Where is Jupiter? On prediction, modeling and unknowability.

Most of us think we have a solid grasp of the basics of gravity and the basic workings of our solar system.

Massive things attract stuff, things in motion stay in motion until acted on, we have 8 (or 9) planets orbiting the sun, and so on.

Image for post
Image for post

We tend to think this knowledge is backed by tons of really high end physics and math and that there are experts calculating with extreme precision where the planets will all be exactly into forever into the future.

This is simply not true. Our knowledge is limited both in what we actually know and in what we could ever know.

Let’s go on a journey together to make this very clear.

At the time of this writing here’s what the JPL/NASA simulator (https://space.jpl.nasa.gov/) reports as the configuration of our solar system:

Image for post
Image for post
August 12, 2019 configuration of solar system from JPL
Image for post
Image for post
Top view August 12, 2019 configurator of solar system from JPL

WolframAlpha has the solar system like this uses standard JPL math (https://ssd.jpl.nasa.gov/?planet_pos and https://ssd.jpl.nasa.gov/?gravity_fields_op):

Image for post
Image for post
WolframAlpha Configuration of Solar System August 12, 2019

Here’s another simulation from https://mgvez.github.io/jsorrery/ that uses standard JPL math (https://ssd.jpl.nasa.gov/?planet_pos and https://ssd.jpl.nasa.gov/?gravity_fields_op) and some other tricks to do these calculations

Image for post
Image for post

and just to make it clear that all these sources AGREE for the current (measured/observed and not predicted state of the solar system) we can rotate the wolframalpha and jpl images and plot red lines to show distance and angle agreement from the sun (using Jupiter and Pluto as easy references).

Image for post
Image for post
Expected and Observed agreement between solar system positioning diagrams.

The initial conditions of these simulation systems seem to be in agreement. The reported source data and source math to initialize these systems is in agreement. But what happens if we ask these systems where everything will be in 5 years? (that’s not too far… and seems reasonable to be able to predict 8 or 9 planets 5 years into the future, right?)

JPL predicts this for August 12, 2024:

Image for post
Image for post
JPL Simulator for August 12, 2024

Wolfram Alpha predicts this for August 12, 2024:

Image for post
Image for post

And the browser simulator:

Image for post
Image for post

Still good alignment between the systems

Image for post
Image for post

How about 2029?

JPL doesn’t bother.

Image for post
Image for post
Image for post
Image for post
Image for post
Image for post

How about 3029?

starting to see some divergence.

Image for post
Image for post
Image for post
Image for post

How about 4029?

We’re starting to see these models be off by quite a bit. Jupiter’s orbit is showing 20–30 degrees difference.

Image for post
Image for post
Image for post
Image for post

Let’s just make it totally clear and go all the way to 9029:

Jupiter, again as easiest to see, is off by almost 90 degrees.

Image for post
Image for post

Put this into perspective. Three systems using the same initial conditions for observed planet positions, physical properties and the exact same mathematical formulas are unable to predict with any sort of accuracy where the largest objects in our ~ 4.571 billion year old (+/- 20 or 30 million years) solar system will be in a mere 7000 years.

This demonstration is very coarse. The actual variance is very hard to get your head around. Our cosmological predictions being off by millions of years and 500 million miles etc is very common and seems small cosmologically, but in human terms these errors beyond even huge. In a computational sense you can’t trust them at all. They are merely directional insights, useful descriptions.

JPL knows this and has lots of information on it. For example, here’s the math behind its simulator. It’s a known low accuracy formula for approximations. These low accuracy things are good because they are very fast/cheap to compute.

JPL articulates the error rates in a nice table:

Image for post
Image for post

JPLs more accurate system HORIZONs is more involved.

So let’s use this and compute the future.

Image for post
Image for post

It does not allow to go out beyond 2599.

Let’s be more modest and compute for August 22, 2019

Wolfram Alpha says jupiter will be here:

Image for post
Image for post
Image for post
Image for post

This all gets very hard to triangulate and compare. Across systems, notation, formula and observations. All of this hardness contributes to the problem.

JPL gives us some insight into this hardness in its discussion of planetary ephemeris.

If it’s not obvious what we often mis-categorize as “good prediction” let’s make the point directly: our predictions aren’t getting better, our observations are.

Understanding of orbital mechanics and planetary dynamics of the solar system improve because we have far more course correcting measurement instruments relaying information back. Our models are growing in COMPLEXITY from a constant stream of CORRECTIVE DATA not from improvements in the mathematical or computational orbital mechanical models. In fact, the complexity of models is almost wholly accounted for by the complexity of the instrumentation and relayed data. The “models” are no longer just models of planets and solar system gravity… but a much larger collection of far more bodies in the universe, other effects like magnetic fields, solar winds and all the models of course correcting instruments plus the machine learning and data science methods of the data crunching.

Again, if it’s not obvious that complexity doesn’t come for free (this instrumentation is extremely hard and expensive to keep running and computing) and it isn’t really increasing our ability to reach further into the future with more accuracy. It’s allowing us to course correct for more and more instrumentation in the adjacent possible of the near past and near future.

This is a very hard point to get our heads around.

One exercise that will make this much more clear for all of us. Let’s all build a solar system from the ground up and see if we can mimic the behavior of our own solar system for even a short timespan.

You the reader should now do some homework!

NSTMF has this wonderful gravitational system simulator:

https://lab.nstmf.org/gravity/

Image for post
Image for post

This system allows you to set up as many objects with mass into a space and see how they interact. Attempt to get good at creating systems that exhibit anything even close to our giant star in the middle with 8 or 9 planets and some large moons around some of them. (you can forgo the asteroid belt, etc)

Image for post
Image for post

What strategy should you pursue?

  1. try to perfectly drop in 9–10 objects at the perfect angular momentum and mass and proportion and distance from each other?
  2. mimic adding the planets in the order we think the solar system made or absorbed them?
  3. start more simply with just a mass or two and let things go for awhile?
  4. randomly try anything and everything between those strategies?

Record how many attempts it takes you and how long your solar system remained stable or achieved anything resembling or solar system. Use whatever measures work for you to assess this.

Use this previously linked browser simulator of the solar system to compare your own:

It is very unlikely you will be able to simulate the solar system for even a brief moment. It is exceedingly unlikely you will create a system that remains stable like the simulators of our meticulously initiated and calculated systems from Wolfram or JPL.

Why is that?

Is the problem the simulators? and what aspect of the simulators? is it the parameters you put into your own simulator? is it the code running the simulators and not just the “math” but something else? are their bugs? Are there unknown assumptions that need to be known?

Do you think there is any possibility for getting accurate predictions of the solar system or any given body in the solar system 100 years? 5000 years? what would accurate predictions be in terms of position, distance, speed?

Finally, if our best math, 100,000 physicists brains, and trillions of dollars of observations cannot predict Jupiter’s position 600 years into future better than what has shown above why are so many of us convinced prediction is a generally possible thing?

And most generally: what is prediction? and What makes something “predictable?”

Written by

I be doing stuff. and other stuff. More stuff. http://www.worksonbecoming.com/about/ I believe in infinite regression of doing stuff.

Get the Medium app

A button that says 'Download on the App Store', and if clicked it will lead you to the iOS App store
A button that says 'Get it on, Google Play', and if clicked it will lead you to the Google Play store