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Mercury's Perihelion Precession
20 years 4 months ago #10210
by Jim
Replied by Jim on topic Reply from
Sorry about the sloppy language reguarding a vital detail. How does MM and GR differ in how this detail is determined?
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20 years 4 months ago #10915
by tvanflandern
Replied by tvanflandern on topic Reply from Tom Van Flandern
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Jim</i>
<br />Sorry about the sloppy language reguarding a vital detail. How does MM and GR differ in how this detail is determined?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">GR is a metric theory, but uses a different metric coefficient in the radial coordinate than in the two transverse coordinates. MM is not a metric theory. It attributes a physical density to the potential field that varies with distance from the source mass. This produces the same numerical effects as GR for light-bending and gravitational redshift (by refraction in the potential field instead of by "space-time" curvature), but a different result for perihelion advance.
Put another way, GR and most competitors change the force in the radial direction to get a perihelion advance. MM adds a new force in the transverse direction instead, a force that is somewhat like a drag force in this variable-density potential field. In doing so, MM gets the correct perihelion advance in a single term. GR has to combine three terms which are individually 133.3%, 33.3%, and -66.6% of the final value. When these are added, the result is 100% of the final value. -|Tom|-
<br />Sorry about the sloppy language reguarding a vital detail. How does MM and GR differ in how this detail is determined?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">GR is a metric theory, but uses a different metric coefficient in the radial coordinate than in the two transverse coordinates. MM is not a metric theory. It attributes a physical density to the potential field that varies with distance from the source mass. This produces the same numerical effects as GR for light-bending and gravitational redshift (by refraction in the potential field instead of by "space-time" curvature), but a different result for perihelion advance.
Put another way, GR and most competitors change the force in the radial direction to get a perihelion advance. MM adds a new force in the transverse direction instead, a force that is somewhat like a drag force in this variable-density potential field. In doing so, MM gets the correct perihelion advance in a single term. GR has to combine three terms which are individually 133.3%, 33.3%, and -66.6% of the final value. When these are added, the result is 100% of the final value. -|Tom|-
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20 years 4 months ago #10215
by Thomas
Replied by Thomas on topic Reply from Thomas Smid
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by tvanflandern</i>
Jupiter's period is not a good approximation of the Sun's motion with respect to a barycenter because Saturn's effect is comparable to Jupiter's. So this assumption is also wrong.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">It is true that Saturn's barycenter distance is not much smaller than Jupiter's, but if you insert the corresponding orbital period and radius into the equation derived above, you will find that Saturn's effect is merely a few percent of Jupiter's.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">I hope the preceding is enough to get you back to the drawing board and interested in learning some basic mechanics, then some celestial mechanics. We have reached and passed the point where you have received helpful advice about your idea. We are now plunging into this becoming a tuition-free seminar on mechanics. I do not think it is reasonable to impose on others in that way. Either learn the subject matter yourself from books, or register for a course and pay the tuition.
It always amazes me when people jump into a new field and assume that all the minds who have been there before made some elementary mistake. This appearance should instead be taken as one's first clue that one's own knowledge is still at a naive level.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">I thought you had an open mind regarding critical arguments, but now you sound exactly the same as those people who try to counter any critics of mainstream science issues merely by pointing out that they have superior knowledge and hence are right by default.
The existence of a scientific theory alone is no proof of its correctness but it has to be able to defend itself against any critical arguments or questions. In this case this is the, in my opinion, logical conclusion that the motion of the barycenter should be taken into account when evaluating Mercury's perihelion precession because
1) The orientation of Mercury's orbit has to be referred to the fixed stars
2) The sun is not in an inertial reference frame relative to the fixed stars because of its motion around the barycenter.
3) As shown, adding the Sun's motion to Mercury's in this sense, changes the equation of motion in a similar way and magnitude as the GR correction does (which leads to the 43" result).
All these points are strictly logical steps without any further assumptions involved.
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Jupiter's period is not a good approximation of the Sun's motion with respect to a barycenter because Saturn's effect is comparable to Jupiter's. So this assumption is also wrong.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">It is true that Saturn's barycenter distance is not much smaller than Jupiter's, but if you insert the corresponding orbital period and radius into the equation derived above, you will find that Saturn's effect is merely a few percent of Jupiter's.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">I hope the preceding is enough to get you back to the drawing board and interested in learning some basic mechanics, then some celestial mechanics. We have reached and passed the point where you have received helpful advice about your idea. We are now plunging into this becoming a tuition-free seminar on mechanics. I do not think it is reasonable to impose on others in that way. Either learn the subject matter yourself from books, or register for a course and pay the tuition.
It always amazes me when people jump into a new field and assume that all the minds who have been there before made some elementary mistake. This appearance should instead be taken as one's first clue that one's own knowledge is still at a naive level.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">I thought you had an open mind regarding critical arguments, but now you sound exactly the same as those people who try to counter any critics of mainstream science issues merely by pointing out that they have superior knowledge and hence are right by default.
The existence of a scientific theory alone is no proof of its correctness but it has to be able to defend itself against any critical arguments or questions. In this case this is the, in my opinion, logical conclusion that the motion of the barycenter should be taken into account when evaluating Mercury's perihelion precession because
1) The orientation of Mercury's orbit has to be referred to the fixed stars
2) The sun is not in an inertial reference frame relative to the fixed stars because of its motion around the barycenter.
3) As shown, adding the Sun's motion to Mercury's in this sense, changes the equation of motion in a similar way and magnitude as the GR correction does (which leads to the 43" result).
All these points are strictly logical steps without any further assumptions involved.
www.physicsmyths.org.uk
www.plasmaphysics.org.uk
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20 years 4 months ago #10218
by tvanflandern
Replied by tvanflandern on topic Reply from Tom Van Flandern
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Thomas</i>
<br /><blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">[tvf]: This appearance should instead be taken as one's first clue that one's own knowledge is still at a naive level.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">I thought you had an open mind regarding critical arguments, but now you sound exactly the same as those people who try to counter any critics of mainstream science issues merely by pointing out that they have superior knowledge and hence are right by default.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">And your response sounds much like the most common I hear from people unwilling or unable to learn the field they wish to criticize: "I have greater insight because my mind is not corrupted by being taught the standard way of thinking."
I merely pointed out that your knowledge of basic mechanics is insufficient to accomplish the task you have set for yourself, after I gave many examples to illustrate this is so. But you are now crossing the line into shifting the burden of proof for your ideas into a burden of proof by others for the mainstream model. Science does not work that way. If you are content to have discovered the secrets of the universe privately, and are willing to take them to your grave, so be it.
But if you want anyone to pay attention to what you have to say, you must learn the conventional theory you are challenging and start by showing what is insufficient about it that your idea will cure without introducing new problems. This is important both to show that your understanding of the subject is sufficient, and as common ground for communication with others.
In the case in point, it is untrue that the standard model assumes a fixed Sun. Placing the Sun at the origin of coordinates does not mean it is fixed any more than placing the origin of coordinates at the observer means the observer is assumed fixed when in reality the observer is on a rotating, moving Earth.
It is also untrue that "centrifugal force" is a real physical force. And it is untrue that centrifugal and centripetal forces "balance" for orbiting bodies. And it is untrue that the barycenter location can influence any force acting on a system of masses. The examples I gave to illustrate these points were ignored. You need to learn basic mechanics and to come to understand why these things are untrue before you can make progress with the task you wish to work on.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">The existence of a scientific theory alone is no proof of its correctness but it has to be able to defend itself against any critical arguments or questions.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">True but irrelevant to this discussion. Solar eclipses can now be predicted centuries in advance with amazing precision. Suppose someone came along and said "The Earth is the center of the solar system, not the Sun. You are doing it all wrong." Exactly how much time does a busy professional owe that person by way of justifying the standard procedures and their theoretical basis? The two conflicting views are so dissonant that communication would be impossible.
Professionals have an obligation to make their knowledge available through teaching and writing books and/or technical papers. But they do not have an obligation to explain this knowledge one-on-one to every naive challenger who comes along. (They would have no time left to carry out the jobs thry are paid for.) It is perfectly reasonable to expect that any challenger will at least have read with understanding what everyone who hopes to contribute to a field of knowledge already knows. To get there requires self-educating or taking courses. But it is unreasonable for anyone to skip both processes and expect to be taken seriously.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">In this case this is the, in my opinion, logical conclusion that the motion of the barycenter should be taken into account when evaluating Mercury's perihelion precession because
1) The orientation of Mercury's orbit has to be referred to the fixed stars
2) The sun is not in an inertial reference frame relative to the fixed stars because of its motion around the barycenter.
3) As shown, adding the Sun's motion to Mercury's in this sense, changes the equation of motion in a similar way and magnitude as the GR correction does (which leads to the 43" result).<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Your premise that motion with respect to an inertial frame has not already been taken into account is false. Your premises that the barycenter has some dynamical significance beyond identifying the inertial frame, and that its location has some dynamical significance, are false. Your premise that the orientation of Mercury's orbit is not already referred to the fixed stars is false. Your technique does not reproduce the 43"/cy without a lot of "tweaking", and does not even address the periodic perturbations that accompany it. Your assumption that "centrifugal forces" and barycenter effects have not already been investigated exhaustively by dozens of people is false. Your understanding that conventional perihelion motion has something to do with Schwarzschild radius is false.
To remedy these deficiencies, you must first learn what centrifugal force is all about, so you need to start with basic mechanics. You need to learn how orbits are computed, so you need an introduction to celestial mechanics. You need to study general relativity at least to the point of understanding where perihelion motion actually comes from in that theory. Then, in the light of seeing that many of your assumptions were false, you can see if you can do better than the standard model.
The "shortcut" is to use a service such as our Professional Manuscript Review Service", which will constructively critique your ideas to show what you must do to get them past peer review and into print in some credible place. There are limits to what you can expect, or what is reasonable to demand, on a Message Board such as this one. As I said, the scope of courteous and helpful replies does not extend into the domain of providing tuition-free private tutoring in the fields where you lack knowledge.
On the other side of the coin, if you have any viewpoint of such a nature that, if someone showed you good and sufficient reason why that viewpoint is wrong, you would disbelieve the argument and cling to your viewpoint anyway, then that position is a "personal belief system" rather than a scientific opinion, and you will always experience frustration when speaking to scientists about it. In science, we must always refrain from any attachment to the ideas we favor, and be ready to drop them on a moment's notice as good reasons to do so become known to us. The corollary is that we must not over-invest time, resources, and ego on our ideas because then we become biased and can no longer recognize the need for change when it is shown to us.
Your tone seems to have turned hostile when you say "you sound exactly the same as those people who try to counter any critics of mainstream science issues merely by pointing out that they have superior knowledge and hence are right by default". I have patiently given you example after example to show that your assumptions are incorrect, and why that is so. The tone of your response then leads me to suspect that you are now over-invested in your own ideas. If so, you must decide whether you prefer to take them to your
<br /><blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">[tvf]: This appearance should instead be taken as one's first clue that one's own knowledge is still at a naive level.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">I thought you had an open mind regarding critical arguments, but now you sound exactly the same as those people who try to counter any critics of mainstream science issues merely by pointing out that they have superior knowledge and hence are right by default.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">And your response sounds much like the most common I hear from people unwilling or unable to learn the field they wish to criticize: "I have greater insight because my mind is not corrupted by being taught the standard way of thinking."
I merely pointed out that your knowledge of basic mechanics is insufficient to accomplish the task you have set for yourself, after I gave many examples to illustrate this is so. But you are now crossing the line into shifting the burden of proof for your ideas into a burden of proof by others for the mainstream model. Science does not work that way. If you are content to have discovered the secrets of the universe privately, and are willing to take them to your grave, so be it.
But if you want anyone to pay attention to what you have to say, you must learn the conventional theory you are challenging and start by showing what is insufficient about it that your idea will cure without introducing new problems. This is important both to show that your understanding of the subject is sufficient, and as common ground for communication with others.
In the case in point, it is untrue that the standard model assumes a fixed Sun. Placing the Sun at the origin of coordinates does not mean it is fixed any more than placing the origin of coordinates at the observer means the observer is assumed fixed when in reality the observer is on a rotating, moving Earth.
It is also untrue that "centrifugal force" is a real physical force. And it is untrue that centrifugal and centripetal forces "balance" for orbiting bodies. And it is untrue that the barycenter location can influence any force acting on a system of masses. The examples I gave to illustrate these points were ignored. You need to learn basic mechanics and to come to understand why these things are untrue before you can make progress with the task you wish to work on.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">The existence of a scientific theory alone is no proof of its correctness but it has to be able to defend itself against any critical arguments or questions.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">True but irrelevant to this discussion. Solar eclipses can now be predicted centuries in advance with amazing precision. Suppose someone came along and said "The Earth is the center of the solar system, not the Sun. You are doing it all wrong." Exactly how much time does a busy professional owe that person by way of justifying the standard procedures and their theoretical basis? The two conflicting views are so dissonant that communication would be impossible.
Professionals have an obligation to make their knowledge available through teaching and writing books and/or technical papers. But they do not have an obligation to explain this knowledge one-on-one to every naive challenger who comes along. (They would have no time left to carry out the jobs thry are paid for.) It is perfectly reasonable to expect that any challenger will at least have read with understanding what everyone who hopes to contribute to a field of knowledge already knows. To get there requires self-educating or taking courses. But it is unreasonable for anyone to skip both processes and expect to be taken seriously.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">In this case this is the, in my opinion, logical conclusion that the motion of the barycenter should be taken into account when evaluating Mercury's perihelion precession because
1) The orientation of Mercury's orbit has to be referred to the fixed stars
2) The sun is not in an inertial reference frame relative to the fixed stars because of its motion around the barycenter.
3) As shown, adding the Sun's motion to Mercury's in this sense, changes the equation of motion in a similar way and magnitude as the GR correction does (which leads to the 43" result).<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Your premise that motion with respect to an inertial frame has not already been taken into account is false. Your premises that the barycenter has some dynamical significance beyond identifying the inertial frame, and that its location has some dynamical significance, are false. Your premise that the orientation of Mercury's orbit is not already referred to the fixed stars is false. Your technique does not reproduce the 43"/cy without a lot of "tweaking", and does not even address the periodic perturbations that accompany it. Your assumption that "centrifugal forces" and barycenter effects have not already been investigated exhaustively by dozens of people is false. Your understanding that conventional perihelion motion has something to do with Schwarzschild radius is false.
To remedy these deficiencies, you must first learn what centrifugal force is all about, so you need to start with basic mechanics. You need to learn how orbits are computed, so you need an introduction to celestial mechanics. You need to study general relativity at least to the point of understanding where perihelion motion actually comes from in that theory. Then, in the light of seeing that many of your assumptions were false, you can see if you can do better than the standard model.
The "shortcut" is to use a service such as our Professional Manuscript Review Service", which will constructively critique your ideas to show what you must do to get them past peer review and into print in some credible place. There are limits to what you can expect, or what is reasonable to demand, on a Message Board such as this one. As I said, the scope of courteous and helpful replies does not extend into the domain of providing tuition-free private tutoring in the fields where you lack knowledge.
On the other side of the coin, if you have any viewpoint of such a nature that, if someone showed you good and sufficient reason why that viewpoint is wrong, you would disbelieve the argument and cling to your viewpoint anyway, then that position is a "personal belief system" rather than a scientific opinion, and you will always experience frustration when speaking to scientists about it. In science, we must always refrain from any attachment to the ideas we favor, and be ready to drop them on a moment's notice as good reasons to do so become known to us. The corollary is that we must not over-invest time, resources, and ego on our ideas because then we become biased and can no longer recognize the need for change when it is shown to us.
Your tone seems to have turned hostile when you say "you sound exactly the same as those people who try to counter any critics of mainstream science issues merely by pointing out that they have superior knowledge and hence are right by default". I have patiently given you example after example to show that your assumptions are incorrect, and why that is so. The tone of your response then leads me to suspect that you are now over-invested in your own ideas. If so, you must decide whether you prefer to take them to your
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20 years 4 months ago #10280
by Thomas
Replied by Thomas on topic Reply from Thomas Smid
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by tvanflandern</i>
And it is untrue that centrifugal and centripetal forces "balance" for orbiting bodies<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote"> I have mentioned before the example of a geostationary satellite which, for an observer rotating with the earth, requires a centrifugal force in order to balance the gravitational attraction. Have a look at any book about mechanics and you find the additional force terms in rotating coordinate systems (i.e. the centrifugal force and the Coriolis force evaluated) (see for instance the copy that I made from Danby, Fundamentals of Celestial Mechanics ( www.physicsmyths.org.uk/imgs/centrifugal.jpg ).
For the sun moving around the barycenter of the solar system, the coordinate system fixed with the sun does of course not rotate but is nevertheless accelerated as it does not move with a constant velocity vector. This acceleration has to be accounted for when changing the system of reference from heliocentric to barycentric or vice versa (as indicated in my mathematical analysis further above).
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Your understanding that conventional perihelion motion has something to do with Schwarzschild radius is false<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">From the references I have seen, the Schwarzschild Radius <i>is</i> the crucial quantity when trying to explain the anomalous precession of Mercury by means of GR (see for instance www.mathpages.com/rr/s6-02/6-02.htm ), and the non-periodic term in the correction of the centrifugal force due to the change of the reference system from the heliocentric to the barycentric ccordinate system corresponds indeed to an increase of the radius vector by about the same amount (as shown by me above).
Anyway, if you attribute the increase in the centrifugal force to an increase of the angular frequency rather than the radius (after all, the main parameters of Mercury's orbit would be assumed to be fixed), you get an increase of ω by a factor √(1+ δr/r) where δr is the radial offset (corresponding to the Schwarzschild Radius or the corresponding expression (Δω/ω)²*(Δr²/r) derived by me above) and you find that this corresponds to an increase in the angular frequency by a factor 3.4*10^-8 which in 100 years (400 Mercury orbits) amounts to 3.4*10^-8 *400*360*3600 = 18" (i.e. not quite the 43" required but nevertheless of the right order of magnitude).
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Solar eclipses can now be predicted centuries in advance with amazing precision<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote"> Solar eclipses maybe, but apparently not the motion of Mercury (which is much more affected by the fact that the sun is not an inertial system).
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Suppose someone came along and said "The Earth is the center of the solar system, not the Sun. You are doing it all wrong."<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">If you are just looking at effects small enough, the heliocentric assumption becomes as invalid as the geocentric one. The point is that the assumption of Kepler ellipses is only exact if you are treating a two-body problem. For more bodies, the orbits can not be described anymore by ellipses and any attempt to fit observations by the classical orbital elements will result in errors. The only accurate way of doing celestial mechanics would be to do a numerical n-body calculation, track the positions and velocities of the objects and compare these with the actual positions and velocities in 3D-space without using the classical orbital theory. I am pretty sure that in this case the discrepancies for Mercury would vanish completely within Newtonian Physics.
www.physicsmyths.org.uk
www.plasmaphysics.org.uk
And it is untrue that centrifugal and centripetal forces "balance" for orbiting bodies<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote"> I have mentioned before the example of a geostationary satellite which, for an observer rotating with the earth, requires a centrifugal force in order to balance the gravitational attraction. Have a look at any book about mechanics and you find the additional force terms in rotating coordinate systems (i.e. the centrifugal force and the Coriolis force evaluated) (see for instance the copy that I made from Danby, Fundamentals of Celestial Mechanics ( www.physicsmyths.org.uk/imgs/centrifugal.jpg ).
For the sun moving around the barycenter of the solar system, the coordinate system fixed with the sun does of course not rotate but is nevertheless accelerated as it does not move with a constant velocity vector. This acceleration has to be accounted for when changing the system of reference from heliocentric to barycentric or vice versa (as indicated in my mathematical analysis further above).
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Your understanding that conventional perihelion motion has something to do with Schwarzschild radius is false<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">From the references I have seen, the Schwarzschild Radius <i>is</i> the crucial quantity when trying to explain the anomalous precession of Mercury by means of GR (see for instance www.mathpages.com/rr/s6-02/6-02.htm ), and the non-periodic term in the correction of the centrifugal force due to the change of the reference system from the heliocentric to the barycentric ccordinate system corresponds indeed to an increase of the radius vector by about the same amount (as shown by me above).
Anyway, if you attribute the increase in the centrifugal force to an increase of the angular frequency rather than the radius (after all, the main parameters of Mercury's orbit would be assumed to be fixed), you get an increase of ω by a factor √(1+ δr/r) where δr is the radial offset (corresponding to the Schwarzschild Radius or the corresponding expression (Δω/ω)²*(Δr²/r) derived by me above) and you find that this corresponds to an increase in the angular frequency by a factor 3.4*10^-8 which in 100 years (400 Mercury orbits) amounts to 3.4*10^-8 *400*360*3600 = 18" (i.e. not quite the 43" required but nevertheless of the right order of magnitude).
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Solar eclipses can now be predicted centuries in advance with amazing precision<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote"> Solar eclipses maybe, but apparently not the motion of Mercury (which is much more affected by the fact that the sun is not an inertial system).
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Suppose someone came along and said "The Earth is the center of the solar system, not the Sun. You are doing it all wrong."<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">If you are just looking at effects small enough, the heliocentric assumption becomes as invalid as the geocentric one. The point is that the assumption of Kepler ellipses is only exact if you are treating a two-body problem. For more bodies, the orbits can not be described anymore by ellipses and any attempt to fit observations by the classical orbital elements will result in errors. The only accurate way of doing celestial mechanics would be to do a numerical n-body calculation, track the positions and velocities of the objects and compare these with the actual positions and velocities in 3D-space without using the classical orbital theory. I am pretty sure that in this case the discrepancies for Mercury would vanish completely within Newtonian Physics.
www.physicsmyths.org.uk
www.plasmaphysics.org.uk
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20 years 4 months ago #10231
by tvanflandern
Replied by tvanflandern on topic Reply from Tom Van Flandern
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Thomas</i>
<br />For the sun moving around the barycenter of the solar system, the coordinate system fixed with the sun does of course not rotate but is nevertheless accelerated as it does not move with a constant velocity vector. This acceleration has to be accounted for when changing the system of reference from heliocentric to barycentric or vice versa (as indicated in my mathematical analysis further above).<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">You are mistaken. As long as the motions are determined in an inertial coordinate system (which they are), you can then switch the origin of coordinates to a fly zipping around at random without any new consequences for the orbits of bodies.
Rotating coordinates would create fictitious, apparent Coreolis and/or centrifugal forces for the reason I described. But we do not have rotating coordinates here. We simply have a conversion from a fixed origin to a translating origin with an irregular path. Switching origins without a rotation does not introduce pseudo-forces because the dynamics were all determined in an inertial reference frame before the origin switch.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">From the references I have seen, the Schwarzschild Radius <i>is</i> the crucial quantity when trying to explain the anomalous precession of Mercury by means of GR<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">One can stick the Schwarzschild radius into many equations where it has no meaningful function. For example, Newton's universal law of gravitation GM/r^2 can be written as R*(c/r)^2, where R is the Schwarzschild radius and r/c is the light-time from source mass to target body. So the acceleration of gravity is the Schwarzschild radius per light-time squared. But neither of these quantities has anything to do with the cause of ordinary gravitational acceleration.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">a factor 3.4*10^-8 which in 100 years (400 Mercury orbits) amounts to 3.4*10^-8 *400*360*3600 = 18" ...<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">I was unable to reproduce your "3.4" or discover where how got it. Using the method in the reference, I end up with 14.5"/cy.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">... (i.e. not quite the 43" required but nevertheless of the right order of magnitude).<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">There may be an unlimited number of ways to get such numerical coincidences. Nonetheless, they are mostly erroneous. This one is badly wrong (i.e., out by a factor of three).
As I explained, the actual perihelion motion in GR has three contributions, one of which is about the size you obtained, another is four times that size, and the third is minus twice that size. When all are combined, the correct answer is three times that size, or 43"/cy.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">The only accurate way of doing celestial mechanics would be to do a numerical n-body calculation, track the positions and velocities of the objects and compare these with the actual positions and velocities in 3D-space without using the classical orbital theory. I am pretty sure that in this case the discrepancies for Mercury would vanish completely within Newtonian Physics.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Then why don't you get or write a numerical integrator and prove your conjecture wrong. Everyone else in the field already has. -|Tom|-
<br />For the sun moving around the barycenter of the solar system, the coordinate system fixed with the sun does of course not rotate but is nevertheless accelerated as it does not move with a constant velocity vector. This acceleration has to be accounted for when changing the system of reference from heliocentric to barycentric or vice versa (as indicated in my mathematical analysis further above).<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">You are mistaken. As long as the motions are determined in an inertial coordinate system (which they are), you can then switch the origin of coordinates to a fly zipping around at random without any new consequences for the orbits of bodies.
Rotating coordinates would create fictitious, apparent Coreolis and/or centrifugal forces for the reason I described. But we do not have rotating coordinates here. We simply have a conversion from a fixed origin to a translating origin with an irregular path. Switching origins without a rotation does not introduce pseudo-forces because the dynamics were all determined in an inertial reference frame before the origin switch.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">From the references I have seen, the Schwarzschild Radius <i>is</i> the crucial quantity when trying to explain the anomalous precession of Mercury by means of GR<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">One can stick the Schwarzschild radius into many equations where it has no meaningful function. For example, Newton's universal law of gravitation GM/r^2 can be written as R*(c/r)^2, where R is the Schwarzschild radius and r/c is the light-time from source mass to target body. So the acceleration of gravity is the Schwarzschild radius per light-time squared. But neither of these quantities has anything to do with the cause of ordinary gravitational acceleration.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">a factor 3.4*10^-8 which in 100 years (400 Mercury orbits) amounts to 3.4*10^-8 *400*360*3600 = 18" ...<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">I was unable to reproduce your "3.4" or discover where how got it. Using the method in the reference, I end up with 14.5"/cy.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">... (i.e. not quite the 43" required but nevertheless of the right order of magnitude).<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">There may be an unlimited number of ways to get such numerical coincidences. Nonetheless, they are mostly erroneous. This one is badly wrong (i.e., out by a factor of three).
As I explained, the actual perihelion motion in GR has three contributions, one of which is about the size you obtained, another is four times that size, and the third is minus twice that size. When all are combined, the correct answer is three times that size, or 43"/cy.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">The only accurate way of doing celestial mechanics would be to do a numerical n-body calculation, track the positions and velocities of the objects and compare these with the actual positions and velocities in 3D-space without using the classical orbital theory. I am pretty sure that in this case the discrepancies for Mercury would vanish completely within Newtonian Physics.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Then why don't you get or write a numerical integrator and prove your conjecture wrong. Everyone else in the field already has. -|Tom|-
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