Mercury's Perihelion Precession

Tom, The numbers you posted: Earth/Venus=365" and Jupiter/Saturn=153" look backword to me-are they about the right ratio? Earth/Venus//Jupiter/Saturn=7/3?

<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 />Tom, The numbers you posted: Earth/Venus=365" and Jupiter/Saturn=153" look backword to me-are they about the right ratio? Earth/Venus//Jupiter/Saturn=7/3?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">I didn't give you a number for Saturn because the planets do not work in pairs. But Saturn contributes about 7" to Mercury's perihelion advance. -|Tom|-

As Thomas says the raduis of the sun is assumed to be 1475meters when doing the calculations to make the numbers fit the observations. Why not use any ol radius one wants to make these calculations and then factor in some new constant? Would that work out math wise? This radius is used by several web sites that post papers on the topic.

<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 />As Thomas says the radius of the sun is assumed to be 1475 meters when doing the calculations to make the numbers fit the observations.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">That is the Schwarzschild radius, not the distance from center to surface. The latter is relevant to tides, the former only to black holes with the Sun's mass. -|Tom|-

<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>
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.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">I can absolutely not agree with this assertion. If you drag the origin of a coordinate system in a circle around a given point (with the orientation of the axes staying the same), the point describes exactly the same path as if you would rotate the coordinate system. Any transformation between coordinate systems not in uniform relative motion to each other (and the sun and barycenter aren't) will create fictitious forces that have to be taken into account accordingly.


<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><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.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">I downloaded actually a numerical n-body program which is based on NASA-JPL's program (see www.moshier.net/ssystem.html ).
First of all, the program does take the motion of the sun into account, but it uses in my opinion a rather questionable adjustment method: if the barycenter moves in the course of one integration step (which it shouldn't if the program is accurate), the position of the sun is adjusted such as to re-establish the position of the barycenter. Now this obviously means that the position of the sun relative to the planets is arbitrarily changed whilst the program thinks it is in the right spot.
Whether or not this inconsistency leads to siginificant effects I don't know, but this is anyhow not the decisive point I was addressing above: the numerical calculation can be as accurate as you want, what it does is merely calculating the x,y,z coordinates and velocities at a certain time from the x,y,z coordinates and velocities at an earlier time. However, what you need in order to define a change of the longitude of Mercury's perihelion is a description of the orbit in terms of the classical orbital elements, which obviously is based on the assumption that you are dealing with ellipses. However, ellipses only exist for two-body problems but not for 3 or more bodies. So trying to fit the data in terms in ellipses (even if corrections are applied) will inevitably lead to deviations from the actual orbit if you are just looking at effects small enough. Strictly speaking, the attempt of trying to fit the movement of the planets through a system of elliptic orbits has as much its limits as Ptolemaeus' attempt to fit everything through embedded circles (the difference is that with the latter theory you just added a new epicycle if the data could not be fitted with the old model, whereas nowadays whole belief-systems like GR are based on the inability to fit the data by elliptic orbits).

---

www.physicsmyths.org.uk
www.plasmaphysics.org.uk

<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"><i>Originally posted by tvanflandern</i>
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.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">I can absolutely not agree with this assertion. If you drag the origin of a coordinate system in a circle around a given point (with the orientation of the axes staying the same), the point describes exactly the same path as if you would rotate the coordinate system. Any transformation between coordinate systems not in uniform relative motion to each other (and the sun and barycenter aren't) will create fictitious forces that have to be taken into account accordingly.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">You are in denial of basic mechanics. Once the motion has been determined in an inertial coordinate system, one can switch to any origin whatever, even a fly's path (as I said before), without further consequences.

This is not my opinion. It is basic mechanics. If you don't already know this, then you do not know enough mechanics to deal successfully with the problem at hand.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">why don't you get or write a numerical integrator and prove your conjecture wrong. Everyone else in the field already has.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">... the program does take the motion of the sun into account, but it uses in my opinion a rather questionable adjustment method: if the barycenter moves in the course of one integration step (which it shouldn't if the program is accurate), the position of the sun is adjusted such as to re-establish the position of the barycenter. Now this obviously means that the position of the sun relative to the planets is arbitrarily changed whilst the program thinks it is in the right spot.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Case in point. Basic mechanics: how to change an origin without disturbing the calculated motions.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Whether or not this inconsistency leads to siginificant effects I don't know<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">It leads to no effects whatever.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">what you need in order to define a change of the longitude of Mercury's perihelion is a description of the orbit in terms of the classical orbital elements, which obviously is based on the assumption that you are dealing with ellipses. However, ellipses only exist for two-body problems but not for 3 or more bodies. So trying to fit the data in terms in ellipses (even if corrections are applied) will inevitably lead to deviations from the actual orbit if you are just looking at effects small enough.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">This is all incorrect. The perihelion point (point of closest approach to the Sun, by definition) is well-defined and, by itself, defines the major apsis that advances. So perihelion motion is well-defined regardless of the type of orbit or complexity of the motion.

You have not yet learned mechanics fundamentals, so you are making assumptions as you go that are mostly incorrect. But you seem happy as a clam doing it your way, so continue as you please. You obviously have no further need of my advice. What do I know? I'm obviously just a dyed-in-the-wool mainstreamer, and Meta Research is just a front that pretends to critique mainstream theories but then supports only ideas that can pass peer review -- which makes them just as bad. Good luck! -|Tom|-