Space Probe vs the Sun - Relativistic Frames of Reference

[Loudzoo]

I've had a good search through the archives and haven't found an answer to this question. Many apologies if this is old ground. . .

Having read the threads on the Pioneer Anomaly a quick question to which I'm sure there is very simple answer (I just don't know what it is !):

When calculating the expected trajectory of a space probe (or other low mass object) as it flys away from the sun (or other high mass object) its velocity will determine to what extent relativistic phenomena begin to become significant vs Newtonian expectations.

Do the rocket scientists consider the frame of reference of the space probe, the sun, or a 3rd party observer (say, the rocket scientist on earth) when calculating the expected trajectory of the probe ?

In a simple relativistic model with two bodies (the sun and the probe) its impossible to say which body is moving away from the other.
From the space probe's frame of reference it could be stationary and the sun could be flying away. Relativistically that would increase the sun's mass, and increase its gravitational influence on the probe that could lead to an otherwise unexpected deceleration in the motion between the two bodies.
From the sun's frame of reference it is stationary, the probe increases in mass due to its velocity but this causes no unexpected deceleration in the probe's trajectory from the sun because that tiny increase in mass (at any velocity other than closely approaching to the speed of light) has no material impact on the shared gravitational attraction between the two bodies.

Which frame of reference is correct to use ? Does it impact what trajectory we measure as a 3rd party observer with a different frame of reference again?

 

[Bill_K]

According to Wikipedia, Pioneer's current velocity is 12 km/sec, well within the domain of Newtonian mechanics.

 

[Loudzoo]

Thanks Bill K - understood. 2 responses:
- At 12km/s that is non-relativistic for the probe but would it not begin to register a relativistic effect on the sun i.e. if the sun was moving away from you at 12 km/s that would generate a small but measurable increase in the mass of the sun vs being at rest

- On a more generic note, if we talk about relativistic velocities - what is the implication for the original question? Which is the correct frame of reference to use ?

 

[Dale]

At 12km/s that is non-relativistic for the probe but would it not begin to register a relativistic effect on the sun i.e. if the sun was moving away from you at 12 km/s that would generate a small but measurable increase in the mass of the sun vs being at rest

12 km/s gives a gamma factor which is different from 1 by only 800 parts per trillion. We cannot currently measure mass to that accuracy.

Regarding the choice of frame of reference, any will work. It is completely arbitrary. That is the whole point of the principle of relativity, you cannot make a wrong choice of coordinate system because the laws of physics are the same in all frames.

 

[Loudzoo]

thanks for the clarification DaleSpam - very helpful. Apologies in advance if I'm totally missing the point (or if my arithmetic is wrong) but to approximate: 800 parts per trillion is nearly 1 part per billion. We can measure mass to that that level of accuracy no ?

In the case of the sun - an increase in mass of 800 parts per trillion would still increase the mass by 1.6^21kg (assuming rest mass of the sun is 2*10^30 kg) - approximately the mass of Saturnian moon, Iapetus.

Admittedly this isn't much but as a non-rocket scientist - I'm amazed this is so easily dismissed !

Regarding the frame of reference question - in the simple 2 body model I envisage (the sun and the probe in motion away from each other) even at what are normally described as non-relativistic speeds there is a material difference between mass of the sun at rest vs the sun in motion (at 12km/s, or more for that matter) that could cause a measurable difference in the gravitational attraction between the two bodies - at close range . . .

Apologies once again if I'm totally missing the point !

 

[Dale]

thanks for the clarification DaleSpam - very helpful. Apologies in advance if I'm totally missing the point (or if my arithmetic is wrong) but to approximate: 800 parts per trillion is nearly 1 part per billion. We can measure mass to that that level of accuracy no ?

No, we cannot even determine the mass of the kilogram prototype to that level of accuracy.

 

[Naty1]

In a simple relativistic model with two bodies (the sun and the probe) its impossible to say which body is moving away from the other.
From the space probe's frame of reference it could be stationary and the sun could be flying away. ...From the sun's frame of reference it is stationary, the probe increases in mass due to its velocity...

This logic is faulty...although the first sentence is correct...we can tell the space probe is accelerating

 

[Loudzoo]

Fair enough. But that shouldn't detract from the notion that the mass of the sun at a velocity of 12m/s still increases by 1.6^21 kg, relative to a body at rest - irrespective of whether we can measure the rest mass accurately to the 12th or 13th decimal place in the first place.
The perceived mass increase still occurs, no ?

 

[Loudzoo]

This logic is faulty...although the first sentence is correct...we can tell the space probe is accelerating

Thanks Naty1 - that's helpful for me to understand. How can we tell the space probe is accelerating ?

 

[Naty1]

Instruments onboard...like an accelerometer...will record such acceleration...

 

[D H]

Instruments onboard...like an accelerometer...will record such acceleration...

Not to the level of accuracy needed to detect the Pioneer anomaly. This anomaly was detected after the fact by analysts on the Earth.

 

[Dale]

Fair enough. But that shouldn't detract from the notion that the mass of the sun at a velocity of 12m/s still increases by 1.6^21 kg, relative to a body at rest - irrespective of whether we can measure the rest mass accurately to the 12th or 13th decimal place in the first place.
The perceived mass increase still occurs, no ?

Sure, you can always assert that an effect which is too small to detect occurs. However, there is no point in doing complicated corrections when their effects are far below the uncertainty of the measurements you can make. The velocity and curvature are so low that Newtonian physics is fine.

To put this in perspective, you are looking at relativistic effect on the order of 800 parts per trillion. Even the mass of a piece of non-reactive metal maintained in carefully controlled conditions is only known to within about 20 parts per billion. And the mass of the sun is only known to within 100 parts per million or so.

 

[bcrowell]

There is a whole field of solar-system tests of general relativity. A classic example is the anomalous precession of Mercury's perihelion. The Cassini probe recently provided some of the most sensitive solar-system tests ever of GR. Even though the relativistic effects are very small, some of the experiments are extremely precise. In the case of Cassini, they measured the round-trip time for radio signals to a precision of 1 part in 10^14.

The main thing that GR tells us about the Pioneer anomaly is that the Pioneer anomaly is almost certainly not gravitational in origin. GR incorporates the equivalence principle, and that aspect of GR has been tested to extremely high precision. If the Pioneer anomaly was caused by a gravitational effect, then it would obey the equivalence principle, and therefore other test masses in the same vicinity of space would experience the same effect. That is contrary to what we observe with the outer planets and their satellites: http://arxiv.org/abs/0912.2947v1

 

[Naty1]

Not to the level of accuracy needed to detect the Pioneer anomaly.

yes...I thought the OP question was about acceleration in general...versus velocity...

 

[pervect]

I've had a good search through the archives and haven't found an answer to this question. Many apologies if this is old ground. . .

Having read the threads on the Pioneer Anomaly a quick question to which I'm sure there is very simple answer (I just don't know what it is !):

When calculating the expected trajectory of a space probe (or other low mass object) as it flys away from the sun (or other high mass object) its velocity will determine to what extent relativistic phenomena begin to become significant vs Newtonian expectations.

Do the rocket scientists consider the frame of reference of the space probe, the sun, or a 3rd party observer (say, the rocket scientist on earth) when calculating the expected trajectory of the probe ?

I believe that the JPL horizons ephermis is one of the ones most usually used to calculate such things - corrections welcome.

http://ssd.jpl.nasa.gov/?horizons
ftp://ssd.jpl.nasa.gov/pub/ssd/Horizons_doc.pdf

There appear to be two main choices described in section 9 - ICRF/J2000, and FK4/B1950.

The above PDF article seems not to distinguish between "frames of reference" and "coordinate systems", treating them as the same.

The ICRF is described at http://rorf.usno.navy.mil/ICRF/

FK4 seems to have been supplanted by FK5, and the ICRF by ICRF2 since the horizon's PDF was written.

Also, I haven't been able to find much on what metric (if any) is associated with the ICRF - nor what solar system metric is used by the Horizon ephermis, though I'm pretty sure the later would be some variant of a PPN metric (not positive, though).

 

[Loudzoo]

Thanks everyone for trying to help me understand this - much appreciated.

At this pre-fledging stage I'm less concerned about measurement problems and measurement inaccuracies (or the pioneer anomaly for that matter) – although they are interesting.

I'd like to understand the real implications of the physics first.

Is it possible to distinguish whether a probe is moving at a constant velocity away from the sun, or whether the sun is moving away from the probe at a constant velocity, from the perspective of the probe, irrespective of the actual velocity?

 

[Dale]

Is it possible to distinguish whether a probe is moving at a constant velocity away from the sun, or whether the sun is moving away from the probe at a constant velocity

No. That is the principle of relativity.

 

[DrGreg]

Is it possible to distinguish whether a probe is moving at a constant velocity away from the sun, or whether the sun is moving away from the probe at a constant velocity, from the perspective of the probe, irrespective of the actual velocity?

Not only can you not distinguish the difference, there is no difference: this is just two different ways of describing the same thing. There's no such thing as "actual velocity", only the velocity of something relative to something else.

 

[bcrowell]

Is it possible to distinguish whether a probe is moving at a constant velocity away from the sun, or whether the sun is moving away from the probe at a constant velocity, from the perspective of the probe, irrespective of the actual velocity?

No, it isn't. That's why it's called relativity.

 

[csmyth3025]

...Is it possible to distinguish whether a probe is moving at a constant velocity away from the sun, or whether the sun is moving away from the probe at a constant velocity, from the perspective of the probe, irrespective of the actual velocity?

The short answer to your question is "no". It just depends on which frame of reference you want to use. If you're (hypothetically) standing on the sun, you can say that the probe is moving away from you. If you're standing on the probe, you can say that the sun is moving away from you.

There is no "absolute" frame of reference. Thanks to good old Albert Einstein, it's all relative.

Chris

 

[Loudzoo]

Thanks DaleSpam, DrGreg, bcrowell and csmyth3025- very clear, and as I understood.

So this is where I get confused. If a probe and the sun are cruising away from each other at 12km/s (or as this is just a little thought experiment let's say 150,000 km/s, or some other relativistically significant speed) and on the presumption you can't tell which object is actually doing the moving it has a massive implication (please forgive the pun).

In the sun's frame of reference the probe is moving away very quickly from it. Fine, no problem - the probe undergoes an increase in mass but that doesn't materially increase the mutual gravitational attraction between the two bodies.

From the probe's frame of reference, it is stationary and the sun is moving at a high velocity away from it. Wouldn't this cause a material increase in the sun's already enormous mass that would cause a material increase in its gravity, resulting in a material increase in the mutual gravitational attraction between the two bodies ?

 

[Dale]

In the sun's frame of reference the probe is moving away very quickly from it. Fine, no problem - the probe undergoes an increase in mass but that doesn't materially increase the mutual gravitational attraction between the two bodies.

You might want to re-think this assertion. Give it a little thought and see if you realize your mistakes.

 

[Loudzoo]

Thanks DaleSpam - more cryptic than I was hoping for ! Would this be a fair summary ?

It doesn't matter (and its impossible to determine) whether one body is moving away from the other or not. They are mutually moving away from each other. The sun's mass (and therefore its gravitational influence) must increase, whatever the frame of reference, determined by its velocity relative to the probe. Likewise the probe must also experience an increase in mass as determined by its relative velocity to the sun.

Is that correct ?

 

[D H]

While velocity does play a role in general relativity, this role isn't what you appear to think it is (which appears to be using the relativistic mass to compute gravitational acceleration).

Just to make things clear, gravitational mass does not increase with speed.

 

[Dale]

It doesn't matter (and its impossible to determine) whether one body is moving away from the other or not. They are mutually moving away from each other. The sun's mass (and therefore its gravitational influence) must increase, whatever the frame of reference, determined by its velocity relative to the probe. Likewise the probe must also experience an increase in mass as determined by its relative velocity to the sun.

Is that correct ?

There are essentially two problems with your statements above:
1) as D H mentioned, the source of gravity in GR is not mass but the entire stress energy tensor. As you boost a system you not only increase its energy, but also its momentum, so other terms in the tensor become significant besides just the energy density component.

2) Even if GR were simply Newtonian gravity with relativistic mass it is only the product of the masses that determines the gravitational force between two objects in Newtonian gravity. So if the sun's mass were to increase by a factor of gamma or if the probe's mass increased by a factor of gamma the force would be the same either way according to the naive approach.

 

[Loudzoo]

Ok - that is where I was getting confused.
1) In my simplistic lack of understanding I thought there was a direct correlation between mass and gravity. I did not realize that an increase in relativistic mass does not cause an increase in the gravitational potential of a body.
I appreciate the time you've all taken to sort out the source of my confusion.
I may be back with other questions, but for the time being - thank you !

 

[Loudzoo]

Just to make things clear, gravitational mass does not increase with speed.

why does the first line of the following abstract say "According to the general theory of relativity, kinetic energy contributes to gravitational mass." ?

(http://arxiv.org/PS_cache/gr-qc/pdf/9909/9909014v1.pdf)

2) Even if GR were simply Newtonian gravity with relativistic mass it is only the product of the masses that determines the gravitational force between two objects in Newtonian gravity. So if the sun's mass were to increase by a factor of gamma or if the probe's mass increased by a factor of gamma the force would be the same either way according to the naive approach.

Although its irrelevant as this approach is naïve and wrong, I disagree with your analysis here. Sun's mass increase by a factor of gamma would be MUCH larger than the probe's mass increase by a factor of gamma. Therefore the product of the masses would be different in each scenario . . . and the gravitational force would be different

 

[Dale]

Although its irrelevant as this approach is naïve and wrong, I disagree with your analysis here. Sun's mass increase by a factor of gamma would be MUCH larger than the probe's mass increase by a factor of gamma. Therefore the product of the masses would be different in each scenario . . . and the gravitational force would be different

No, this is very basic algebra. Just write down the Newtonian equation for the gravitational force and multiply the mass of the Sun by gamma. Then write down the Newtonian equation for the gravitational force and multiply the mass of the probe by gamma. Then compare the two results.

 

[D H]

why does the first line of the following abstract say "According to the general theory of relativity, kinetic energy contributes to gravitational mass." ?

(http://arxiv.org/PS_cache/gr-qc/pdf/9909/9909014v1.pdf)

That article is talking about the kinetic energy of an object in the object's rest frame -- in other words, the object's temperature. The intrinsic mass of a collection of particles is not the sum of the rest masses of the particles that comprise the collection. It is instead the sum of the relativistic masses of the particles with respect to the collection's center of mass frame.

 

[Loudzoo]

No, this is very basic algebra. Just write down the Newtonian equation for the gravitational force and multiply the mass of the Sun by gamma. Then write down the Newtonian equation for the gravitational force and multiply the mass of the probe by gamma. Then compare the two results.

I must need remedial algebra classes I'm afraid ! even simpler:

if gamma = 1.5

(suns mass x 1.5)+(probe's mass) > (sun's mass)+(probe's mass x 1.5)

As you said the assumptions are all wrong but this is what I was referring to.

 

[Loudzoo]

That article is talking about the kinetic energy of an object in the object's rest frame -- in other words, the object's temperature. The intrinsic mass of a collection of particles is not the sum of the rest masses of the particles that comprise the collection. It is instead the sum of the relativistic masses of the particles with respect to the collection's center of mass frame.

Ok - thanks again. I'm ready to wave the white flag at this point I think - but here's another stab at it:

Kinetic energy in the form heat increases the gravitational mass - yes?
Kinetic energy in the form of rotation increases the gravitational mass - yes ?
But kinetic energy in the form relative velocity does not increase the gravitational mass ?

 

[Dale]

if gamma = 1.5

(suns mass x 1.5)+(probe's mass) > (sun's mass)+(probe's mass x 1.5)

So what? What does this have to do with the gravitational force? Look at the expression for the gravitational force between two masses:
http://hyperphysics.phy-astr.gsu.edu/hbase/grav.html#grav

 

[Loudzoo]

So what? What does this have to do with the gravitational force?

As you eloquently argued above it has nothing to do with gravitational force. Just showing where my miscalculation came from.

 

[Dale]

Ah, I understand your post now.

 

[Naty1]

Loudzoo:

Post # 25:

"Originally Posted by Loudzoo
It doesn't matter (and its impossible to determine) whether one body is moving away from the other or not. They are mutually moving away from each other. The sun's mass (and therefore its gravitational influence) must increase, whatever the frame of reference, determined by its velocity relative to the probe. Likewise the probe must also experience an increase in mass as determined by its relative velocity to the sun.

Is that correct ?

There are essentially two problems with your statements above:
1) as D H mentioned, the source of gravity in GR is not mass but the entire stress energy tensor. As you boost a system you not only increase its energy, but also its momentum, so other terms in the tensor become significant besides just the energy density component.

2) Even if GR were simply Newtonian gravity with relativistic mass it is only the product of the masses that determines the gravitational force between two objects in Newtonian gravity. So if the sun's mass were to increase by a factor of gamma or if the probe's mass increased by a factor of gamma the force would be the same either way according to the naive approach..."

First, just to mention, aspects of this stuff are VERY subtle...and the guys answering your questions here helped me with similar questions several years ago...still do...

I learned along the way that their answers are often more sophisticated than they appear and so deserve very careful reading, a lot of thought, but still may not become clear until other perspectives from other discussions are studied...so keep at it!. A related issue if you studied this stuff many years ago as I did is that language (terminology) and explanation preferences change over time...[/QUOTE]

Dalespam's point #2 deserves careful attention...the difference between Newtonian and GR is MORE than just changes in mass...

I still scratch my head sometimes reading this stuff...For example when Dalespam says above

the source of gravity in GR is not mass

I think he means..."not JUST mass"...

You posted:

Kinetic energy in the form heat increases the gravitational mass - yes?
Kinetic energy in the form of rotation increases the gravitational mass - yes ?
But kinetic energy in the form relative velocity does not increase the gravitational mass ?

I'd like to hear from an expert on those questions.

Regarding terminology, I think that in terms these guys prefer, they'd tend to say gravitational attraction changes rather than MASS...

My take is that all three affect gravitational attraction in GR. In othr words, any energy has gravitational effects...even when there is no rest mass...like light...