Dear Dr. Edward Patrick,

Thank you for your message.

I've had a look at your related article. It appears that your caption to Fig. 1 is an oversimplification; it is actually the barycenter of the Earth-Moon system that orbits the Sun on a Kepler orbit, and Earth's centre oscillates aroung this orbit (this is known as "lunar perturbations"). Only because the barycenter is still within Earth, it is not so obvious, and this might lead to the imprecise statement in the figure caption.

For Pluto and Charon, you notice correctly that the barycenter is outside Pluto. But again, it is this barycenter that follows the orbit, and not Pluto itself, thus your Fig. 2 is not an adequate description. The large distance from Earth makes the system difficult, but not impossible to observe.  Actually, it were orbital variations of Pluto (causing variations of the lightcurve and of the apparent elongation of the body) that lead to the discovery of Charon - see e.g. Christy and Harrington, ICARUS 44, 38--40 (1980). So, of course there is evidence for a situation similar to your Fig. 3, and no need for a new explanation. The four small moons are actually "circumbinaries" that orbit the combined mass of Pluto and Charon.

The fact that the (mutual) gravitational force between Pluto and Charon is larger than that between them and the Sun does not mean that it would "break the orbit". It just keeps them orbiting around each other, or rather, around their barycenter. Otherwise, the formation of the planets and their satellites would have dissolved the solar system.

Dear Dr. Jan-Martin Hertzsch,

Thank you very much for your important information.

I shall reply you after study the discovery of the Charon.

Dear Dr Jan-Martin Hertzsch,

First, the orbit of the Earth around the Sun is always perturbed by the Moon. But, in theory, it is noted that, the Hill sphere is usually neglected in considering the orbit. In calculation, there is GMSmM/R2=2.5GMEmM. If it was true, the Moon should have been moved to the Sun. But, in fact, the Moon is orbiting around the Earth.

So, although the Earth is perturbed by the Moon, how to consider this perturbation is an important problem. However, I have not known how to understand “it is actually the barycenter of the Earth-Moon system that orbits the Sun on a Kepler orbit” as the Hill sphere is considered.

Second, from the Wiki, I read that:

Christy noticed that a slight elongation appeared periodically. Later, the bulge was confirmed on plates dating back to April 29, 1965.

Subsequent observations of Pluto determined that the bulge was due to a smaller accompanying body. The periodicity of the bulge corresponded to Pluto's rotation period, which was previously known from Pluto's light curve. This indicated a synchronous orbit, which strongly suggested that the bulge effect was real and not spurious. This resulted in reassessments of Pluto's size, mass, and other physical characteristics, because the calculated mass and albedo of the Pluto–Charon system had previously been attributed to Pluto alone.

https://en.wikipedia.org/wiki/Charon_(moon)

However, this cannot be related to the variation of the orbit.

I am very sorry I cannot read the reference you refer

Till now, I have not known the observation that can deny my sentence:

If the direction of the Pluto is moving as shown in Fig. 3, it is very easy to be observed. The period of the Pluto-Charon orbiting their barycenter is 6.38723 Earth days. The variation of the direction of the Pluto’s motion relative to the orbit is also in a period of almost 6. 38723 days. Till now, no observation has shown such a variation. And, there are other problems in Fig. 3.[7]

If you know any observation that showed that the direction of the Pluto moving along the orbit around the Sun is varied in a period of 6.3 days, please inform me. I shall thank you very much.

An excellent resource for information on astronomical and astrophysical topics is "The SAO/NASA Astrophysics Data System" at http://adsabs.harvard.edu/ - it allows you to search for articles and abstracts, and shows you which ones are on-line. While some online resources are only accessible to subscribers, you might be able to order copies through a library.

As for your comparison of the gravitational effects of Earth and Sun on the Moon, do not forget that the Sun also exerts a gravitational force on Earth. The same applies to Sun, Pluto, and Charon. This is why we need the size of the Hill sphere to know whether one body can be a satellite of another.

Also, it seems that you have started from an oversimplified description of the motions of moons and planets, and that may have caused you some trouble. Remember classical mechanics: the center of mass of a system of particles moves as if it were a point mass on which the external force acts. Thus, in a binary system such as a planet and its moon the two bodies orbit their centre of mass, and if there is a third, heavier body further out, such as a star, the barycenter of planet and moon and the center of mass of the star will orbit the barycenter of that system. Because the star is usually so much heavier than the planets and moons, the barycenter of a solar system is very close to the center of the star, and the difference will be hardly noticeable. That is explained in detail in student textbooks on Newtonian mechanics.

See also Olkin, Wasserman, and Franz, Icarus 164 (2003) 254-259 for observations of the motion of Pluto and Charon about the system barycenter using the Hubble Space Telescope.

Dear Dr Jan-Martin Hertzsch,

Maybe, I did not express my opinion clear.

First, I read a lot of the references about the orbit, the Pluto and its moons.

Second, if the Hill sphere is considered, the barycenter for the Earth-Moon system (or Pluto-moons) is invalid to determine the orbits of them. Because the gravitational force of the Sun on the Earth is F=GMSmE/R2 while on the Moon only is tidal force. So, the Moon has not been moved to the Sun. In another words, if the barycenter for the Earth-Moon system was valid, the Moon should have been moved to the Sun.

If you should want to understand this problem, you could consider the problem: Why the Moon has not been moved to the Sun.

Third, if the Pluto and Charon was binary planet, it must have been observed that: The variation of the direction of the Pluto’s motion relative to the orbit is also in a period of almost 6. 38723 days.

It is certain, till now, no observation has shown such a variation. And, I do not think that you can find such an observation.

I'm sorry, but you do not express yourself clearly at all. In fact, you seem to confuse or misunderstand basic and well-established principles of mechanics. Most obviously, in your discussion of the relative strength of the gravitational forces between three bodies, you neglect that all three exert forces on each other. That seems to be the root of your troubles.

A last piece of advice: Check textbooks on celestial mechanics on the discussion and treatment of the three-body problem. This is actually what your question relates to.

Dear Dr Jan-Martin Hertzsch,

Thank you for your answer.

I think, the key for this problem is that it is impossible:

The variation of the direction of the Pluto’s motion relative to the orbit is also in a period of almost 6. 38723 days.

Why should this be impossible? If you read carefully the story of Charon's discovery, you will find that this has been concluded from the observations, in particular those of the light curve. That's how they learned that Pluto and Charon are tidally locked to each other, because their individual rotation periods are the same as the rotation period of the Pluto-Charon system about its center of mass.

Dear Dr Jan-Martin Hertzsch,

Please cite an original sentence. Not a concluding by yourself.

If there was such a variation, it should be described with many of references.

It's not my conclusion, but that of the discoverers. A few more references (you don't need "many"), just in case you haven't been aware of them yet:

D.J. Tholen, E.F. Tedesco: Pluto's lightcurve: Results from four oppositions. Icarus, 108 (1994), pp. 200–208

Marc W. Buie et al, 2006, The Astronomical Journal 132, 290

I strongly recommend that you read them (in particular the first, and possibly some of the references therein) carefully and revisit the scientific (physical and mathematical) background, too. It may take some time, but it will be worth it. Until later, perhaps!

Dear Dr Jan-Martin Hertzsch,

Please copy the original sentence here.

I know what you saied. But, you do not seriously consider this problem.

First, very simple, if that:

The variation of the direction of the Pluto’s motion relative to the orbit is also in a period of almost 6. 38723 days.

was true, it had been introduced in the book for initial reader and had been generally-known by many general readers.

Second, you must have a whole (but not a piece) of knowledge about the three-body problem and Hill sphere. For example, you have to understand why the Moon have not been moved to the Sun. And, the other four small moons are out of the Hill sphere of the Charon, what is the force of the Charon on the four moons?

Third, for specialists, you have to know the current conclusion about the orbit of Pluto and Charon. For example, it is currently known that there is a difference between the center of light and the center of body for the Pluto-Charon system.

Now, I read all of the references that you referred. I certainly knew that it is the current conclusion that the Pluto and the Charon is binary planet. They orbit around the barycenter of the Pluto-Charon system. And, I knew, this conclusion is that in the references that you referred.

But, I do not think this conclusion is right as it is considered in the Sun-Pluto-moons system. I think, my arguments in references[1,2] are very clear.

References

[1]https://www.researchgate.net/publication/295672153_The_neutralization_of_gravitational_field_and_the_orbits_of_moons_of_the_Pluto

[2]https://www.researchgate.net/publication/295672153_The_neutralization_of_gravitational_field_and_the_orbits_of_moons_of_the_Pluto

Research Proposal The neutralization of gravitational field and the orbits of ...

I have let this discussion rest for a few days and am reluctant to take it up again. Nevertheless, let me recommend that you do not give publications geared towards the "general reader" more importance than those in peer-reviewed journals. As you are surely aware, the former are usually simplified. This may have been the reason why you found it difficult to agree with the conclusions in the articles cited above. Also, you can probably also imagine that not every discovery makes it into a "book for the initial reader" ...

Dear Dr Jan-Martin Hertzsch,

If you should copy an original sentence to support your opinion, I should thank you very much.