# Why are these objects moving at Vastly Different Speeds along the same orbit?

UPDATE: The on-line simulation seems to be working beautifully now! I'd recommend anyone to go back and take another look to enjoy both the mathematical beauty of orbital mechanics, and the aesthetics of the solar system visualization!

New York Times article Visualizing the Cosmic Streams That Spew Meteor Showers links to a solar system viewer that allows one to visualize aspects of meteor-shower-inducing comet orbits by Ian Webb.

Now, astronomers and engineers have created an animation that lets you witness the entire journey. Using data from the Cameras for Allsky Meteor Surveillance, a network of about 60 cameras pointed at the sky above San Francisco Bay, researchers have recorded more than 300,000 meteoroid trajectories since 2010. They plan to use the data to confirm more than 300 potential meteor showers that scientists have observed, but not verified.

“Each dot that you see is a shooting star that was captured by one of our cameras,” said Peter Jenniskens, an astronomer at the SETI Institute and NASA Ames Research Center in Silicon Valley, Calif., who runs CAMS. His interactive transforms meteor showers like the Geminids and the Orionids into shimmering rivers of space rocks. Viewers can pinpoint the moment the Lyrids or Eta Aquarids light up the night by watching when their streams intersect with the Earth’s orbit, shown in blue. There is even an option to see all the meteor showers at once, making it look like a meteor hurricane.

I need some help understanding what I'm looking at. When I first open it up I believe I see a number of objects following the same general hyperbolic (or very elliptical) orbit. What bothers me is that some seem to zip past very fast, some seem to crawl slowly, and some are moving at intermediate speed. If they are all associated with one primary comet, and follow similar paths in this large (roughly 10 AU) view, shouldn't they have at least roughly similar velocities?

Edit: I've snapped screenshots from 30-10-2017 to 04-11-2017 at a speed setting of 0.005 and made two GIFs below The second one is annotated with a red, green, and blue arrow indicating three objects (slow, medium, and fast) following nearly the same orbit with at least a factor of 10 different speeds between them.

I have replayed viewing from different angles, they follow nearly the same orbit in 3D, all the way around the sun and back into space - it is not related to a particular view.

I believe this to be completely unphysical!

Red, Green Blue (slow to fast)

• You're basically right. That kind of variation in the visual is simply not possible. It's bad graphics. – userLTK Apr 3 '17 at 11:49
• @userLTK When a web site that is supposed to provide a science-based graphic representation has "bad graphics", are there more candid adjectives that apply? Look at the display for Haley's comet for example, it is total nonsense/non-science. And yet this gets a write-up in the New York Times Science section. I went back there and looked more carefully. This animation has been created my named "astronomers and engineers", one at NASA Ames Research Center. – uhoh Apr 3 '17 at 12:09
• I know this is bothering you (and the bounty proves it), however I'd suggest the only people who can properly explain what's happening are the NYTimes and maybe NASA Ames, as it's their display. I think you'd be better off contacting the NY Times (first) to ask for their source for the display and then (presumably) whoever at NASA Ames they direct you to and explaining your issue. I think it's beyond the scope of what anyone else can explain. Actually there's an argument that they have a responsibility to clarify the issue. – StephenG Apr 5 '17 at 11:36
• @StephenG to which category does the poster of this answer belong? I don't think it's wise to speak for everyone here, especially when you are saying they all don't know something, nor could any of them ever figure it out. – uhoh Apr 5 '17 at 16:36
• The point is that you have good leads to the sources of the data and it's far more likely they can provide an explanation than that someone else (who incidentally doesn't have the data or code) will. It's the obvious avenue of attack for a definitive answer and you clearly want a definitive answer. – StephenG Apr 5 '17 at 19:19

Looking at the simulation, and the gifs attached here, some things are clear. The dots cannot represent actual meteoroids in their orbits, as the 6 orbital elements fully determine the state vectors of a body. You can't be in the same orbit, at the same place, at the same time and have very different velocity. Thus the dots don't obey Kepler's third law.

It is not clear that they obey the second law either (that equal areas are swept out in equal times) They do seem to move faster at perihelion but perhaps not fast enough.

The graphic doesn't seem to show the "lumpiness" of some meteor streams. Notably the Leonids, which have a very intense storm, roughly every 33 years. Other streams are also lumpy which doesn't seem to be apparent in this graphic.

What it does show is the variation in orbit of the meteoroids that form a meteor shower. This is where (I guess) Nasa was involved. From the observation of a meteor (ideally several observations of the same meteor to triangulate its position) it should be possible to work out its orbit before it fell into Earth's gravitational field and hit the atmosphere. Observe enough meteors and you can get an idea of the distribution of orbits: the mean and standard deviation in the inclination, eccentricity, semimajor axis, ascending node and angle of perihelion. From these, you can get a distribution of elliptical orbits. There may be some modelling work do be done: we can only observe those meteorids that hit the Earth, but we can suppose the they are distributed all around the parent body. But from our sample of meteoroids that hit the Earth, we can model the distribution of those that never will.

The dots are drawn on these Keplerian orbits, but the speed at which the move on the orbit doesn't seem to represent the actual speed of meteoroids in space. Rather it is a way of illustrating the variation in elliptical orbits, without drawing a solid ring for each orbit.

• That's a pretty thorough, and well thought out analysis! I have the same impression on the speed as you mention, but decided that trying to start measuring it was a little too much work. – uhoh Apr 5 '17 at 16:16
• I've noted at the top of the question that the bug is fixed, and the simulation now looks really great! – uhoh Apr 20 '17 at 1:02

Over time, small objects relatively close together at the start will be pulled into quite different orbits by the perturbations of larger objects (like Jupiter) and even Earth if they approach closely.

Relatively small changes at close approach can have quite large effects when the objects reach their furthest approach.

The orbits are approximately elliptical (some may be hyperbolic) and the orbital velocity will vary in such an orbit (unlike a circular orbit). So you'll see objects drifting along at the furthest reach of their orbit and speeding up as they "fall" in to the closest point of their orbit. They'll again slow down as they "rise up" away from the closest approach (exactly as a stone you throw into the air).

So the combination of these things means that the objects can separate significantly over time into quite distinct orbits that have quite significant differences in orbital velocities.

• Can you add some math to that? I'd like to understand how the orbits can appear so close together and yet have what looks like as much as a factor of five or 10 difference in speed at 5-10AU. – uhoh Apr 1 '17 at 9:58
• "Appear close together" is the issue here. They're only close together in terms of closest approach, and they separate out the other end of their orbits. Some maths here and here. This page also shows how the eccentricity affects the difference between orbital velocity at closest approach and furthest. Note also the effect of semi-major axis on velocity. – StephenG Apr 1 '17 at 10:08
• OK I'd better get more quantitative in my question to show mathematically why I feel they should not have such a large range in speeds. I'm talking only about the objects that follow closely the comets orbit, not about all of the incidentals. Give me a few minutes to write it up, thanks! – uhoh Apr 1 '17 at 10:17
• Keep in mind also that numerical simulations are prone to introducing larger errors as the close approach (in particular) is very sensitive numerically. Time-step can be quite a significant issue in simulations like these (because the process is quite sensitive to exactly how you interpolate between steps). – StephenG Apr 1 '17 at 11:41
• After playing with a way to "prove it" using the vis-viva equation, and with simulations, I decided that I shouldn't have to defend the premise that objects can travel on nearly the same orbit around the sun with speeds that vary by an order of magnitude. I take this truth to be self evident. It's possible you didn't look at the simulation as carefully as I did. So I've made some GIFs to better illustrate to what I'm referring. – uhoh Apr 3 '17 at 5:50