Solar System barycenter - Orbit of planets

[Andrew1955]

My understanding was that the Earth orbits the Earth-Moon barycenter, which itself orbits the solar system's barycenter.

Andrew1955 said:
>>As far as I know the Earth orbits around the Sun Earth barycenter while the Sun orbits the Solar System BaryCenter formed by the changing center of mass of the Solar >>system. So even while the Sun orbits the SSBC and Earth orbits the Sun-Earth BC it would not be true to say the Earth orbits the SSBC.My understanding was that the Earth orbits the Earth-Moon barycenter, which itself orbits the solar system's barycenter.

Drakkith,

Are you still making the same distinction you are describing in that post?

Ie You stressed the Earth-Moon barycenter orbits the SSBC, compared to my view the Earth moon barycenter orbits the Sun Earth barycenter?

Can you expand a bit on what you are getting at please if so?

Directly related to that, you also said this in response to me:

>>Andrew1955 said: ↑
It seems to me that the force of Jupiter's gravity at the surface of the Sun is absolutely tiny, and if we calculate where the gravitational center of the Solar system is it is very near the center of the Sun.If by gravitational center you mean the center of mass, then I don't see how you're coming to that conclusion since the barycenter is the center of mass of the system

The point i was making was the center of mass of the solar system is not a gravitational center for the purposes of calculating the Earths orbit. The gravitational center is much closer to the center of the Sun than the SSBC is for Earths orbit.

Thanks

 

[Drakkith]

Drakkith,

Are you still making the same distinction you are describing in that post?

Ie You stressed the Earth-Moon barycenter orbits the SSBC, compared to my view the Earth moon barycenter orbits the Sun Earth barycenter?

I was mistaken in my earlier post. The Earth-Moon BC is NOT orbiting the SSBC 'directly', but the Sun-Earth-Moon BC. But we don't usually use barycentric coordinates with respect to the SSBC, so it's still correct to say that the Earth orbits the Sun.

Can you expand a bit on what you are getting at please if so?

Sure. Here's my understanding. The ISS obviously orbits the Earth. However, the Earth itself orbits the Earth-Moon barycenter, and as such the ISS will 'orbit' around both points. In other words, the orbit of the ISS, as viewed from an inertial coordinate system, will have two components: the motion around the Earth, and the motion of the Earth-ISS around the Earth-Moon barycenter. Assuming the ISS had a perfectly circular orbit around the Earth, its motion according to our coordinate system will be a circle whose center point (the center of the Earth) moves in an elliptical pattern around another point in space which is the Earth-Moon barycenter (or more accurately the Earth-ISS-Moon barycenter) This barycenter in turn moves around the Sun-Earth-Moon-ISS barycenter, and the Sun moves around the solar system barycenter.

The point i was making was the center of mass of the solar system is not a gravitational center for the purposes of calculating the Earths orbit. The gravitational center is much closer to the center of the Sun than the SSBC is for Earths orbit.

I agree for the usual definition of orbit, which is the motion around the Sun. For that we usually use a coordinate system centered on the Sun, which does not include the SSBC as far as I know. I think this is a heliocentric coordinate system instead of a barycentric coordinate system, but I'm not certain.

All the above is my current understanding of the subject anyhow. I can't say with any certainty that it is correct.

 

[phinds]

... I need a website to publish it on, as it's not just a single image file that I can just upload somewhere.

I've got plenty of space on my hosted server accounts. What kind of server facilities do you need? I think both the ones I use run Apache and have a pretty standard set of available utilities (none of which I use, other than the FTP upload capability)

 

[Drakkith]

I've got plenty of space on my hosted server accounts. What kind of server facilities do you need? I think both the ones I use run Apache and have a pretty standard set of available utilities (none of which I use, other than the FTP upload capability)

Don't worry about it. If I make something a little more presentable I might hit you up on that offer.

 

[Andrew1955]

The Earth-Moon BC is NOT orbiting the SSBC 'directly'

Thanks the words 'directly' and 'indirectly' might provide a solution for me.

For my purposes I can say;

1. The planets only indirectly orbit the SSBC.

2. The planets directly orbit the Sun with minor perturbations.

 

[ianchristie]

A big part of the confusion here is that word "orbits". Another big part is the constant chopping and changing of frames of reference.

At any moment a body (star, planet, moon ...) will move with an instantaneous velocity and be subject to an acceleration due to the local gravitational field. (This is the Newtonian description and these properties are relative to some frame of reference.) That local gravitational field will be the sum of the gravitational fields of all the other masses in the universe. Depending on the point of view we wish to discuss we ignore some or most of these contributions. For example, we usually ignore everything outside the MIlky Way Galaxy except when we are interested in the future collision with the Andromeda Galaxy.

If we ignore all contributions (big and small) except those of two bodies which we wish to discuss we get a two-body problem which is easy to describe mathematically. If one of those two bodies is much more massive than the other, say Sun & Earth, or Earth & ISS, we can simplify things even more by taking the centre of the more massive body as the origin for our frame of reference. This makes the more massive body stationary in the chosen frame of reference and the path followed by the less massive body in this frame of reference becomes a Keplerian conic section. We often use the word "orbit" to describe this sort of path.

For bodies where the difference in mass is not so great (say Alpha Centauri A and B, or Pluto and Charon), a better frame of reference is one where the origin for our frame of reference is a point between the two masses with a distance from the centre of each in inverse proportion to the relative masses of each, i.e. the barycentre, centre of mass or centre of gravity of the system. In this frame of reference the paths of both bodies are Keplerian conics. Once we chose a frame of reference which is not fixed relative to either of these frames of reference the paths of the bodies are not Keplerian conics. Note that these are simplifications, we have ignored most of the universe and General Relativity!

If you need a more accurate description of the path of a body relative to some frame of reference then the nature of your description depends on which bits of the simplification you dispense with: do you allow for Jupiter? other planets? the Moon? the Sun? the Milky Way?. Do you use General Relativity or Newton? What do you use for a frame of reference? Do you need to account for the solar wind? Light pressure?

One of the ways of dealing with the need for more accuracy than the simple two-body solution is to use the two body solution and the barycentre frame of reference and then "add in" an instantaneous adjustment to account for whatever extra bits we wish to consider. These "add ins" are often referred to as perturbations.

If you go back to just considering the intantaneous acceleration of a body at two consecutive moments and calculate the position of the intersection of the two acceleration vectors, the point of intersection can be described as the point about which the body is "orbiting" at that time.

The idea of an "orbit" is a simplified description of a complex path.

 

[Andrew1955]

Ian, Perhaps I should have made it clearer in my original post that:

1. One discussion group is saying the Earth system directly orbits the SSBC where, in this argument, the SSBC is the principal focus of the orbit, and the Sun Earth distance changes accordingly by relatively large amounts.

2. Another discussion group, including me, is saying the principal focus of the Earth system orbit is the Sun-Earth BC, where the effect of the other planets creates only very minor changes to the Sun Earth distance.

3. Neither 1 or 2 are correct but 2 is far more correct than 1, and this reality is known to the number 2 discussion group.

(4. I later learned that Newton said “The focus of the orbit of the Earth [is] in the common centre of gravity of Venus, Mercury and the Sun.” – Mathematical Principles of Natural Philosophy Vol III pp28 )

Yes, I know this is a physics forum discussion, but the actual topic I am interested in is not really very complicated at all.

 

[ianchristie]

Andrew;
Orbital mechanics is not my speciality so there is a limit to my understanding here. However, as I said, the problem is that word "orbits", whether it is qualified by the adverb "directly" or not. "Orbit" is a human description of the path of motion not a property of the body in question. The body has time, position, velocity, acceleration, and mass, nothing else. These are in all measured in some frame of reference. Which frame you choose effects the description you derive from your calculations of how these properties change with time. When you use the term "focus" to describe an "orbit" you are thinking of an idealised Keplerian elliptical orbit. You have simplified the system to a two body system and are using either the centre of mass of the more massive object as the origin of your frame of reference or you are using the centre of mass of the two body system as a whole. As soon as you start talking about a dynamic n-body system and its barycentre you need to specify the frame of reference you are using to locate that barycentre. Diagrams showing the "changing position" of the Solar system barycentre are almost always drawn to show its position in heliocentric co-ordinates. In this schema the Sun does not move and the barycentre oscillates all over the place. A better way of describing this would be to use the Solar system barycentre as the origin of the co-ordinate system and show how the Sun wobbles around it.

Consider the direction of the acceleration vector. The acceleration vector always points towards the barycentre of the system. For a two body system this lies on the line between the two centres of the bodies. For an n-body system it may be in open space somewhere. For the Solar system it is sometimes inside the Sun but sometimes above it. It is not always on the line between the centre of the Earth and the Centre of the Sun.

So taking your four points:-
1 The Earth is always accelerating towards the SSBC. If we define a frame of reference with origin at the SSBC, the Earth's path relative to that point at a given instant in time will be an ellipse with one focus at that point. At another instant in time it will also be an ellipse, but not necessarily the same ellipse. (Using Newtonian gravity.) If we define a frame of reference with origin anywhere else and moving relative to the SSBC the Earth's path will be some wobbly line. For example if we use galactic co-ordinates the Earth's path is a wiggly spiral of some sort. The Sun Earth distance changes. According to Wikipedia's sources the variation is about 5 million kilometres. The distance from the Earth to the SSBC varies. The distance from the Sun to the SSBC also varies. The net result of the two variations is that 5 million kilometres. The diameter of the Sun is about 1.4 million kilometres and the furthest possible point from the centre of the Sun to the SSBC is about 1.9 million kilometres. You can see that most of the variation in Sun Earth distance is not due to the distance of the Sun from the SSBC.
In my opinion that 5 million kilometres is not "relatively large". If you draw an accurate ellipse to the scale of the Earth's orbit it looks like a circle to the naked eye.
The expression "directly orbits" is meaningless.

2. To say that the "orbit" of the Earth has a "principal focus" is semantics. These terms have meaning only in a simplified two body model. This is not reality.

3. This statement has no real meaning. 1 and 2 are both simplifications.

4. The system described by Newton is still a simplification.

Have a browse through the Wikipedia article on "The n-body problem." this is the best description of the problem I can find. Ignore all the maths. Just skim through and note all the mentions of words like "intractable" and "approximation". The essence of the article is that all solutions are simplifications of some sort and the Keplerian/Newtonian concepts of ellipses etc are gross simplifications.

The net result of this is that both groups are wrong, you are both using simplifications, neither group is specifying frames of reference for their claims, the things you are referring to are human concepts, not properties of the bodies in question and arguing over who is less wrong is pointless.

Cheers!
Ian

 

[Bandersnatch]

Consider the direction of the acceleration vector. The acceleration vector always points towards the barycentre of the system.

This isn't true outside special cases. I believe it has been already pointed out by others in this thread.

 

[ianchristie]

What am I missing here? I can't conceive how the acceleration can point to any place other than the solar system barycentre. The acceleration vector is in the direction of the net force surely? And the net force always points to the solar system barycentre? (Simplifying to the extent that we ignore masses outside the Solar system.) And what are those "special cases"? How can the force of gravity act in a direction other than along the line towards the net position of the masses doing the attracting?

 

[Andrew1955]

What am I missing here? I can't conceive how the acceleration can point to any place other than the solar system barycentre. The acceleration vector is in the direction of the net force surely? And the net force always points to the solar system barycentre? (Simplifying to the extent that we ignore masses outside the Solar system.) And what are those "special cases"? How can the force of gravity act in a direction other than along the line towards the net position of the masses doing the attracting?

The barycenter is a mathematical point established with reference to distance and mass. A large distance from the Sun for say Neptune which is only 17 times the mass of the Earth means the mathematical point is positioned large distances from the Sun by Neptune

In reality distant objects in the solar system have almost no ability at all to create changes upon Earths orbit because gravity is inversely proportional to the square of the distance *and* both the Sun and the Earth are both almost equally influenced by the planets gravity.

Barycenter wise the planets beyond Jupiter have a similar barycentric influence as Jupiter, but in reality their combined gravitational influence is very much weaker

Relative gravitational influence upon the Sun taking Earth as unity.

m/r2
====
Hg=0.3672
V=1.559
E=1
Ma=0.04
J=11.733
S=1.0363
N=0.0189
U=0.0393

 

[Bandersnatch]

What am I missing here? I can't conceive how the acceleration can point to any place other than the solar system barycentre. The acceleration vector is in the direction of the net force surely? And the net force always points to the solar system barycentre? (Simplifying to the extent that we ignore masses outside the Solar system.)

When you drop an apple, does the acceleration vector point towards the SSBC or somewhere else? It's easy to calculate the acceleration the apple experiences from the Sun's attraction and from Earth's, and see which is greater.

And what are those "special cases"? How can the force of gravity act in a direction other than along the line towards the net position of the masses doing the attracting?

By special cases I mean those situations where it does actually act towards the barycentre. Drakkith provided one such setup in post #22. A two-body problem is another such case (but it's indistinguishable from saying that the forces act towards the two bodies), which was mentioned by DH in post #26 in discussion with Andrew.

The one thing to take away from this is that there is no single spot in space towards all forces acting on all planets point, or even net force acting one planet always points to. When you add all the force vectors acting on any particular body in the N-body system, you end up with a vector that is constantly varying in time and pointing all over the place.@Andrew1955: proposition 1 and 2 have an easily verifiable difference in predictions - the Sun-Earth distance. You can change the bodies in question to the Sun-Venus system, and use DH's graph in post #26 to resolve this.

As long as the point of contention can be rephrased to: if we were to model planetary motion using keplerian conic sections, which point at the focus results in motion that resembles actual motion more: SSBC or Sun-planet BC? Then proposition 2 is a better one.

 

[ianchristie]

Ah... yes. I see what I was missing. The barycentre position is a function of the inverse of the distance and the mass, the gravitational force is a function of the inverse of the square of the distance and the mass. So the net force and acceleration vectors point in the same direction but it is not towards the SSBC except in the two body case and only coincidentally then. I stand corrected.

So .. is there a name for the location towards which a given body accelerates under the gravitational influence of n-1 other bodies? "Centre of Gravity" sounds right but has a different meaning. Can we call it the "Momentary Centre of Revolution"? The implication here is that from moment to moment the direction of the acceleration vector changes and the position of the intersections of these vectors changes from moment to moment also. So for the Earth we have a Momentary Centre of Revolution - Earth or MCoRE for short!

I did say "Orbital mechanics is not my specialty so there is a limit to my understanding here."

Given that correction about the point towards which the Earth is accelerating most of what I have said previously about semantics and simplifications still seems to hold, with the exception of a couple of bits about the variation in the Sun Earth distance.

Lets see if I can do better this time. Going back to the four points in Andrew's post #42 of last week:-
1. This point of view is wrong. This group is probably working under the same misunderstanding as I was. The SSBC is not the point to which the acceleration and force vectors point. If you substitute MCoRE for SSBC in my statements above a lot of what I said follows with the exception of the actual distances from Sun and Earth to MCoRE and also note that the MCoR will be in a different position for every body in the Solar System. Hence that dropped apple accelerates towards the Earth not the SSBC. (I do like a simple reductio ad absurdum to show me how thick I have been!)

2. To say that the "orbit" of the Earth has a "principal focus" is semantics. These terms have meaning only in a simplified two body model. This is an approximation, not reality. Whether or not you think it is a "rough" approximation depends on your definition of "rough". See my previous comments about simplifications in post #41. Note that if we were talking about Mercury, not Earth, it would be more obviously "rough" and we would need to use General Relativity to get a "smooth" approximation.

3. Viewpoint 1 is just plain wrong, (like I was), 2 is an approximation. Does that make it "wrong" or just "less correct"? That all depends on how precise you want to be. It might be better to say viewpoint 2 is accurate within certain limits of precision. Those limits of precision must be greater than the effects of the other planets.

4. The arrangement described by Newton is still a simplification.

Bandersnatch's third last paragraph in #47 above is a fair summary. Note that it does not use the words "focus" or "orbit". (And now I know more orbital mechanics than previously.)

An aside: In my role as a science educator I often come across similar debates amongst students which ultimately derive from a combination of misconceptions, (like mine), poorly defined terms, poorly defined frames of reference and lots of semantics. The semantics are often like those here with terms being used which are human descriptions not properties of objects. On occasion I come across debates in similar places to this where the initial post stems from these confusions. One of the difficulties which responders often have is detecting those misconceptions and confusions and addressing them. Responders often go into long and convoluted explanations which add layers of complexity but which never dig to the base of the misconceptions and they often add their own semantic confusion. (And then there are the loonies who add their own peculiar personal confusions which are occasionally entertaining but often just a rabbit hole of distraction. This discussion appears to have escaped their attention so far.)

There is good research to show that unless misconceptions are addressed explicitly real understanding will not take hold if it conflicts with the misconception. Given a choice between new, correct idea and old, wrong idea, students throw away the new one. This discussion has been the first time I have been made aware of a misconception of my own which has been a block to understanding.

Have I missed anything pertinent to the original post?

 

[Andrew1955]

Ah... yes. I see what I was missing. The barycentre position is a function of the inverse of the distance and the mass, the gravitational force is a function of the inverse of the square of the distance and the mass. So the net force and acceleration vectors point in the same direction but it is not towards the SSBC except in the two body case and only coincidentally then. I stand corrected.

So .. is there a name for the location towards which a given body accelerates under the gravitational influence of n-1 other bodies? "Centre of Gravity" sounds right but has a different meaning. Can we call it the "Momentary Centre of Revolution"? The implication here is that from moment to moment the direction of the acceleration vector changes and the position of the intersections of these vectors changes from moment to moment also. So for the Earth we have a Momentary Centre of Revolution - Earth or MCoRE for short!

I did say "Orbital mechanics is not my specialty so there is a limit to my understanding here."

Given that correction about the point towards which the Earth is accelerating most of what I have said previously about semantics and simplifications still seems to hold, with the exception of a couple of bits about the variation in the Sun Earth distance.

Lets see if I can do better this time. Going back to the four points in Andrew's post #42 of last week:-
1. This point of view is wrong. This group is probably working under the same misunderstanding as I was. The SSBC is not the point to which the acceleration and force vectors point. If you substitute MCoRE for SSBC in my statements above a lot of what I said follows with the exception of the actual distances from Sun and Earth to MCoRE and also note that the MCoR will be in a different position for every body in the Solar System. Hence that dropped apple accelerates towards the Earth not the SSBC. (I do like a simple reductio ad absurdum to show me how thick I have been!)

2. To say that the "orbit" of the Earth has a "principal focus" is semantics. These terms have meaning only in a simplified two body model. This is an approximation, not reality. Whether or not you think it is a "rough" approximation depends on your definition of "rough". See my previous comments about simplifications in post #41. Note that if we were talking about Mercury, not Earth, it would be more obviously "rough" and we would need to use General Relativity to get a "smooth" approximation.

3. Viewpoint 1 is just plain wrong, (like I was), 2 is an approximation. Does that make it "wrong" or just "less correct"? That all depends on how precise you want to be. It might be better to say viewpoint 2 is accurate within certain limits of precision. Those limits of precision must be greater than the effects of the other planets.

4. The arrangement described by Newton is still a simplification.

Bandersnatch's third last paragraph in #47 above is a fair summary. Note that it does not use the words "focus" or "orbit". (And now I know more orbital mechanics than previously.)

An aside: In my role as a science educator I often come across similar debates amongst students which ultimately derive from a combination of misconceptions, (like mine), poorly defined terms, poorly defined frames of reference and lots of semantics. The semantics are often like those here with terms being used which are human descriptions not properties of objects. On occasion I come across debates in similar places to this where the initial post stems from these confusions. One of the difficulties which responders often have is detecting those misconceptions and confusions and addressing them. Responders often go into long and convoluted explanations which add layers of complexity but which never dig to the base of the misconceptions and they often add their own semantic confusion. (And then there are the loonies who add their own peculiar personal confusions which are occasionally entertaining but often just a rabbit hole of distraction. This discussion appears to have escaped their attention so far.)

There is good research to show that unless misconceptions are addressed explicitly real understanding will not take hold if it conflicts with the misconception. Given a choice between new, correct idea and old, wrong idea, students throw away the new one. This discussion has been the first time I have been made aware of a misconception of my own which has been a block to understanding.

Have I missed anything pertinent to the original post?

>>2. To say that the "orbit" of the Earth has a "principal focus" is semantics. These terms have meaning only in a simplified two body model. This is an approximation, not reality.

By principal focus I meant it is the lead focus. Eg principal Architect or Principal (teacher). In the two body model there is only one focus and the word 'principal' would be redundant. I made it perfectly clear that 2 was an approximation. I made it perfectly clear it is not reality.

1. May not be absolutely wrong if barycenter can mean center of gravity rather than CoM. In my discussion elsewhere, One subgroup were claiming CoM was a center of gravity and another subgroup were saying all objects gravitate in the direction of CoM - even though they agreed there is no center of gravity at CoM.

 

[D H]

So .. is there a name for the location towards which a given body accelerates under the gravitational influence of n-1 other bodies? "Centre of Gravity" sounds right but has a different meaning. Can we call it the "Momentary Centre of Revolution"?

No, there isn't. You can easily find the direction in which an object is accelerating, but attaching a radius to that makes no sense in the N-body problem.

An aside: In my role as a science educator I often come across similar debates amongst students which ultimately derive from a combination of misconceptions, (like mine), poorly defined terms, poorly defined frames of reference and lots of semantics.

That is exactly what is going on here.

From a 16th century perspective (and maybe even a 21st century backyard astronomy perspective), saying that planets have elliptical orbits about the Sun is perfectly fine. From a 21st century perspective where we send probes to Mercury, Venus, the Moon, Mars, Jupiter, Saturn, and Pluto (going to Uranus and Neptune is so last century), that perspective is anything but fine. One needs to drop the notion of elliptical orbits.

By principal focus I meant it is the lead focus.

What does that mean? You haven't changed a thing. By saying "focus" you are implicitly assuming elliptical orbits. That's a 16th century notion, one that is still good enough for backyard astronomy. That notion falls apart when it comes to sending spacecraft to other planets or pointing telescopes with arc second or better pointing requirements at another planet.

 

[Andrew1955]

No, there isn't. You can easily find the direction in which an object is accelerating, but attaching a radius to that makes no sense in the N-body problem.That is exactly what is going on here.

From a 16th century perspective (and maybe even a 21st century backyard astronomy perspective), saying that planets have elliptical orbits about the Sun is perfectly fine. From a 21st century perspective where we send probes to Mercury, Venus, the Moon, Mars, Jupiter, Saturn, and Pluto (going to Uranus and Neptune is so last century), that perspective is anything but fine. One needs to drop the notion of elliptical orbits.
What does that mean? You haven't changed a thing. By saying "focus" you are implicitly assuming elliptical orbits. That's a 16th century notion, one that is still good enough for backyard astronomy. That notion falls apart when it comes to sending spacecraft to other planets or pointing telescopes with arc second or better pointing requirements at another planet.

I am sorry that you think i am saying it must be an eliptical orbit. I also made it clear that my 2. Was not correct.

 

[D H]

I am sorry that you think i am saying it must be an eliptical orbit. I also made it clear that my 2. Was not correct.

You used the word "focus". What other than Keplerian orbits have foci?

Humankind have been sending objects to other solar system bodies for fifty years and have been doing high precision solar system astronomy for well over fifty years. That's plenty of time to learn how to do it best, where "best" means predicting the vehicle will go with minimal error, or predicting where to point that high-precision telescope such that the desired object is in its field of view. In this context, "best" is very clear: Completely toss the notion of Keplerian orbits, and that includes your notion of a "primary focus". It turns out that using a barycentric frame using cartesian equations of motion and geometric integrators does a much, much better job than does using a heliocentric frame with perturbed Keplerian orbits.

 

[Drakkith]

Ah... yes. I see what I was missing. The barycentre position is a function of the inverse of the distance and the mass, the gravitational force is a function of the inverse of the square of the distance and the mass. So the net force and acceleration vectors point in the same direction but it is not towards the SSBC except in the two body case and only coincidentally then. I stand corrected.

Wow, I never made that connection!

 

[Andrew1955]

You used the word "focus". What other than Keplerian orbits have foci?

Humankind have been sending objects to other solar system bodies for fifty years and have been doing high precision solar system astronomy for well over fifty years. That's plenty of time to learn how to do it best, where "best" means predicting the vehicle will go with minimal error, or predicting where to point that high-precision telescope such that the desired object is in its field of view. In this context, "best" is very clear: Completely toss the notion of Keplerian orbits, and that includes your notion of a "primary focus". It turns out that using a barycentric frame using cartesian equations of motion and geometric integrators does a much, much better job than does using a heliocentric frame with perturbed Keplerian orbits.

A barycentric frame only means the use of that mathematical point as the basis for a coordinate system. True?

If a heliocentric frame means the use of a mathematical point that begins near the center of the Sun then the results are going to be comparable. True? If a helocentric frame means the frame is moving with the center of the Sun then the results will not be automatically comparable.

It was never my intention to say the Earth system has the center of the sun as the orbital center, however according to JPL the best available ephemerides show this is approximately true where the Earth Sun distance is 'constant' over large numbers of years. The same applies for the distance of the other planets from the Sun.

To be honest i am not sure what you are getting at here.

This thread has already covered all the points raised in the argument i was having. The conversation was not so advanced that we were talking about sending vehicles to Neptune or needing to know more than Newton would know. Additionally prior to 1984, the best available ephemerides for the inner planets (excluding Earth?) used 1898 methodology, and as of at least 2004 GPS satellites were still being sent ephemerides that are 'keplerian in nature'.

reference. From JPL.NASA. URL no longer working (http://iau-comm4.jpl.nasa.gov/XSChap8.pdf

CHAPTER 8: Orbital Ephemerides of the Sun, Moon, and Planets

E. Myles Standish and James G. Williams

8.1 Fundamental Ephemerides

The fundamental planetary and lunar ephemerides of The Astronomical Almanac, starting in the year 2003, are DE405/LE405of Caltech’s Jet Propulsion Laboratory (JPL). They replace JPL’s DE200 which have been used in the almanac since 1984. Previous to 1984, the fundamental ephemerides were based upon analytical “theories”; these are described in Section 8.2.

8.2 Previous Ephemerides used in the Astronomical Almanacs

8.2.1 Ephemerides Prior to 1984

Before 1984, the ephemerides for the Sun, Mercury, Venus, and Mars were based on the theories and tables of Newcomb (1898). Computerized evaluations of the tables were used from 1960 through 1980. From 1981 to 1983, the ephemerides were based on the evaluations of the theories themselves. The ephemerides of the Sun were derived from the algorithm given by S. Newcomb in Tables of the Sun (Newcomb, 1898). Newcomb’s theories of the inner planets (1895–1898) served as the basis for the heliocentric ephemerides of Mercury, Venus, and Mars. In the case of Mars, the corrections derived by F.E. Ross (1917) were applied.

Ephemerides of the outer planets, Jupiter, Saturn, Uranus, Neptune, and Pluto, were computed from the heliocentric rectangular coordinates obtained by numerical integration (Eckert et al., 1951).

 

[Andrew1955]

@Andrew1955: proposition 1 and 2 have an easily verifiable difference in predictions - the Sun-Earth distance. You can change the bodies in question to the Sun-Venus system, and use DH's graph in post #26 to resolve this.

As long as the point of contention can be rephrased to: if we were to model planetary motion using keplerian conic sections, which point at the focus results in motion that resembles actual motion more: SSBC or Sun-planet BC? Then proposition 2 is a better one.

Thanks

I now have a chart of the Earth Sun distance comparable to the Venus Sun distance chart produced by DH. Unfortunately I was dealing with people who prefer to believe in conspiracies rather than recognise they have some incorrect ideas about barycenters being gravitational centers. Unfortunately the barycentric thinking also crept into this thread, and made it hard for me to understand what people were telling me.

As long as the point of contention can be rephrased to: if we were to model planetary motion using keplerian conic sections, which point at the focus results in motion that resembles actual motion more: SSBC or Sun-planet BC? Then proposition 2 is a better one.

From my point of view and the point of view of the discussion I was having, all I need to know is the almost unchanging Earth Sun distance as calculated/measured by JPL to great accuracy reflects some easily understood ideas, so that nobody needs to rely on NASA/JPL to know the Earth does not orbit the SSBC and it is understandable why the Earth Sun distance is apparently 'constant' over large periods of years.

By my own calculations, Jupiter for example, which pulls on both the Earth and the Sun can only create a differential pull upon the 'orbiting' Earth compared to the Sun sufficient to create 2000km or less movement. 2000km is totally trivial in comparison to the variation in the Earth Sun distance that would be created by the Earth 'orbiting' the SSBC.

 

[pugwazup19755]

This question in my opinion is the same as does the moon orbit the sun.

 

[D H]

A barycentric frame only means the use of that mathematical point as the basis for a coordinate system. True?

Your use of "only" in that sentence casts away a lot of physics.

I'll start assuming Newtonian mechanics and ignoring gravitation from nearby stars, the rest of the galaxy, and the rest of the universe. All we care about is interactions amongst the bodies that comprise the solar system. A non-rotating frame in which the solar system barycenter moves at a fixed velocity is an inertial frame of reference. The most convenient is a non-rotating frame with the barycenter at the origin. Finding the barycenter is a bit of simple math in Newtonian mechanics. (It's not quite trivial in general relativity, which I'll get to below.) Making sure it is not rotating is non-trivial. The best effort in these regards is the International Celestial Reference Frame.

In contrast, a heliocentric frame (a frame whose origin is at the center of the Sun) is not an inertial frame. Strictly speaking, $F=ma$ does not apply in such a frame. One can make use Newton's second by introducing fictitious forces. Sometimes this is exactly what you want to do. Modeling the behavior of a spacecraft in low Earth orbit is best done from the perspective of a geocentric frame. Modeling the behavior of a spacecraft orbiting Ceres is best done from the perspective of a Ceres-centered frame. The fictitious forces introduced by such non-inertial perspectives are called third body perturbations.

If on the other hand you want to accurately model the behavior of the solar system, it turns out that a barycentric frame is the way to go. Accurately modeling the solar system in a 21st century context means using general relativity. The third body perturbations that result from using a heliocentric frame are but a small part of the problem. The relativistic perturbations are much more easily expressed in a barycentric frame than a heliocentric frame. Time also gets rather messy from a heliocentric perspective.

It was never my intention to say the Earth system has the center of the sun as the orbital center, however according to JPL the best available ephemerides show this is approximately true where the Earth Sun distance is 'constant' over large numbers of years.

You completely misread that reference.

For the last fifty years, the best available ephemerides have come from the Jet Propulsion Laboratory and the Russian Academy of Sciences. Both use a barycentric frame. Both use general relativity.

 

[Andrew1955]

DH, I am now totally confused as to what you are wanting to tell me. I can see it is important but have no idea what point you are wanting to make to me. Is what you are saying relevant to my original post or are we now going off in another direction?

I my last reply I said:

"It was never my intention to say the Earth system has the center of the sun as the orbital center, however according to JPL the best available ephemerides show this is approximately true where the Earth Sun distance is 'constant' over large numbers of years."

You quoted that text and said "You completely misread that reference"

I am assuming you are wanting to say something about the text of mine you quoted??

Earlier you produced a chart of the Venus Sun distance showing Venus was not 'orbiting' the SSBC. I have seen a similar chart for Earth.

Are you saying the Sun Earth is not more or less constant as shown by JPL and very largely unaffected by the planets? My own calculations show the path of the Earth only has tiny changes created by the influence of the planets because both the Sun and the Earth are being influenced by the planets in similar amounts.

 

[D H]

DH, I am now totally confused as to what you are wanting to tell me. I can see it is important but have no idea what point you are wanting to make to me. Is what you are saying relevant to my original post or are we now going off in another direction?

Your original post had a problem in that it didn't say what "orbit" means, and by implying that there is only one answer. In my opinion, the correct answer to the question "does the Earth orbit the Sun or the solar system barycenter" is YES.

If, on the other hand, your goal is to most accurately model the behavior of the solar system, you need to do some very completed stuff. Amongst them is modeling objects as orbiting the solar system barycenter. Modeling objects as orbiting the Sun yields reduced accuracy.

I my last reply I said:

"It was never my intention to say the Earth system has the center of the sun as the orbital center, however according to JPL the best available ephemerides show this is approximately true where the Earth Sun distance is 'constant' over large numbers of years."

You quoted that text and said "You completely misread that reference"

JPL did not say that. You are quoting from a chapter that was intended to be a part of the Explanatory Supplement to the Astronomical Almanac. (For whatever reason, that chapter never made it into the explanatory supplement). The Astronomical Almanac has not been the best available ephemerides for over fifty years. That title goes to JPL's Development Ephemerides, or perhaps the Russian Academy of Science's Ephemerides of Planets and the Moon. Both use general relativity, and both use a barycentric model.

 

[Andrew1955]

JPL did not say that. You are quoting from a chapter

?

The following text has nothing to do with Chapter 8 of that JPL reference.

"It was never my intention to say the Earth system has the center of the sun as the orbital center, however according to JPL the best available ephemerides show this is approximately true where the Earth Sun distance is 'constant' over large numbers of years."

My text could be made clearer. I am meaning, according to the best available JPL ephemerides, the planets influence on the Earth Sun distance is tiny, compared to the very large differences that would be created by (in lay persons terms) 'orbiting the solar system barycenter'

If you are saying that is not correct then please provide some references to support the idea.

 

[D H]

I am meaning, according to the best available JPL ephemerides, the planets influence on the Earth Sun distance is tiny, compared to the very large differences that would be created by (in lay persons terms) 'orbiting the solar system barycenter'.

That "in lay person's term" is the heart of the problem with this thread. You are interpreting "orbiting the barycenter" in terms of Keplerian orbits. People who say that the bodies in the solar system orbit the solar system barycenter are not talking about Keplerian orbits.

 

[ianchristie]

I do love a circular (elliptical) argument!

 

[Andrew1955]

That "in lay person's term" is the heart of the problem with this thread. You are interpreting "orbiting the barycenter" in terms of Keplerian orbits. People who say that the bodies in the solar system orbit the solar system barycenter are not talking about Keplerian orbits.

>>You are interpreting "orbiting the barycenter" in terms of Keplerian orbits.

Wrong. I am interpreting it as meaning the Earth Sun distance will vary by up to to 2 million kms due to the influence of the planets. Nothing like this is observed to be happening at all.

>>People who say that the bodies in the solar system orbit the solar system barycenter are not talking about Keplerian orbits.

For my purposes there are two types of people that I need to consider:

Type 1. This type is utterly confused and has no idea of what they are talking about other than they think the SSBC has some magic abilities to cause all objects to gravitate towards it.

Type 2. This type is the kind of person you are talking about when you say "People who say that the bodies in the solar system orbit the solar system barycenter are not talking about Keplerian orbits"

If my audience had people of type 2 in it I would not have come to physics forum. I needed a method to calculate the effect of the planets gravity upon Earth so I could know by what amount the Earth Sun distance could vary as caused by the planets gravity. I now know from my calculation that in terms of the huge Earth Sun distance the amount the planets change the path of the Earth, in terms of the Earth Sun distance, is very small.

If you are challenging me on the Earth Sun distance you need to provide a reference.