Pluto and Charon

[Catastrophe]

The entire Pluto system is interesting on a wider level, but not least is the Pluto/Charon barycentre - which depends on the masses of dwarf planet and satellite - or are they joint dwarf planets?

Pluto's moon Charon sports a red polar cap that forms as seasons change | Space.com Forums

Cat

 

[Catastrophe]

Charon (moon) - Wikipedia

Pluto - 9th Planet - First Dwarf Planet - First Dwarf Planet with 5 moons.

Cat

 

[Pogo]

Yeah, I’mnot sure that they have ever defined at what point does a planet/moon or dwarf planet/moon becomes a double. I guess it would have to with the difference between the geographic center and the barycenter.

 

[Catastrophe]

Personally, I think the centre of gravity (barycentre) being outside either object is a major factor. Of course, if they were of equal mass, the cog would be in the middle of the distance between them.

Cat

 

[Catastrophe]

Imgur: The magic of the Internet

Imgur: The magic of the Internet

NASA

 

[Helio]

Personally, I think the centre of gravity (barycentre) being outside either object is a major factor. Of course, if they were of equal mass, the cog would be in the middle of the distance between them.

How 'bout a double dwarf planetary system? [I'm thinking about a two-scoop ice cream cone for some reason. ]

If the solar system were just Jupiter and the Sun, the barycenter would be about 6% more than the radius of the Sun.

 

[Catastrophe]

How 'bout a double dwarf planetary system? [I'm thinking about a two-scoop ice cream cone for some reason. ]

If the solar system were just Jupiter and the Sun, the barycenter would be about 6% more than the radius of the Sun.

You are very welcome! I try my best to suggest relevant material on the thread topic.

Is that outside the Sun? Wow.

 

[Helio]

Is that outside the Sun? Wow.

Yep. It's your simple FBD.

Hmmmm, perhaps a graphic would be interesting for all to enjoy...

This shows the barrycenter is 6% beyond the solar photosphere, though this will vary for the orbital variations. The others have much less effect.

https://imgur.com/mdLuijV

View: https://imgur.com/mdLuijV

 

[Catastrophe]

These show animation around the barycentre of Pluto:

https://i0.wp.com/mathscinotes.com/wp-content/uploads/2015/06/plutocharonanim.gif?ssl=1

+ is the barycentre.

Source: Barycenter of Pluto and Charon | Math Encounters Blog (mathscinotes.com)

Cat

 

[Helio]

These show animation around the barycentre of Pluto:

https://i0.wp.com/mathscinotes.com/wp-content/uploads/2015/06/plutocharonanim.gif?ssl=1

+ is the barycentre.

Source: Barycenter of Pluto and Charon | Math Encounters Blog (mathscinotes.com)

I couldn't get your Source to load.

Charon at wiki shows almost no eccentricity. So either it's wrong or the cool animation is.

 

[Catastrophe]

Helio, sorry about that The top one works, and I've fixed the lower on one on #9. I think you will like it now.

Cat

 

[Helio]

Helio, sorry about that The top one works, and I've fixed the lower on one on #9. I think you will like it now.

It’s working now, but it’s wrong by showing a Barry center that moves back and forth . Here’s a paper showing zero eccentricity.

 

[Catastrophe]

Helio, you have me confused.

I see my top link in #9 showing the barycentre stationary in the middle (correctly) and the schematic motion relative to barycentre quantified at approx. 14%. Are you saying something is wrong with this?

Cat

 

[Helio]

Helio, you have me confused.

I see my top link in #9 showing the barycentre stationary in the middle (correctly) and the schematic motion relative to barycentre quantified at approx. 14%. Are you saying something is wrong with this?

Notice how the center marking ("+") moves in distance from the surface of Pluto. It oscillates to and fro. This only happens when you have an eccentric orbit. If e=0, there is no oscillation, at least I can't imagine one.

 

[Catastrophe]

Notice how the center marking ("+") moves in distance from the surface of Pluto. It oscillates to and fro. This only happens when you have an eccentric orbit. If e=0, there is no oscillation, at least I can't imagine one.

As far as I can see, the horizontal axis is time going between about 19 and 22. Because this is repeating, the visual is repeating between these values. Because the bodies are moving in our view of them, this time cycling also corresponds to a cycling of the declination up and down in variance with the time movement.

It is difficult to see, with the dec scale moving up and down, but it appears to me that the barycentre + appears stationary. Is this not how you see ?

Cat

 

[Catastrophe]

Notice how the center marking ("+") moves in distance from the surface of Pluto. It oscillates to and fro. This only happens when you have an eccentric orbit. If e=0, there is no oscillation, at least I can't imagine one.

It is making 'my "ead 'urt" but I am seeing Pluto just overlap the edges of the + at the NSEW positions. I would not swear to it, but I would guess that the surface of Pluto remains equidistant from the centre of the barycentre +.

Cat

 

[billslugg]

The barycenter cannot wobble. The center of mass of an isolated system has a constant velocity.

 

[Helio]

https://imgur.com/0rJgZpy

View: https://imgur.com/0rJgZpy


This shows, to me at least, that there must be some eccentricity with the orbit of Charon, contrary to NASA with an e=0.

 

[Catastrophe]

Bill, I think I made it clear that ("in a real world") the barycentre is fixed (in orbit), and does not wobble. Any 'wobble' in the graphic is, of course, due to the cycling of time and declination.

In the real reality, of course, there is one thing for a two body problem and something else entirely for a multi body problem. What would you predict, for example, for the Pluto-Charon plus three more moons system? And what if it were Pluto plus 4 Charon-sized moons?

Cat

 

[Catastrophe]

Helio, you are correct. Between Charon at 'N' and 'S' via 'W' Pluto does seem to jump in and out of its orbit around +'

What is the origin of this graphic? It is certainly not a movie of Pluto and Charon from above! So do we know the assumptions or source of data in making this graphic? Perhaps, as you observe, there must be some eccentricity in the orbit of Charon? Why should there not be?

Cat

P.S. Have you noticed the slip where the time sequence restarts?

 

[Catastrophe]

The dance between Pluto and Charon creates a variable gravitational field that sends the tinier moons in the system “tumbling erratically”. The elongated, non-spherical shape of the moons amplify this effect.
"Prior to the Hubble observations, nobody appreciated the intricate dynamics of the Pluto system,” Showalter said. “Our research provides important new constraints on the sequence of events that led to the formation of the system.”
Nix And Hydra Are Brighter, Kerberos Much Darker
Analyses of the Hubble data also found Nix and Hydra to be much brighter than previously believed. Because brightness is used to calculate size, researchers found that the two moons are only half the size previous studies indicated.
By contrast, the moon Kerberos is “as dark as a charcoal briquette” with a reflectivity of only 4%. This is a surprising find because it was believed the moons would all be similar since they are made of the same material and probably formed at the same time. One possibility is that Kerberos is a pristine, left over piece, from the collision between a proto-Pluto and a proto-Charon.

Source: Google search

barycenter of pluto and its moons

Cat

 

[Helio]

In the real reality, of course, there is one thing for a two body problem and something else entirely for a multi body problem. What would you predict, for example, for the Pluto-Charon plus three more moons system? And what if it were Pluto plus 4 Charon-sized moons?

Agreed. But the graphic is very likely a 2-body model. It may be a model that simply used an assumed eccentricity to emphasize how most 2-body orbits look, failing to note that e=0 in this case. It is very rare to see a e=0, btw. Neptune comes very close.

Adding the moons may or may not cause that much shown relative motion between Pluto and the barycenter. I will do the math if you want me to check, but it might not be worth the effort. Why show a normal 2-body animation that is supposed to represent a multi-body model but leave out the other bodies?

It's no big deal. The yellow color for Charon is a bigger issue, at least for me.

 

[billslugg]

Helio - You are quoting Catastrophe and crediting it to me.
Catastrophe - I was not trying to challenge what you said, I was simply summarizing the argument you and Helio were making.

As for Catastrophe's question: "What would you predict, for example, for the Pluto-Charon plus three more moons system? And what if it were Pluto plus 4 Charon-sized moons?"

The same thing would happen for any number of bodies in an isolated system. The barycenter does not move around. Its velocity vector cannot be changed except by an external influence.

 

[Helio]

Helio - You are quoting Catastrophe and crediting it to me.

Oops. Sorry. I was rushing to get done to get to a meeting.

As for Catastrophe's question: "What would you predict, for example, for the Pluto-Charon plus three more moons system? And what if it were Pluto plus 4 Charon-sized moons?"

The problem with other bodies is their relative mass, distance and periods. The animation doesn't seem to represent any of those variables.

The same thing would happen for any number of bodies in an isolated system. The barycenter does not move around. Its velocity vector cannot be changed except by an external influence.

I'm unclear what you mean. The barycenter is a dynamic c.g., so it all depends on what one chooses to use for a reference frame, though the barycenter itself is the normal one, so, by definition it doesn't move, to your point. Yet, relative to "space coordinates", if one could establish them from say 2 light years away, it does wobble as planets align, for instance.

A see-saw analogy, though limited, might help. With two people on a balanced see-saw, there is one fixed c.g. (baryenter). But what happens when one big person is on one side and you have four little guys moving back and forth on the other side? An auto-c.g. centering mechanism would have to either move the board quickly (and all that are on it) or move along the ground. Either way, it must be moved.

 

[billslugg]

The velocity vector of the center of mass of an isolated system, as measured in an inertial coordinate frame, cannot change except from an external influence.

As the planets in a Solar System move around and change places the velocity vector of the barycenter of that sytem will not change as observed from an inertial reference frame.

If you are basing your coordinate frame on one of the revolving planets then it is not an inertial frame and the barycenter will be seen to wobble all around.

In the seesaw case it is not an isolated system. As the four little people move around they are pushing the seesaw legs against the Earth and moving the Earth slightly. When the Earth's mass and position is considered as part of the isolated system, the COG will not move.

When a space ship sits somewhere out in space and then fires its engines to travel to the far end of the Solar System, its center of mass never moves. The mass of the payload at one end of the Solar System is exactly balanced by the mass of the exhaused propellant on the other side of the Solar System.