Want to take a guess at what NASA’s longest running continuous research program in physics is? The answer: Gravity Probe-B. Although the satellite wasn’t launched until 2004, its origins go back to 1959, with NASA funding beginning in 1964. GP-B is a laboratory in space, one that uses four precision gyroscopes to measure two effects that grow out of Einstein’s general theory of relativity. The geodetic effect is caused by the mass of the Earth warping local space-time. The frame-dragging effect results from the rotating Earth dragging local space-time along with it.

**Image**: With its telescope aimed at IM Pegasi, a far-off guide star serving as a fixed reference point, the experiment measured tiny changes in the direction of spin of four gyroscopes. Credit: Stanford University.

And if these things seem far too minute to examine, we’re beginning to learn that GP-B is up to the challenge, at least as far as the geodetic effect is concerned. The first look at data from the experiment was released at the American Physical Society meeting in Jacksonville (FL) on April 14. GP-B’s gyroscopes should shift by a tiny amount due to the geodetic effect during the course of a year, departing from their initial alignment by 6.606 arc-seconds (0.0018 degrees).

So far that shift is confirmed to a precision of better than one percent. “It’s fascinating,” says Francis Everitt (Stanford), principal investigator of Gravity Probe B, “to be able to watch the Einstein warping of space-time directly in the tilting of these GP-B gyroscopes — more than a million times better than the best inertial navigation gyroscopes.”

Fascinating indeed. *Centauri Dreams* might have chosen the term ‘awe-inspiring’ — imagine noting an effect this small and using it to confirm insights that grew out of raw theory and the genius of a single man. The mind reels in admiration at both theorist and experiment.

The frame-dragging effect is still in play. Theory says it should cause the spin axis to shift by an angle of 0.039 arc-seconds (0.000011 degrees). That’s 170 times smaller than the geodetic effect and the Stanford team is still trying to extract its signature from the available data. Torque and sensor effects have to be modeled and removed from the result.

But here’s a much more interesting way to put this ongoing work, spoken by GP-B program manager William Bencze:

“We anticipate that it will take about eight more months of detailed data analysis to realize the full accuracy of the instrument and to reduce the measurement uncertainty from the 0.1 to 0.05 arc-seconds per year that we’ve achieved to date down to the expected final accuracy of better than 0.005 arc-seconds per year. Understanding the details of this science data is a bit like an archeological dig. A scientist starts with a bulldozer, follows with a shovel, and then finally uses dental picks and toothbrushes to clear the dust away from the treasure. We are passing out the toothbrushes now.”

Those toothbrushes are going to be busy. For more on the problematic torque and sensor effects, this Stanford news release is helpful. As to the GP-B spacecraft itself, data collection ended in September of 2005 and the team has been working on the analysis of more than a terabyte of information ever since. To perform these extraordinary measurements, the spacecraft and gyroscope spin axes were aligned with IM Pegasi, used as a guide star throughout the mission. Expect the data analysis to be completed in December. Regarding the outcome, we may well have a hunch, but Francis Everitt offers a useful reminder: “Always be suspicious of the news you want to hear.”

Here is the Executive Summary for Gravity Probe B:

http://einstein.stanford.edu/content/exec_summary/GP-B%20PFA%20Report-Pref-ExecSum-scrn.pdf

And here is a 90-minute MPEG-4 streaming video of the complete

public lecture and subsequent Q&A period delivered by Gravity Probe

B Principal Investigator, Francis Everitt in the Hewlett Teaching Center

at Stanford on Thursday, May 18, 2006:

http://einstein.stanford.edu/highlights/hl_video_everitt051806.html

Wet blanket time. With all the fiscal pressure on pure science I honestly feel that there must more deserving experiments that this one to be flown at a cost of a couple hundred million. There was little controversy regarding frame dragging’s reality. Who expected a negative result? This project was a sop to physicists.

Well, it’s either the geodetic effect, or someone left a fingerprint on it during assembly. ;)

Just read through this. At the bottom of the article, right under “Always be suspicious of the news you want to hear”, Google adverts put, in big letters across the article:

JESUS DIDN’T EXIST?

Hmmm…

Gravity is not a conservative force, and I can prove it.

Let’s examine a thought model consisting of two equally massive bodies of material that are weakly interacting. They both experience gravity, but they can freely pass through each other without colliding (think, dark matter).

Let’s say that the two bodies are moving toward each other. They approach with relative velocities that are above escape velocity at infinity. As they approach each other, the pull of gravity increases on each body and they accelerate toward each other.

As the two bodies slide through each other, they are at the peak of their respective velocities.

Then, as they move away from each other they begin to decelerate due to the pull of gravity. They leave each other’s influence with the exact relative velocities they had when they entered each other’s influence. Has work been performed?

Yes! They are both farther along in their respective trajectories than they would have been had they not had the encounter. Gravity isn’t diminshed. Mass isn’t lost. Relative velocities, kinetic energy, and momentum are returned to their pre-encounter quantities. However, the warped space of gravity has caused a measurable shift in their relative positions in space beyond where they would’ve been had they not had the encounter.

Gravity has performed the work of displacing the two bodies ahead, without any cost in energy, mass, or force. Obviously, energy, mass, and force are conserved in the encounter, but the position advancement changes the relative kinetic energy potentials each mass has with any other observer in the universe. Energy potential is therefore changed without cost, due to the influence of gravity. Therefore, gravity is not a conservative force! Or more accurately perhaps, gravity affects the conservation of energy.

Eric, you’ve changed the position of the two bodies from the perspective of an observer outside the 2-body system, however that changes neither the kinetic energy nor the momentum of either body. These are conserved. Position is not in the equation of either quantity (Ek = 1/2 mv^2; p=mv). Yes, these do change for each body during the encounter, though from the perspective of that outside observer the total system energy and momentum is conserved throughout. In the case where both bodies have equal mass, Ek=p=0 (observer co-moving with the system barycenter).

Ok, I’m not a physicist, so hopefully I’ve made no fundamental errors above.

Eric James; Your definition of “conservative force” is incorrect. ANY force is going to cause particles to end up in different positions than they would have been if they hadn’t interacted – so in your definition, any system which includes forces is nonconservative!

Ron S – kinetic energy is NOT conserved (fairly obvious – the speed of the particles changes during the encounter) – total energy is. Since the potential energy DOES depend on position, you have a position-dependent energy.

See conservative force on Wikipedia for a description – basically, what a conservative force means is that if you move a particle along a closed path, no net work is done.

andy, in my post I did distinguish the energy of each object versus the energy of the system of two objects. I thought I said this clearly – maybe not. As for the position I tried to simplify what I wanted to focus on – where the interaction between the bodies was negligible/significant – but, again, looks like I failed at that. I have no disagreement with what you state.

Ah darn, you guys are no fun at all. Let me try a different tack:

It depends really on your definition of “the system.” In the two body system described, I have already stated (more or less) that conservation holds. However, should the definition of the system include certain outside observers, kinetic energy values can indeed change as a result of the little gravity warp/acceleration I described.

Think about it in terms of the much coveted concept of a warp/spacedrive. Do you think you might suddendly and rapidly move from point A to point B in a propellantless fashion, without disrupting the relative kinetic energy potentials between your spacecraft and the rest of the universe?

Furthermore, think about it in terms of energy:

Let’s say our two bodies exhibit inertia, but are unaffected by gravity. Wouldn’t it require work to suddenly accelerate them and decelerate them in such a fashion that they are displaced in space similarly? Would you say that accelerating a body to a greater speed and then decelerating it to its prior speed is not work?

In the isolated system of the body and all the propellant expended it really isn’t work. The total momentum is still conserved, but again the displacement affects kinetic potentials with the spacecraft and other bodies outside the system. Therfore in the context of the great chaos that is the universe, it can be argued that conservation is broken, right?

From what I can tell from your explanation, you’re not being consistent about the reference frame you’re analysing the problem in. If you change reference frame, you’re going to get different values for the kinetic energy.

Let’s take a simple example: an object moving in free space (no forces, so total energy is just kinetic energy). If a 1 kg object goes past you at 1 m/s, it has kinetic energy 0.5 J. However in the reference frame of the object, it is moving at 0 m/s, and has kinetic energy 0 J. This does not mean that energy is not conserved! You’re just analysing the problem in a different reference frame – the conservation laws still apply in the new reference frame, but to the quantities as calculated in that reference frame.

Andy,

Good observations. You’re seeing some inconsistencies. You’re noticing the narrowness of thought. Let’s expand our understanding of the system then.

The gravity warp I described directly affects only the two bodies in question and therefore it seems logical to only consider those two bodies as they relate to one another.

However, the point isn’t to find the symmetry and conservation of simple systems. The point is to examine systems from a broader perspective in order to ask the question: Is the universe truly a model of conservation?

In the case of my model, perspective is everything. From the perspective of objects that may now avoid an interaction with one or the other body (due to the displacement provided by the brief period of acceleration) energy potentials have indeed changed. So has it change with bodies that are now in jeopardy of an interaction. An interaction that otherwise would have been avoided.

It’s all in how you define the system. A narrow view leads to conservation. A broader view can lead to something else entirely.

From some perspectives, kinetic potentials increase. For others, the opposite. All in all though, things can definitely be manipulated one way or the other. For instance: If the objects that will now miss are smaller and relatively slower than the ones that will now interact, the kinetic energy of the interacting system has sharply increased – right?

By definition, any change in the energy potenials requires work. Therefore work is accomplished in either case, right?

Another interesting thought model:

Consider the case where a man picks up a stone on a Pacific beach in California. He walks clear across the continent and deposits his stone on an Atlantic beach in Virginia. Has work been performed?

As far as I can see it (I might be completely wrong here because your explanations are rather vague and hand-wavy), you’re assuming there’s some quantity called “energy” that every observer agrees on. This is not the case. In fact, the idea of relativity (using the term in the general, not specifically Einsteinian sense) is that the laws of physics remain the same for all observers, not that all observers agree on the values of quantities.

Take, for example, a simple system of two masses (for the sake of putting some numbers in, make them 5 kg and 2 kg), undergoing an elastic collision in one dimension, analysed in two reference frames. The first frame is the zero-momentum frame, the second is one in which the first particle is (initially) stationary. We’ll use Newtonian physics and Galilean relativity.

Let’s start by defining the problem in the zero-momentum frame. The first mass is moving rightwards at 2 m/s, the second moves leftwards at 5 m/s.

The total momentum is 5 kg*2 m/s + 2 kg*(-5 m/s) = 0 (this is the zero momentum frame after all!)

The total energy in this example is just the sum of the kinetic energies = 1/2*5 kg*(2 m/s)² + 1/2*2 kg*(5 m/s)² = 35 J

After the collision, the first mass moves leftwards at 2 m/s, the second moves rightwards at 5 m/s.

The total momentum is now 5 kg*(-2 m/s) + 2 kg* 5 m/s = 0 (conserved)

The total energy is now 1/2*5 kg*(2 m/s)² + 1/2*2 kg*(5 m/s)² = 35 J (conserved)

Now let’s transform the initial and final states into the frame where the first mass is initially stationary.

The initial velocities are now 0 m/s and -7 m/s.

The initial momentum is 5 kg*0 m/s + 2 kg*(-7 m/s) = -14 kg m/s

The initial energy is 1/2*5 kg*(0 m/s)² + 1/2*2 kg*(7 m/s)² = 49 J

The final velocities are now -4 m/s and 3 m/s

The final momentum is 5 kg*(-4 m/s) + 2 kg*(3 m/s) = -14 kg m/s

The final energy is 1/2*5 kg*(4 m/s)² + 1/2*2 kg*(3 m/s)² = 49 J

So despite both momentum and energy having different values in the new reference frame, they are still conserved!

At some point in any kind of quantitative discussion, you’re going to have to impose coordinates on the problem – this means you’ve defined a reference frame. Provided the reference frame obeys certain properties (under Galilean and special relativity, the requirement is that the frame is inertial, in general relativity the frame has to be freely-falling), the conservation laws hold in that frame. The same set of conservaton laws hold in other frames (provided those frames also obey the required properties), however the values of the conserved quantities are different! Only certain quantities are invariant when transformed into a new reference frame (in special relativity, examples of invariants are the speed of light and the energy-momentum invariant E²-p²c²).

If you’re going into a non-inertial frame, then Newtonian mechanics no longer holds. To recover Newtonian mechanics in such frames you have to add “fictitious” forces (in a rotating frame, the centrifugal and Coriolis forces).

As for your question about the stone, let’s model the problem as follows: the planet is spherical and nonrotating and there are no frictional forces. In this situation, there is no net work done. The potential and kinetic energies of the stone are the same at the start and at the end of the process! During the process of moving the stone, work is done on the stone (e.g. when it moves up or increases its velocity) and the stone does work (e.g. when it moves down or decreases its velocity). However these effects end up cancelling at the end of the path.

If you want further explanations, I suggest you go study a classical mechanics course – a lot of this stuff is taught at school level!

Oooh. A lecture

anda veiled insult. Maybe you can finish my setup then? Perhaps you already know the answers to the questions I was going to pose? Please… do continue.No I don’t. But I did try to answer the questions you had posed, and I still maintain they are phrased quite vaguely. Could you give a concrete example, with some numbers involved – it would be far easier to see what’s going on with your arguments. If you could give a complete example of what you’re driving at, instead of drip-feeding partial scenarios, that would be more helpful!

Oooh. A lecture

anda veiled insult.I don’t mean to be insulting (though maybe on second reading the mention of school courses could be taken that way – when I wrote it I was thinking more about the level and availability of the material… my apologies if you took it in the wrong way), it’s just that there are far better sources for this kind of information than by pestering commenters to a blog! (Especially since when an issue might need a longer explanation, it gets taken as a lecture…)

Andy,

I haven’t been vague. Why do you think I’ve been vague? In my first two posts I clearly identified the reference frame. It’s the whole universe.

In the first post, perhaps you were confused by my examination of “

a thought model consisting of two equally massive bodies” that functions within that frame?Didn’t this part make it clear: “

…but the position advancement changes the relative kinetic energy potentials each mass has with any other observer in the universe.”In my second post I clearly reiterated this from a different standpoint. I even stated: “

It depends really on your definition of “the system.”‘ and then went on to describe it thusly: “should the definition of the system include certain outside observers…I then likened it with a spacedrive in this sentence: “

Do you think you might suddenly and rapidly move from point A to point B in a propellantless fashion, without disrupting the relative kinetic energy potentials between your spacecraft and the rest of the universe?”I have consistently stressed this point. The universe is the reference frame. How could you miss it? This paragragh should’ve made it plain: “

However, the point isn’t to find the symmetry and conservation of simple systems. The point is to examine systems from a broader perspective in order to ask the question: Is the universe truly a model of conservation?”Did you even read the content before you replied?

I also made lots of references to conservation in isolated systems, but I’ll spare you the references. Read them yourself.

In response to your use of math, it doesn’t even apply to my model. Kinetic energy increases with proximity in gravitational collisions (due to acceleration). Since I was writing about a gravitational model, don’t you think that might be important?

Math sounds authoritarian, even when it’s completely incorrect for the application. That’s why I’d rather stick to thought models (like Einstein used). They’re much easier on the ordinary Joe’s who might like to join in (or not).

The stone question was an analogy in regards to the topology of the universe. In this case though, the topology is fixed. There are no moving parts. More was to follow, but I’ll stop.

Anyway, I was just trying to have some lighthearted fun, examining the consequences of a warp drive (using gravity as an equivalence). I’m sorry you felt “pestered” by it.

P.S. When you’re feeling pestered, why do you respond? Why not just click onto the next heading?

Ok, my apologies for trying to interpret your examples. Also sorry that you found my writing style insulting – I’ll try to watch out for that in future.

I’ve always considered the advance of perhelion to be no more than ‘frame dragging’ due to the solar mass. If you calculate the advance of each planet in the solar system as a length along the planets orbit instead of the usual angular measure (which is different for each planet) you will find the advance is the same for each planet.

Mars and frame-dragging: study for a dedicated mission

Authors: Lorenzo Iorio

(Submitted on 10 Mar 2008)

Abstract: In this paper we preliminarily explore the possibility of designing a dedicated satellite-based mission to measure the general relativistic gravitomagnetic Lense-Thirring effect in the gravitational field of Mars. The focus is on the systematic error induced by the multipolar expansion of the areopotential and on possible strategies to reduce it. It turns out that the major sources of bias are the Mars’equatorial radius R and the even zonal harmonics J_L, L = 2,4,6… of the areopotential.

An optimal solution, in principle, consists of using two probes at high-altitudes (a\approx 9500-9600 km) and different inclinations, and suitably combining their nodes in order to entirely cancel out the bias due to \delta R. The remaining uncancelled mismodelled terms due to \delta J_L, L = 2,4,6,… would induce a bias \lesssim 1%, according to the present-day MGS95J gravity model, over a wide range of admissible values of the inclinations. The Lense-Thirring out-of-plane shifts of the two probes would amount to about 10 cm yr^-1.

Comments: LaTex2e, 15 pages, 5 figures, no tables

Subjects: General Relativity and Quantum Cosmology (gr-qc); Astrophysics (astro-ph); Space Physics (physics.space-ph)

Cite as: arXiv:0803.1286v1 [gr-qc]

Submission history

From: Lorenzo Iorio [view email]

[v1] Mon, 10 Mar 2008 18:51:12 GMT (607kb,D)

http://arxiv.org/abs/0803.1286

Gravity Probe B comes last in NASA review

Panel recommendation is to cut funding of mission by September

http://physicsworld.com/cws/article/news/34284