Starship Asterisk*

guest137 wrote: ...
Interesting discussion about absence of epicycles in the lunar orbit. Early in the history of the Earth-Moon system there likely would have been. The inner moons of Jupiter and Saturn should also show epicycles in plots like these. But Titan, with an orbit in Saturn's 'equitorial regeim' does not show epicycles.

1. Of the 69 moons listed for Jupiter, All moons within Io's orbit (4) show epicycles (loops). Io is just beyond the epicycle limit.
2. All moons from Io to S/2003 J 5 (60) show wiggles with curvature sign change, but no loops
3. The remaining outer moons (5) curvature sign does not change (every point in the orbits are locally "convex")

1. Wiggles with curvature sign change diminishingly occurred out to ~68% of the current orbital radius.
2. For all larger radii, the orbit showed, and will show, no curvature sign change.

Chris Peterson wrote:

Rules For wrote:

Chris Peterson wrote:
Well, why should [the Moon] be on the [Earth's] equatorial plane? Satellite orbits are stable at any inclination.

I don't know, other than that nearly all of the other major moons in the Solar System orbit very near to their planet's equatorial plane.

The Moon is a complex example, given that it likely resulted from a massive collision which would have produced debris at a range of random inclinations, because of the complexity of the Sun-Earth-Moon tidal forces, and because of the way angular momentum is transferred between rotations and orbits.

               obliquity/axial tilt
-----------------------------------
Jupiter 	       3.13°
Venus 	         2.64°
Moon 	          1.54° (with respect to ecliptic)
Mercury 	       0.034°

Chris Peterson wrote:

MarkBour wrote:Finally, what is the meaning of the red "X" ? If it is not a collision, then is it the point at which the Earth was "removed" ? I am then guessing that throughout the video the mass of the Earth was perhaps being steadily reduced to zero ?

The "X" is when the Earth was removed. Otherwise, nothing was changing during the video except the scale factor (shown by the Earth-Moon distance). The actual orbit is what you see when the scale factor drops to one (the distance is just shown as 380 m.km.) That's what the lunar orbit around the Sun-Earth system looks like- a dimpled ellipse. Then the Earth is removed, and the Moon continues to follow the same orbit, just unperturbed by the Earth.

The loops/epicycles are just there at the beginning to emphasize what you can get with a three body system. They do not exist in the Earth-Moon-Sun system.

Rules For wrote:

Chris Peterson wrote: Well, why should it be on the equatorial plane? Satellite orbits are stable at any inclination.

I don't know, other than that nearly all of the other major moons in the Solar System orbit very near to their planet's equatorial plane.

Chris Peterson wrote:

moontrail wrote:I miss in the lovely animation both earth and moon orbiting the center of masses of its binary system instead of moon just circling earth.

We wouldn't be able to see it at this scale. The distance from the Earth to the Moon is about 380 000 km. The Earth-Moon barycenter is less than 5 000 km from the center of the Earth (beneath the surface). That's just over 1% of the orbital radius of the Moon- at the scale of this video, less than a pixel. It's entirely possible the model used to create this video actually does have the two bodies orbiting around their barycenter.

Rules For wrote:

Chris Peterson wrote:It's also a problem that the Moon isn't in a circular orbit, and doesn't lie on our equatorial plane.

I've long wondered why the Moon's orbit lies so much closer to the ecliptic than to the celestial equator, but I've had a difficult time finding explanations online. Does anybody here have any?

Chris Peterson wrote: ...
The loops/epicycles are just there at the beginning to emphasize what you can get with a three body system. They do not exist in the Earth-Moon-Sun system.

Chris Peterson wrote: Well, why should it be on the equatorial plane? Satellite orbits are stable at any inclination.

MarkBour wrote:Finally, what is the meaning of the red "X" ? If it is not a collision, then is it the point at which the Earth was "removed" ? I am then guessing that throughout the video the mass of the Earth was perhaps being steadily reduced to zero ?

Chris Peterson wrote:

MarkBour wrote:

bystander wrote:<<Youtube video>>Be sure to watch it all.

This lovely animation is not what is happening, though. The moon is not getting closer to the Earth, it is getting farther away (currently, 3.8cm per year). https://en.wikipedia.org/wiki/Lunar_dis ... astronomy) Perhaps there was some reason for this animation to depict what it is showing, with the Moon spiraling in and colliding with the Earth..

That's not what it was showing. It was showing what the Moon's orbit looks like as you zoom outward to actual scale, and then what it looks like if you make the Earth go away. There was no collision, and none of the orbital distances were changing over the course of the animation.

moontrail wrote:I miss in the lovely animation both earth and moon orbiting the center of masses of its binary system instead of moon just circling earth.

MarkBour wrote:

bystander wrote:<<Youtube video>>Be sure to watch it all.

This lovely animation is not what is happening, though. The moon is not getting closer to the Earth, it is getting farther away (currently, 3.8cm per year). https://en.wikipedia.org/wiki/Lunar_dis ... astronomy) Perhaps there was some reason for this animation to depict what it is showing, with the Moon spiraling in and colliding with the Earth..

bystander wrote:<<Youtube video>>Be sure to watch it all.

Catalina wrote: I have never pondered that idea before--interesting. Is there a diagram illustrating the moon's solar orbit somewhere?

Chris Peterson wrote:

Rules For wrote:

Chris Peterson wrote:It's also a problem that the Moon isn't in a circular orbit, and doesn't lie on our equatorial plane.

I've long wondered why the Moon's orbit lies so much closer to the ecliptic than to the celestial equator, but I've had a difficult time finding explanations online. Does anybody here have any?

Well, why should it be on the equatorial plane? Satellite orbits are stable at any inclination.

Keep in mind, as well, that dynamically it's better to see the Moon in orbit around the Sun than the Earth. It experiences no epicycles; its orbital pattern around the Sun looks like an ellipse with little dimples every month. If the Earth just disappeared, the Moon would continue right along in practically the same orbit it's currently in. Just the dimples would disappear.

Rules For wrote:

Chris Peterson wrote:It's also a problem that the Moon isn't in a circular orbit, and doesn't lie on our equatorial plane.

I've long wondered why the Moon's orbit lies so much closer to the ecliptic than to the celestial equator, but I've had a difficult time finding explanations online. Does anybody here have any?

Chris Peterson wrote:It's also a problem that the Moon isn't in a circular orbit, and doesn't lie on our equatorial plane.

Guest wrote:
The ring made me wonder. Does a body require more than 1 moon to provide conditions for a ring to form? And rings seem to be pretty common in our solar system; Around big planets and the midgets too. Does the Earth not have a ring because we have less than 2 moons?

https://en.wikipedia.org/wiki/Ring_system wrote:
<<It had previously been theorized by some astronomers that Pluto might have a ring system. However, this possibility has been ruled out by New Horizons, which would have detected any such ring system.

10199 Chariklo, a centaur, was the first minor planet discovered to have rings. It has two rings, perhaps due to a collision that caused a chain of debris to orbit it. The rings were discovered when astronomers observed Chariklo passing in front of the star UCAC4 248-108672 on June 3, 2013 from seven locations in South America. While watching, they saw two dips in the star's apparent brightness just before and after the occultation. Because this event was observed at multiple locations, the conclusion that the dip in brightness was in fact due to rings is unanimously the leading theory. The observations revealed what is likely a 19-kilometer-wide ring system that is about 1,000 times closer than the Moon is to Earth. In addition, astronomers suspect there could be a moon orbiting amidst the ring debris. If these rings are the leftovers of a collision as astronomers suspect, this would give fodder to the idea that moons (such as the Moon) form through collisions of smaller bits of material. Chariklo's rings have not been officially named, but the discoverers have nicknamed them Oiapoque and Chuí, after two rivers near the northern and southern ends of Brazil.

A second centaur, 2060 Chiron, is also suspected to have a pair of rings. Based on stellar-occultation data that were initially interpreted as resulting from jets associated with Chiron's comet-like activity, the rings are proposed to be 324 (± 10) km in radius. Their changing appearance at different viewing angles can explain the long-term variation in Chiron's brightness over time.

Ring systems may form around centaurs when they are tidally disrupted in a close encounter (within 0.4 to 0.8 times the Roche limit) with a giant planet. (By definition, a centaur is a minor planet whose orbit crosses the orbit(s) of one or more giant planets.) For a differentiated body approaching a giant planet at an initial relative velocity of 3−6 km/s with an initial rotational period of 8 hours, a ring mass of 0.1−10% of the centaur's mass is predicted. Ring formation from an undifferentiated body is less likely. The rings would be composed mostly or entirely of material from the parent body's icy mantle. After forming, the ring would spread laterally, leading to satellite formation from whatever portion of it spreads beyond the centaur's Roche Limit. Satellites could also form directly from the disrupted icy mantle. This formation mechanism predicts that roughly 10% of centaurs will have experienced potentially ring-forming encounters with giant planets.>>

Guest wrote:The ring made me wonder. Does a body require more than 1 moon to provide conditions for a ring to form? And rings seem to be pretty common in our solar system; Around big planets and the midgets too. Does the Earth not have a ring because we have less than 2 moons? I'm talking the celestial type of ring, not the bathtub type...

rstevenson wrote:

Guest wrote:... PS: If you don't want kids asking questions, just say so. Don't bust them over the head with 'silly anti spam bot questions'

The silly anti spam bot questions are not there to prevent children asking questions. They're there to prevent -- amazing coincidence! -- spam bots from littering the forum with spam, which they would happily do (if spam bots can be happy.)

Guest wrote:... PS: If you don't want kids asking questions, just say so. Don't bust them over the head with 'silly anti spam bot questions'

Fevered wrote:
Clicked on the "ring discovered" link, took me to a very curious looking dog. Is his name ring? Is he the discoverer of the ring? Inquiring minds want to know!

https://en.wikipedia.org/wiki/Pete_the_Pup wrote:

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<<Pete the Pup (original, 1924 – June 1930) was a character in Hal Roach's Our Gang comedies (later known as The Little Rascals) during the 1930s. Otherwise known as "Pete, the Dog With the Ring Around His Eye", or simply "Petey", he was well known for having a circled eye that was added on by Hollywood make-up artist Max Factor and credited as an oddity in Ripley's Believe It or Not. The original Pete (sired by "Tudor's Black Jack") was an American Pit Bull Terrier named "Pal the Wonder Dog", and had a natural ring almost completely around his right eye; dye was used to finish it off.>>