Solar System barycenter - Orbit of planets

[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.