by other bodies in the Solar system. Because ET was based on subjective Earth time, the Earth's orbit introduced periodic non-uniformities when comparing ET against the true independent time variable of the ephemerides. Earth time ticks slower when it is near perihelion and speeds up in its orbit (in January) and faster near aphelion (in July).
So, the question of what sort of time to use depends on what you are observing. If you are observing something on Earth, Terestial Time (TT) is what you want to use - the clock ticks are uniform for local phenomenon. If you're studying distant events, you want to use some other time scale. (TCG, perhaps - you'll see it's quite an alphabet soup if you read the entire wikipedia article).
K.J.Healey
#3
Jun29-07, 12:19 PM
P: 641
Hmm, well assuming an atomic clock on earth then. I'm simnply asking for confirmation of my understanding that there IS a GR time effect from:

1. Earths Mass
2. Earths Rotation
3. Sun's Mass
4. Earth's Solar Orbit(barycentric is fine)

Correct?

pervect
#4
Jun29-07, 12:35 PM
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P: 7,634
No such thing as a stupid question, just stupid..

What are you observing? If you are observing something on Earth, there isn't any effect from (for example) the Earth's solar orbit.

If you are comparing an Earth clock to a distant clock (somewhere off-Earth), then you do have to take the Earth's orbit into account.

One way of looking at this - all clocks tick at 1 second per second. When we talk about "clocks ticking at different rates", it's not that the clocks are "really" ticking at different rates. There isn't any way to single one clock out as "better" than another. Rather, the fact that the clocks don't appear to tick at the same rate is due to the way in which we compare them, and the details of the rate depend on what clocks we are comparing and how the comparison process is done.
K.J.Healey
#5
Jun29-07, 12:55 PM
P: 641
Ahh, sorry I wasn't more clear. I have a decent grasp of time, and I meant, our earth-time as compared to some external observer, by the external observer (who is stationary to the sun) at some distance.

Lets say the comparison is done by a guy in a ship watching his watch, and a 1-earth second light pulse emitted from the earth (thats a toughie, since the rotation of the earth itself makes a problem for the light emitters being in view, and then whether they CAN emit a simultaneous pulse with eachother since even the emitter's time is different from eachother, if only slightly).
But I feel for that effect, you can wave your hands, say you have a pulse at 4 points on the equator, quartered. It does not matter if we know how they're timed with eachother, it only matters that the OBSERVER knows.

So there would be a difference between an observer at a distance, and some clock on earth from the observers standpoint by:

1. The gravity of the earth causing an effect.
2. The acceleration felt by any rotating body, regardless of mass.
2. The gravity of the sun.
3. The acceleration felt by any revolving body, regardless of mass.

This isn't part of any fancy self-theory or crap like that, merely clarifying my understanding. That both gravitic fields AND normal acceleration (wrt to observer who is noninertial), cause discrepencies in the time of that object by said observer.

I guess the point of GR is actually to turn all these rotational/orbital accelerations into an added mass, that adds to the effective mass, and changes the time stictly from a gravitational viewpoint. (right?). Inertial bodies are more "massful" in the sense they have an increased gravitational field?
pervect
#6
Jun29-07, 03:04 PM
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P: 7,634
Quote Quote by Healey01 View Post
Ahh, sorry I wasn't more clear. I have a decent grasp of time, and I meant, our earth-time as compared to some external observer, by the external observer (who is stationary to the sun) at some distance.

Lets say the comparison is done by a guy in a ship watching his watch, and a 1-earth second light pulse emitted from the earth (thats a toughie, since the rotation of the earth itself makes a problem for the light emitters being in view, and then whether they CAN emit a simultaneous pulse with eachother since even the emitter's time is different from eachother, if only slightly).
But I feel for that effect, you can wave your hands, say you have a pulse at 4 points on the equator, quartered. It does not matter if we know how they're timed with eachother, it only matters that the OBSERVER knows.

So there would be a difference between an observer at a distance, and some clock on earth from the observers standpoint by:

1. The gravity of the earth causing an effect.
2. The acceleration felt by any rotating body, regardless of mass.
2. The gravity of the sun.
3. The acceleration felt by any revolving body, regardless of mass.

This isn't part of any fancy self-theory or crap like that, merely clarifying my understanding. That both gravitic fields AND normal acceleration (wrt to observer who is noninertial), cause discrepencies in the time of that object by said observer.

I guess the point of GR is actually to turn all these rotational/orbital accelerations into an added mass, that adds to the effective mass, and changes the time stictly from a gravitational viewpoint. (right?). Inertial bodies are more "massful" in the sense they have an increased gravitational field?
I'm sorry, but I'm having a hard time following exactly what it is that you are asking. Probably you are trying to ask something very simple, and I'm getting lost in the technical complexities.

I think the best simple answer I can give is that in GR, it is the metric that tells all, and that what you need/want to do is to learn about the GR metric.

The way that GR works is this. One assigns coordinates to events in space-time. The particular assignment of coordinates to events is allowed to be totally arbitrary. In astronomy, there are certain conventions as to how to do this in a "standard" manner - the flexibility to use any coordinates one wants is good, but to communicate results it's good to have a 'standard' set.

Digging around for a reference, aa.usno.navy.mil/colloq180/Proceedings/petit.ps seems to be pretty good, though it's rather technical as I mentioned (it's also in postscript).

http://www.bipm.fr/utils/en/pdf/CCTF14-EN.pdf around page 113 also discusses some of these issues.

Such a coordinate system defines a metric - furthermore, defining the metric defines the coordinate system. The approach in the above document is to define the coordinate system by defining the metric.

Some issues arise because the definition isn't exact - some terms are specified simply as being "small", rather than being given exact values. There is work ongoing in this area.

Given the metric, the propagation of signals such as light can be analyzed (it follows a null geodesic).

Going through your list:

Earth mass: affects the metric. Knowing the metric tells us all we need to know about the Earth mass (and sun mass, and other important bodies).

Rotation of the Earth: very very small metric effects due to frame-dragging, mostly the rotation of the Earth affects the velocity of the source.

Gravity of the sun: included in the metric

The acceleration felt by any body: computable from the metric.

So when we know the metric, we know everything we need to know to compute any particular experimental results.

In fact, the manner in which the standards bodies specify the coordinates is to define the metric.


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