Hey Crazies.
The Earth orbits the Sun in a nearly-perfect circle.
It’s simple, regular, and reliable.
But not all orbits are like that.
Some of them can get really weird.
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Ok, let’s start with the basics. The word "orbit" is pretty broad.
It’s defined as any path where gravity is the only influence.
Like I said, it’s pretty broad.
Wouldn’t that mean free fall is an orbit?
Um. Yeah. Yes, it would.
What?!
I know. It seems weird.
How can this be an orbit?
It’s a straight line that starts and ends.
That last part is where I think most of our trouble comes from.
How can a path that ends be an orbit?
I think it’ll help if we imagine what would happen if the Earth didn’t get in the way.
This is just a portion of a much larger path.
One that goes all the way through the Earth.
If we dig a big tunnel and remove all the air, then there’s nothing in the way.
The squirrel will fall forever, back and forth through the Earth.
That feels a little more like an orbit, doesn’t it?
Ok, if you’re still not convinced, it’ll be more obvious if we make him move sideways too.
Say we launch the squirrel off a building using a slingshot.
Introductory physics tells us the squirrel’s path will be a parabola.
But that’s only approximately true.
Let’s zoom out and launch him way harder.
We can see now that his path is actually a small portion of a large ellipse,
an ellipse he would travel along if the Earth didn’t get in the way.
Ellipses are very common orbit shapes.
Parabolas happen too, just not near the Earth’s surface.
In fact, using Newton’s laws on a pair of objects is called the two-body problem
and there are only five types of solutions for those problems.
Lines, circles, ellipses, parabolas, and hyperbolas.
That’s it. Just five basic shapes.
Lines are just free fall, like the squirrel in the tunnel.
Circles and ellipses are what we expect for planets orbiting stars or moons orbiting planets.
Even moons can have moons.
We call them moon moons.
Parabolas and hyperbolas are the orbits of things that zip in and then zip right back out.
You know, like that Oumuamua object everyone was all excited about a couple years ago.
These five basic solutions are what we call the conic sections
because they can be found when a plane cuts through a cone.
They’re the solutions of the two-body problem.
Actually, those aren’t very realistic examples.
I know. I know.
Ok, here’s the deal.
There’s really no such thing as an exact two-body problem.
We like to think the Earth’s orbit is only affected by the Sun,
but it’s also affected by the Moon.
That makes it a three-body problem.
This might look circular or at least elliptical,
But, if I exaggerate things, you can see these orbits aren't any of the conic sections.
They’re kind of wavy.
Gravity is still the only influence though, so they’re still considered orbits.
On the whole, three-body orbits tend to be chaotic and unstable.
Many look like they have no pattern at all.
Some will collapse together to form one big object.
Others will throw an object into deep space and become a two-body system.
The vast majority of three-body solutions are like this.
But not all of them.
I mean, the Sun–Earth–Moon system is stable and regular, right?
There must be other stable examples.
And there are, but some of them are kind of unexpectedly weird.
We call these free fall orbits because they act kind of like the squirrel falling through the Earth.
Each object moves along its own path, but those paths are not loops.
They’re segments.
They each have a beginning and an end.
Will they do that forever?!
Sure. Well, unless they get nudged by a fourth object.
Free fall orbits are extremely sensitive.
They’re like a tiny island of stability in a sea of chaos.
One little gravitational nudge and it’s all over.
Which brings me to my next point:
There’s no such thing as an exact three-body problem either.
If we consider the entire solar system,
there’s the Sun, the 8 planets, a bunch of dwarf planets, and countless asteroids and comets.
That’s a many-body problem.
The early solar system was a very chaotic and unstable place.
Things were moving all over, running into each, being thrown out of the solar system.
The only reason it’s stable now is because the big stuff that remains is pretty far apart.
Those vast distances make each planet behave as if it forms a two-body system with the Sun.
And that means the conic sections work fairly well in the short term.
But, in the long term, we have to make some corrections.
The most well-known of these corrections is orbital precession.
Also, known as the precession of the perihelion.
I know. Those are fancy names, but they're actually not that complicated.
In an elliptical orbit like this, the perihelion is the point where the planet is closest to the Sun.
It’s literally what the word "perihelion" means.
But, we’ve already said that orbits are only that simple in a two-body problem.
The solar system is not a two-body problem!
Even though they’re really far apart, the planets do still tug on each other a little.
Those tugs are gravitational, so the path is still considered an orbit.
It just makes the orbit precess.
The perihelion of the ellipse shifts around over long time periods.
The precession isn’t really that big for planets around a normal star.
Fine. Thanks for the reality check.
He’s right as usual.
You’ll only see a precession this large around a neutron star or black hole.
Around a normal star, the shift is much smaller.
You'd have to observe the planet for decades before you'd notice.
This precession happens with all the planets in our solar system,
but none of them are as famous as Mercury’s.
When we measure Mercury’s precession, the shift is 5600 arcseconds every century.
Um. What’s an arcsecond?
It’s just an itty bitty tiny angle.
Circles are divided into 360 degrees, right?
Well, 1/60th of a degree is called an arcminute
and 1/60th of an arcminute is called an arcsecond.
That makes Mercury’s 5600 arcseconds a little over a degree and a half per century.
Since 360 degrees would be one full cycle,
Mercury’s perihelion won’t come back to where it is now for 23,143 years.
That’s a long time!
We do have a minor problem though.
When we consider all the tugs with Newton’s laws,
we only predict that Mercury precesses by 5557 arcseconds every century.
The prediction is off by 43 arcseconds.
That might sound small, but it means the prediction of the full cycle is off by 179 years.
It cannot be written off as measurement error.
Unfortunately, we'd have to wait until 1915 for Einstein and his friends to solve it.
We needed the general theory of relativity, or just general relativity for short,
which says that gravity is actually spacetime curvature.
I’ve got an entire playlist about it if you’re interested, but here’s the basic idea.
Gravity isn’t actually a force that pulls things together.
Gravity is just the name we give to the physical distortion of space and time.
We still call it gravity though, so any paths curved by that distortion are still considered orbits.
It just tweaks the rules a little bit so we can fix some of the errors we were getting with Newton’s laws.
You know, like that missing 43 arcseconds of precession every century for Mercury.
Those types of errors, while important to fix, are ordinarily pretty negligible.
99% of the things in 99% of the universe obey Newton’s laws.
But sometimes things aren’t ordinary.
Sometimes they’re extraordinary.
The craziest example being a black hole, which isn’t actually hole.
Black holes are roughly spherical. They’re balls.
Black balls in space!
Spacetime is so curved around these things that some really weird [censor] happens.
The path that light takes can get bent too, which leads to some very strange optics.
If that light is close enough to a black hole, it can actually orbit on a close loop
or even fall in just like anything else.
A little further out, even the orbits of massive objects can do unexpected things.
They can zoom in and then out, whirling around as they go.
That’s why we call orbits like this “zoom-whirl orbits.”
Actually, this is really calming. Maybe I’ll just let it play for a little bit.
What? Huh? What? What?
Where was I? Right! Black holes.
All orbits up to this point have been planar.
That means each orbit stays in its own plane.
But almost all black holes are rotating and that does even weirder [censor] to orbits.
Planar orbits like this one are only possible in the equatorial plane of the black hole.
In that plane, we can still find zoom-whirl orbits.
Outside of that plane, all bets are off.
The spacetime curvature pulls the orbit out of the plane and into three dimensions.
This is the weirdest looking orbit that I can think of.
So how weird can orbits get?
Pretty weird actually.
We like to think of orbits as simple conic sections: circles, ellipses, parabolas, or hyperbolas;
but that’s only approximately true.
Those shapes can precess.
They could have some waviness to them.
They might look kind of like free-fall.
They could zoom and whirl like this orbit around a black hole.
They might even do whatever this is.
It all depends on how accurate you want to be and extreme you want to get.
So were you surprised by any of these orbits?
Let us know in the comments.
Thanks for liking and sharing this video.
Don’t forget to subscribe if you’d like to keep up with us.
And until next time, remember, it’s ok to be a little crazy.
To everyone overwhelmed by my last video.
Yes, I know it was kind of a niche topic, but I started it over a year ago.
I had to let it go so I could move on to bigger and better things.
Hopefully, today’s video was more to your liking and thanks for watching.