I've written a small text on a calculation
of the time dilatation for satellites.
Now, I'm not a GR expert, so I can be werong.
If it is wrong, point it out please !
Here we go...
Time dilatations and satellites.
1) The Schwarzschild metric:
An acceptable solution of the Einstein equations for a
spherically symmetric, non-rotating object, outside
the object itself, is given by the Schwarzschild metric,
(in god's unit system)
ds^2 = - (1 - 2M/r) dt^2 + dr^2/(1 - 2M/r)
+ r^2(d theta ^2 + sin^2 theta dphi ^2)
Moreover, one can show that for r --> inf. this
thing becomes flat Minkowskian, so an interpretation
is that very far from the mass, t can be seen as
a time coordinate, and r,theta, phi as spherical coordinates.
In the low gravity limit, those spherical coordinates remain
a very good approximation.
Hence, one has the relationship, for observers who are
"stationary" wrt eachother (dr/dt = d theta/dt = dphi/dt = 0)
that the clockrate (that is the rate of proper time wrt
to a clock very far from the object which has proper time
(d tau)^2 = - (ds)^2 for stationary observers -->
d tau / dt = sqrt(1 - 2M/r)
In SI units, this becomes:
d tau / dt = sqrt ( 1 - 2MG/(c^2.r))
So the closer you come to the object, the slower the
clocks appear to tick wrt a clock very far away.
Hence high clocks tick faster than low clocks.
The clockrate of a *stationary* observer at the orbit height
of a satellite at distance r2 from the center of the object,
wrt to a clock on the surface (so, at distance r1 from the
surface), using the low-gravity approximation so that r represents
a real radial coordinate, is:
clockrate up there = sqrt ( ( 1 - 2MG/(c^2.r2) / ( 1 - 2MG/(c^2.r1) )
where clockrate means: wrt a clock on the surface.
2) Orbit, classical calculation:
We assume a circular orbit.
In order for the satellite to keep this orbit, it has
to have such a velocity that the gravity pull is
balanced by the centripetal force:
v^2/R = G.M/R^2
Hence, v^2 = GM/r2 if we use r2 as the orbit radius.
3) Special relativity time dilatation.
Wrt our stationary observer, the clocks in a satellite moving
at a velocity v are slowed down by a factor gamma:
clockrate moving satellite / clockrate stationary observer,
such as seen by the stationary observer = sqrt(1 - v^2/c^2)
Now, this is sqrt( 1 - GM/(c^2.r2))
4) everything together:
CR = clockrate in *moving* satellite, such as seen by an observer
on the ground:
CR = sqrt( 1 - GM/(c^2.r2)) . [...]
[...] sqrt ( ( 1 - 2MG/(c^2.r2) / ( 1 - 2MG/(c^2.r1) )
Numerically, for the earth, 2MG/c^2 = 0.0044 m
Let us call nu = 2MG/(c^2.r1), which is a small, dimensionless
number: it is (r1 = 6366000 m): 6.9e-10.
Let us call rho = r2/r1, it is a dimensionless number,
a bit larger than 1.
CR = sqrt( (1-2*nu/rho) * (1-nu/rho) / (1 - 2*nu) )
A series devellopment (using MuPAD) wrt nu gives:
clockrate := sqrt( (1-2*nu/rho) * (1-nu/rho) /(1 - 2*nu) );
/ / nu \ / 2 nu \ \1/2
| | - --- + 1 | | - ---- + 1 | |
| \ rho / \ rho / |
| ---------------------------- |
\ - 2 nu + 1 /
/ 3 \ 2 / 3 1 \ 3
1 + nu | - ----- + 1 | + nu | - ----- - ------ + 3/2 | + O(nu )
\ 2 rho / | 2 rho 2 |
\ 8 rho /
So, for the MIR, we have, to first order:
rho is about 1.1
clockrate on MIR = 1 + 6.9e-10 * (1 - 3/(2*1.1)) = 1 - 6.9e-10*0.364
= 1 - 2.5e-10
meaning that a clock on the MIR looses about 22 microseconds per
For the GPS satellites, we have (they are at an altitude of
20.200 km above the earth, so rho is 1+20200/6366 = 4.17
clockrate on GPS = 1 + 6.9e-10 * (1 - 3/(2*4.17)) = 1 + 6.9e-10*0.64
= 1 + 4.42e-10
* note the different sign ! *
meaning that a clock on GPS *gains* 38 microseconds per day.
I've done this from scratch, the only thing I looked up
was the Schwarzschild metric. So if I'm wrong, please
explain me !
Ok, I'll switch off my "bashing Keith" mode for a moment :-)
keith stein wrote:
> PRINT " TIME-DILATIONS IN ORBIT"
> PRINT "This program gives the SR and GR predicted time-dilations for"
> PRINT "an Earth Satelite in a circular orbit, at any given altitude."
> REM VALUES OF THE PHYSICAL CONSTANTS USED
> c = 2.99792E+08
> G = 6.67259E-11
> m = 5.976E+24
> R = 6378000
> DO: REM prompt user for 'ALTITUDE OF SATALITE'
> PRINT "Enter M (or m) to simulate the 'MIR Space Station at 300 km'"
> PRINT "OR Enter G (or g) to simulate the 'GPS Satelites at 20,000 km'"
> INPUT "OR Enter the altitude of the satelite in 'km' "; h$: PRINT
> h = VAL(h$) * 1000
> IF h$ = "M" OR h$ = "m" THEN h = 300000!: PRINT "MIR SPACE STATION"
> IF h$ = "G" OR h$ = "g" THEN h = 2E+07: PRINT "GPS SATELITES"
> LOOP UNTIL h > 0
> velocity = SQR(G * m / (R + h))
> gamma# = (1 - velocity ^ 2 / c ^ 2) ^ -.5
> SRtd = (gamma# - 1) * 24 * 60 * 60
This is correct, I think.
> GRtd = G * m * (1 / (R + h) - 1 / R) / c ^ 2 * 24 * 60 * 60
This is not 100 % correct but I think it is a very good approximation,
actually, let's see if I can find your thing back as a series
mu = G.M/c^2, r1 = R, r2 = R + h, I find for the GR part:
dilatgr := sqrt((1-2*mu/r2)/(1-2*mu/r1));
/ 2 mu \1/2
| - ---- + 1 |
| r2 |
| ---------- |
| 2 mu |
| - ---- + 1 |
\ r1 /
/ 1 1 \ 2
1 + mu | -- - -- | + O(mu )
\ r1 r2 /
Which is your factor, except for the sign...
But that's ok, because you also changed the sign of the 1 - gamma.
> NETtd = INT((GRtd + SRtd) * 10 ^ 7) / 10
> PRINT "Altitude = "; h; "m"
> PRINT "Velocity = "; INT(velocity); " m / s "
> PRINT "gamma = "; gamma#
> PRINT "Time lost per day due to SR time dilation = "; SRtd; "sec"
> PRINT "Time lost per day due to GR time dilation = "; GRtd; "sec"
> PRINT "Net time lost per day in satelite = "; NETtd; "micro sec"
> PRINT "N.B. These are Einstein predictions, not mine! - K.Stein "
> Well done Patrick! You did the sums! ,even if you failed to get the
> answers quite right:-(
> I notice that our predictions are similar,but not identical. If on
> reflection you think that you are correct,and that i am therefore
> a little less than correct,i would be gratefull to see your suggested
> modification to my little BASIC program.
about getting the answer right for the MIR,
I took very roughly rho = 1.1 = (R + h) / R for I thought that MIR
was hovering at about 600 km. But you say it is at only 300 km.
Just modify the rho in my formula to the right value (for example,
if you say that MIR is at only 300 km, then my rho should be 1.05.
That brings my prediction to:
clockrate on MIR = 1 + 6.9e-10 * (1 - 3/(2*1.05)) = 1 - 6.9e-10 * 0.428
= 1 - 2.96e-10
and this comes to about 25.5 microseconds per day...
Close enough ?
CONGRATULATIONS KEITH !! ONE DAY YOU WILL BE A TRUE RELATIVIST
> Thank you Patrick.
> keith stein
GRtd = G * m * (1 / (R + h) - 1 / R) / c ^ 2 * 24 * 60 * 60
NETtd = INT((GRtd + SRtd) * 10 ^ 7) / 10
PRINT "Altitude = "; h; "m"
PRINT "Velocity = "; INT(velocity); " m / s "
PRINT "gamma = "; gamma#
PRINT "Time lost per day due to SR time dilation = "; SRtd; "sec"
PRINT "Time lost per day due to GR time dilation = "; GRtd; "sec"
PRINT "Net time lost per day in satelite = "; NETtd; "micro sec"
PRINT "N.B. These are Einstein predictions, not mine! - K.Stein "
Well done Patrick! You did the sums! ,even if you failed to get the
answers quite right:-(
I notice that our predictions are similar,but not identical. If on
reflection you think that you are correct,and that i am therefore
a little less than correct,i would be gratefull to see your suggested
modification to my little BASIC program.
I think your derivation is valid (although I believe the MIR's orbit
is actually about 360 miles up), but I'm always a little uneasy about
splitting up a problem into separate SR and GR components. I suppose
your reason for doing that was to highlight the effects that would be
induced with just the relative velocities in the absence of a
gravitational field. However, as your results show, the velocity
effect is about the same size as the gravitational effect - with the
net result actually changing sign in the range of interest - so I
think it's fair to say that measuring proper time lapses in orbit is
not really a very robust way of testing SR (as opposed to GR)
specifically, for the simple reason that the results won't come
anywhere close to what SR predicts unless we agree to apply the GR
corrections, but if we agree that GR is correct then the status of
SR is moot (because GR totally subsumes SR).
All of which you already know. Anyway, just for fun here's a pure
GR derivation of orbital proper time. It's actually simpler (in my
opinion) than trying to split up the problem into gravitational
and non-gravitational effects. As you said, in the vicinity of an
isolated non-rotating spherical body whose Scwartzchild radius is
2M the metric has the form
ds^2 = A dt^2 - B dr^2 - C d theta^2 - D d phi^2
where A = (1 - 2M/r), B = 1/A, C = r^2, D = r^2 sin^2(theta),
phi = latitude and theta = longitude (e.g., theta=0 at the North
Pole and theta=PI/2 at the equator). Let's say our radial position
r and our latitude phi are constant for each path in question
(treating r as the "radius" in the weak field approximation).
Then A and D are both constants, and the metric reduces to
ds^2 = A dt^2 - D d phi^2
If I'm sitting on the Earth's surface at the North Pole, I have
D=0, so it follows that ds = sqr(1-2M/r) dt where r is the
radius of the Earth.
On the other hand, if I'm in an equatorial orbit with radius R then we
have theta=PI/2, sin^2(theta)=1, and so D is simply R^2. Now, recall
Kepler's law w^2 R^3 = M, which also happens to hold exactly in GR
(where w, M, and R have their GR meanings). Since w = d phi/dt we
have D = R^2 = M/(w^2 R) = (dt/d phi)^2 (M/R). Thus the path of the
orbiting particle satisfies
ds^2 = (1 - 2M/R) dt^2 - (M/R) dt^2
= (1 - 3M/R) dt^2
Now for each test particle, one sitting at the North Pole and one
in a circular orbit of radius R, the path parameter s is the local
proper time, so the ratio of the orbital proper time to the North
Pole's proper time is
d s_orbit / 1 - 3M/R
------------- = / --------------
d s_earth \/ 1 - 2M/r
To isolate the *difference* in the two proper times, we can
expand the above function into a power series in M/r to give
----------- = 1 + (1 - 3r/(2R)) (M/r) + ...
The mass of the earth, represented in geometrical units by half the
Scwartzchild radius, is about 0.00443 meters, and the radius of the
earth is about 6.38(10)^6 meters, so this gives
ds_orbit = ds_earth + (6.9E-10) (1 - 3k/2) ds_earth
which shows that the discrepancy in the orbit's lapse of proper time
during a given lapse delta_T of proper time measured on Earth is
/ 3r \
(delta_T) (6.9E-10) ( 1 - ---- )
\ 2R /
Consequently, for an orbit at the radius R=3r/2 (about 2000 miles
up) there is no difference in the lapses of proper time. Thus, if
someone wants to get a null result, that would be their best choice.
(Perhaps this should be named the "sci.physics radius".) As you
noted, for orbits lower than 3r/2 the satellite will show slightly
less lapse of proper time (i.e., the above discrepancy will be
negative), whereas for higher orbits it will show slightly more
elapsed time than the corresponding interval at the North Pole.
For example, in a low Earth orbit of, say, 360 miles, we have
r/R = 0.917, so the proper time runs about 22.5 microseconds per
day slower than a clock at the North Pole. On the other hand, for
a 22,000 mile orbit we have r/R = 0.18, and so the orbit's lapse of
proper time actually EXCEEDS the corresponding lapse of proper time
at the North Pole by about 43.7 microseconds per day. Of course,
as R continues to increase the orbital velocity drops to zero and
we are left with just coordinate time for the orbit, relative to
which the North Pole on Earth is "running slow" by about 60 micro-
seconds per day, due entirely to the gravitational potential of the
earth. (This means that during a typical human lifespan the Earth's
gravity stretches out our lives to cover an extra 1.57 seconds of
| /*\ |
| MathPages / \ http://www.seanet.com/~ksbrown/ |
> Just modify the rho in my formula to the right value (for example,
> if you say that MIR is at only 300 km, then my rho should be 1.05.
> That brings my prediction to:
> clockrate on MIR = 1 + 6.9e-10 * (1 - 3/(2*1.05)) = 1 - 6.9e-10 * 0.428
> = 1 - 2.96e-10
> and this comes to about 25.5 microseconds per day...
> CONGRATULATIONS KEITH !! ONE DAY YOU WILL BE A TRUE RELATIVIST
WELL I WILL IF THEY FIND ANYTHING OVER 2O MICROSECONDS/DAY ON THE MIR PATRICK!!
but that's an awfull lot of time dilation to find, Patrick.
YOU JUST COULDN'T MISS THE 'SR TIME DILATIONS' ON THE MIR,
COULD YOU PATRICK ?
Just to put this problem in perspective,
there are 8.64 X 10^10 microseconds in a day.
I think that there are reasonable size
quartz or atomic clocks which have a stability
of about 1 part in 10^14 per day.
This should be an easy experiment to make.
Tom Potter http://pobox.com/~tdp
Easy, in principle; extremely difficult in practice -- probably impossible.
To get an experiment lifted up to MIR, you would need to convince
NASA or the Russian Space Agency that:
1. Your experiment is scientifically sound.
2. Your experiment is "worth" the resources required -
weight, astronaut time, spacecraft volume, $/Rubles, etc.
3. Your experiment is "more valuable" than other competing
4. You (and your collaborators) are qualified and experienced
enough to make the experiment a success.
5. You have or can get the necessary funding.
6. There are probably more items on this list....
I seriously doubt such an experiment would be able to satisfy even
one of these requirements.
The first requirement above could probably be met if you
collaborate with several physicists who are experienced in
space experiments and with several physicists who are experts in
SR and GR. But that is probably an impossible selling job --
why should they work with you?
And also, as others have noted in this newsgroup, there are General
Relativistic effects which are comparable in magnitude to the
effects of Special Relativity. It is NOT clear to me that such an
experiment could ever be considered a definitive test of SR.
The problem with so many of the people who post to this newsgroup
is that they assume the world is a "simple" place which conforms to
their wishes. It simply ain't so.
Tom Roberts tjro...@lucent.com
: I think that there are reasonable size
: quartz or atomic clocks which have a stability
: of about 1 part in 10^14 per day.
: This should be an easy experiment to make.
The point is, there are already 24 such clocks up there.
It is called the GPS system. So it is "feasible".
That doesn't mean it is cheap. While I think that
the accuracy of the best clocks is of the order
of what you quote, that doesn't mean that they're
of the size of a wrist watch.
What I don't know if these clocks can keep their
calibration during the violent motions at takeoff
and landing. I think the clocks keep their integrity,
but I don't know if they don't get offset by all those
vibrations and accelerations. It is not easy
to do an experiment with a precision of 14 digits
while getting a kick in the butt.
After all, the GPS clocks were only switched
on AFTER they were in orbit.
Moreover, I think that the best place to do such
an experiment is NOT the MIR, but is good old
space shuttle. The orbit is similar, the time
is ok (a few days) and the take off and landings
aren't too violent.
Now I would also like to see the experiment done
if it isn't too difficult. But putting something
on the shuttle isn't really that cheap.
Nevertheless, it would be fun if it were done.
Not because I have the slightest doubt about the
outcome, but it would have other advantages:
1) We would have a clearcut experiment to show to
the ARNs. Well, that won't cut it.
2) MUCH MORE IMPORTANT: it could be a great
public relations stunt. After all, I'm quite
convinced that 99% of the population hasn't got
the slightest idea of what time dilatation is.
So if it could break the news that Einstein's
theory has been confirmed (once more) by the
advances in technology and space crafts and so
on blah blah blah, the great nation etc...,
has shown the STARTLING RESULT THAT TIME IS NOT
ABSOLUTE, which should shock the average citizen.
KEITH's principle shown false ! Big astonishment !
It is just weird enough to tickle fantasies in
the public, and not too complicated so that nobody
actually understands what it is all about.
If well organised, sales of "dilatation T-shirts"
with sqrt(1-v^2/c^2) written on it, TV - shows
in which old professors come and explain the
twin paradox to people, in between dazzling spectacles
We could also add a lot of bullshit like infinity
lifetime when reaching c, and asking people to fund
research to reach c.
And by the end of the day, requests to Congress to
fund more fundamental research etc...
Yes... if well handled, the money spend on a clock
on the shuttle could very well be a good investment.
This computation is not well coded; it will suffer significant loss of
accuracy due to cancellation errors : if the double precision number
can represent about 13 significant figures, errors in gamma will be
a few times 10^-13; and as gamma-1 is not much larger than that, the
numeric noise will be appreciable in the result. In this sort of
circumstance it's better to expand
(1 + x)^p -1 as
px + p(p-1)x^2/2! + p(p-1)(p-2)^p^3/3! ....
and compute as many terms as make a difference.
> GRtd = G * m * (1 / (R + h) - 1 / R) / c ^ 2 * 24 * 60 * 60
similarly were h/R smaller here it would be worth doing the trick for
(Gm/R)( (1+h/R)^-1 - 1).
> i would be gratefull to see your suggested
> modification to my little BASIC program.
See comments about the sources of numerical error above.
Personal mail to steve#windsong.demon.co.uk (encrypted mail preferred)
PGP public key at http://www.windsong.demon.co.uk/ or on keyservers
pegwit v8 public key =74e039aa21adac343be35a|My opinions, not those of GDS
f006fb0ade30df0401d6306f690c9beec49fb1ef11 |Corporation or its affiliates.
Of course not. He will insist that the clock had to be
painted in pink. Blue clocks don't count.
: HOW MANY TIMES HAVE I GOT TO SAY THIS PATRICK!
: "If clocks on the Mir lose anything over 20 microseconds/day then
: I'M A RELATIVIST."
I DON'T BELIEVE YOU !
: : HOW MANY TIMES HAVE I GOT TO SAY THIS PATRICK!
: : "If clocks on the Mir lose anything over 20 microseconds/day then
: : I'M A RELATIVIST."
: I DON'T BELIEVE YOU !
(No comments regarding whether your belief is correct, but ...)
Well said, Patrick.
Fate may be arbitrary; but it is not biased.
Maybe I'm a little off base here, but I think that the
experiments in question have been pretty much done long ago. Didn't the
early "Timation" satellites settle most of the fundamental question about
velocity and time wrt Einstein and the rest? I was under the impression
that by the mid 70s gathered data was so close to prediction that managers
figured there was no more point in continuing tests--at least until a
whole new generation of timekeeping technology had come around.
I was under the impression that the Time Gods (NRL and NRO gurus)
had pretty much given up on trying to disprove basic relativity and were
into better engineering rather than "pure science"---once again because
everything was checking out. I could hardly believe that anything
approaching 20 microseconds a day could be "lost" ( or not lost as
expected) without a great deal of whooping and hollering---in large part
by designers who would *love* to have an excuse to abandon the
complications of designing in relativistic corrections.
Could you give a little more precise description of the kind of
experiment you would like? If you mean running two clocks, one on the
ground and one in orbit, and comparing them---that should be old hat. How
many decimal places do you want, and with what parameters?
: Big astonishment !
: It is just weird enough to tickle fantasies in
: the public, and not too complicated so that nobody
: actually understands what it is all about.
: If well organised, sales of "dilatation T-shirts"
: with sqrt(1-v^2/c^2) written on it, TV - shows
: in which old professors come and explain the
: twin paradox to people, in between dazzling spectacles
: We could also add a lot of bullshit like infinity
: lifetime when reaching c, and asking people to fund
: research to reach c.
: And by the end of the day, requests to Congress to
: fund more fundamental research etc...
: Yes... if well handled, the money spend on a clock
: on the shuttle could very well be a good investment.
Hmmmm. You are starting to sound an awful lot like Leon Lederman :-).
Steven j Forsberg at au...@imap2.asu.edu wizard 87-01
You are absolutely correct. However, these news groups have several
people who make a job out of denying all this stuff.
> : Now I would also like to see the experiment done
> : if it isn't too difficult. But putting something
> : on the shuttle isn't really that cheap.
> : Nevertheless, it would be fun if it were done.
> : Not because I have the slightest doubt about the
> : outcome, but it would have other advantages:
> : 1) We would have a clearcut experiment to show to
> : the ARNs. Well, that won't cut it.
> : 2) MUCH MORE IMPORTANT: it could be a great
> : public relations stunt. After all, I'm quite
> : convinced that 99% of the population hasn't got
> : the slightest idea of what time dilatation is.
> : So if it could break the news that Einstein's
> : theory has been confirmed (once more) by the
> : advances in technology and space crafts and so
> : on blah blah blah, the great nation etc...,
> : has shown the STARTLING RESULT THAT TIME IS NOT
> : ABSOLUTE, which should shock the average citizen.
> : KEITH's principle shown false !
> Maybe I'm a little off base here, but I think that the
> experiments in question have been pretty much done long ago.
No way. If they had anything like the predicted 24,000 ns/day on Mir,
they wouldn't be offering these very dubious experiments on planes
were the total time dilations were never more than a few hundred ns,
The GPS satelites do have an even larger (claimed) dilation
than the Mir, but that one is opposite in direction to the 'SR' time
dilations. Also in the case of the GPS we are relying on the accuracy
of a time keeping signal transmitted over 20,000 km which is a very
long way. In the case of the Mir it would be possible to compare the
clocks while they were adjacent on the Mir, eliminating any possible
error to signal transmission.
the Mir experiment would be a much more accurate and direct test of
relativity than anything previously published.
> early "Timation" satellites settle most of the fundamental question about
> velocity and time wrt Einstein and the rest? I was under the impression
> that by the mid 70s gathered data was so close to prediction that managers
> figured there was no more point in continuing tests
They have nothing comparable with the decisiveness of the MIR TEST,for sure.
--at least until a
> whole new generation of timekeeping technology had come around.
> I was under the impression that the Time Gods (NRL and NRO gurus)
> had pretty much given up on trying to disprove basic relativity
That's the problem. Where they ever trying to 'disprove' basic relativity ?
I rather think that they were trying to 'prove' it, but they never did eh!
> into better engineering rather than "pure science"---once again because
> everything was checking out.
Right 'better engineering' puts in things like automatic recalibration
of GPS system, so that the system will work whatever the clocks do. I
can't beleive any engineer would really rely on a clock not to lose
the odd nonosecond in ten years, but some scientists seem to think that's
how it works eh!
> I could hardly believe that anything
> approaching 20 microseconds a day could be "lost" ( or not lost as
> expected) without a great deal of whooping and hollering---in large part
> by designers who would *love* to have an excuse to abandon the
> complications of designing in relativistic corrections.
Exactly if it was there, someone would have been hollering about it
before now eh!
> Could you give a little more precise description of the kind of
> experiment you would like?
Sure. 1.Syncronise two clocks
2.Take one to the Mir.
3.Some days later take, on the next lauch,take up the other.
4.Compare the clocks in space.
If the clocks are still syncronised then SR IS WRONG!
If you mean running two clocks, one on the
> ground and one in orbit, and comparing them---that should be old hat. How
> many decimal places do you want, and with what parameters?
I really don't care how many decimal places,i just want to be convinced
that SR clock slowing, like claimed for those twins happens 'at all'.
So far all test haven't even added up to 1 microsecond, and you expect
people to beleive in tales of travelling twins saving years.It's not true,
By the way, it's interesting to note that this ratio goes to zero
when the orbit radius R equals 3M. That's because 3M is the radius
of the orbit of light. This suggests that even if something prevented
a massive object from collapsing within its Schwarzschild radius 2M,
it would still be a very remarkable object if it was just within
3M, because then it could (theoretically) support circular light
orbits, although I don't know how stable such orbits would be (even
neglecting interference from infalling matter). If neutrinos are
massless I suppose there could also be neutrinos in 3M orbit around
such an object.
Recognizing that there are probably all kinds of reasons why this
couldn't actually occur, I wonder if theoretically there would be
any reason to expect orbiting photons and/or neutrinos to be
concentrated in one plane, or if the orbits would be distributed
evenly about all axes. In other words, could there be a stable
solution consisting of a solid mass inside 3M surrounded by a
spherical "shell" of orbiting photons at 3M? Presumably this
could only work as long as the energy content of the shell was
small enough that it didn't significantly affect the field.
Also, how would a photon get INTO a circular orbit at 3M? Maybe
if it was emitted by a decay of some infalling particle right
at 3M and in precisely the right direction, but that seems
highly improbable. Is there be any mechanism by which a free
photon could be "captured" into a circular orbit?
Exactly. But Keith thinks that only *his* experiment will test
the theory, ignoring the fact that it relies on exactly the
same principles as the GPS satellites.
>No way. If they had anything like the predicted 24,000 ns/day on Mir,
>they wouldn't be offering these very dubious experiments on planes
>were the total time dilations were never more than a few hundred ns,
When was the first time the US flew on Mir?
When were the airplane experiments done? What is the relative cost?
What other experiments have been done with satellites?
This will suggest why experiments were done with an economical
and accessible mode of transportation, and why it is not realistic
to expect people to pay for two shuttle launches to test Keith's
theory that everything about GPS is wrong.
>The GPS satelites do have an even larger (claimed) dilation
>than the Mir, but that one is opposite in direction to the 'SR' time
Keith is able to reject that GPS navigation works, but is sometimes
willing to accept evidence that time intervals are affected by gravity
and uses this to argue that time intervals are absolute.
> The GPS satelites do have an even larger (claimed) dilation
>than the Mir, but that one is opposite in direction to the 'SR' time
>dilations. Also in the case of the GPS we are relying on the accuracy
>of a time keeping signal transmitted over 20,000 km which is a very
>long way. In the case of the Mir it would be possible to compare the
In the case of GPS satellites, it looks like you are confusing TD ("in
the opposite direction") with the artificially induced error in the
civilian band of the GPS signal. The GPS system broadcasts at two
frequencies:1.023 MHz (civilian) and 10.23 MHz (military). The
civilian frequency has random errors purposely inserted into the data
stream to REDUCE accuracy in order to maintain military security. The
random errors produce an uncertainty of approximately 25 meters,
however, recent techniques using differential measurement have yielded
accuracies up to 1 cm (as of 1995). The military frequency uses an
encrypted code to prevent foreign militaries from achieving high
accuracy from our GPS.
In addition to the above induced delay, sensitive measurements need to
be calibrated to account for delays due to changing ionosphere
conditions. This is done by a comparison of both the civilian and
military signals (since they are at different frequencies).
Incidentally, after achieving centimeter accuracy in 1995, the next
step was to get it down to one millimeter ... haven't heard any word
on that though.
Todd Spohnholtz roo...@wwa.com
University of Illinois at Chicago
: > Maybe I'm a little off base here, but I think that the
: > experiments in question have been pretty much done long ago.
: You are absolutely correct. However, these news groups have several
: people who make a job out of denying all this stuff.
Ahhhhhh. Of course, it's Usenet! And to think, I was going to
look up the guy that used to subject me to long lectures on the travails
of relativistic corrections when trying to statistically correlate
"How's it going Fred?"
"I'm glad you asked. If a geosynch Hydrogen Maser fails to 3
sigma with an overpolar LEO c-beam......"
"Uh, Yeah, nice talkin' to you Fred. Gotta go!"
Steven j Forsberg at au...@imap2.asu.edu Wizard 87-01