All these worlds…

 

Jupiter's Great Red Spot (NASA via http://wanderingspace.net/category/jupiter/)
Jupiter’s Great Red Spot (NASA via http://wanderingspace.net/category/jupiter/)

 

I started to write a Facebook post when I figured, hey, it’s been 18 months or so since I’ve posted anything here…I should probably justify the cost of this website or something.  LOL.

As you may know, NASA’s Juno probe has arrived at Jupiter and will soon start sending back epic images of the planet and it’s moons, as well as critically important data about the structure of Jupiter’s interior.  Jupiter is the most planet-est planet in the solar system because it started to form first and got first dibs on all the yummy material in the Sun’s accretion disc.  So, to understand how it formed and what it’s made of is to understand the earliest point in our solar system.  I can’t wait to see some new amazing images.  Personally, I’m hoping for a monolith…

...my God, it's full of stars...
…my God, it’s full of stars…

Fun fact.  Jupiter (the Roman god) was a notorious adulterer and most of its moons (such as Io, Europa, Callisto, and Ganymede) are named for his lovers.  Juno, however, the name of the probe that was sent to check in on Jupiter and discover it’s secrets, was the name of Jupiter’s wife.  If that’s not poetically amusing, I don’t know what is.  Well played NASA…

My purpose for writing this, however, is not to talk about Jupiter per se, but to address a set of ridiculous number of articles I’ve seen on The Tubes talking about how Jupiter is so big “it doesn’t even orbit the Sun!!”  This irritates me for a couple of reasons.  First, a title like that makes sound like we just discovered this fact, which isn’t true.  Second, it makes it sound like it’s a fantastic idea that no one ever considered and is amazing (!!), which is also not true.  For reasons unknown to me, I feel compelled to talk about it.

Obey Gravity, It’s The Law!

When Issac Newton dropped his Law of Universal Gravitation on the Royal Society back in the day (that day, by the way, was April 21st, 1686 when he read his “Discourse Concerning Gravity and its Properties”, which would become a section of his magnum opus, the Principia, to his bros), he definitively showed that the mechanism that determined how the planets moved through the sky was the same as that which determined how the apocryphal apple feel to the ground.

Bro, do you even lift?
Bro, do you even lift?

The result was a deceptively simple relationship between the force of gravitation felt between two massive bodies and the distance between them.

gravity

He noted that the force is inversely proportional to the square of the distance between the bodies.  So, if you double your distance from a mass, the gravitational force it exerts on you is decreased by 4 times.  He also pointed out that the gravitation force was proportional to each mass.  Triple the mass, triple the force.  That force is felt by each body and is ruled by the more massive of the two.  The Earth, for instance, is about 6 times more massive than the Moon, and as such contributes more to the gravitational force than the Moon.  Which is, of course, why the Moon orbits the Earth and not the other way around.  But wait, there in lies the rub; each body exerts a force on the other.  You can never think of just a single thing gravitating another thing, they are always gravitating each other!  They are essentially gravitationally locked into a single “object” that we refer to as a two-body system.  One object never orbits another object, they always orbit each other.  The “G”, by the way, is Newton’s gravitational constant, commonly referred to as “big G”, as opposed to the “little g” of 9.8 m/s² that represents the acceleration near Earth’s surface due to gravity.

Now, in a two-body system, or in any distribution of mass, there is a concept known as the center of mass.  If you’re talking about, say, the Earth by itself, or the Moon, the center of mass would be (ideally) in the center of their spheres.  Of course, neither body is perfectly uniform, so even alone the Earth’s center of mass wouldn’t be in the exact center.  Hell, the Earth isn’t even really a sphere, but that’s beside the point.  We physicists like to ignore crap like that and call everything uniform spheres and that works to an amazing degree of precision…until we have to toss a Jiffy Pop container full of hermetically sealed apes at the Moon, when we have to give it a bit more thought.

...uniform sphere my ass.
…uniform sphere my ass.

When you put two massive things together, however, the center of mass (sometimes called the center of gravity) is not in the center of either object.  If you draw a line between the two object’s individual centers of mass, the system’s center of mass will lie somewhere along that line.

IMG_8074

Where on the line that point is depends on the masses.  If the masses were exactly the same, the point would be exactly half way between them.  As one of the masses becomes more massive, the center of masses moves along the line towards it.  If one of the masses was infinite, then the center of mass would be in its center; the other mass wouldn’t matter.  The center of mass is essentially a weighted average of the centers of mass of all pieces involved.

When bodies in a two-body system are orbiting each other, they do so about the center of mass.  When referring to orbits, this point is usually known as the barycenter.  In the case of the Earth-Moon system, the barycenter is about 4,700 km from the Earth’s center; the radius of the Earth is about 6,400km.  So, both the Moon and the Earth’s individual centers of mass orbit around this point.  That means that the Earth “wobbles” as the Moon orbits.

barycenter-earth-and-moon

The barycenter of the Earth-Sun system is well within the Sun, since the Sun is around 333,000 times more massive than the Earth…but it is still not in the center.  If the Earth and the Sun were by themselves, the Sun would still “wobble”.  There is a lot of talk nowadays about the discovery of extrasolar planets.  This barycenter dance that multi-body systems do is one of the main ways we find them in the first place; look at a star, see if it wobbles, if is does, something’s orbiting it and we can immediately calculate it’s mass from the wobble.  Science is cool.

Now to the main point: Jupiter.  Jupiter is waaaay more massive than the Earth.  In fact, Jupiter is about 2.5 times more massive that all of the other planets combined!  It clearly rules the playground.  If you find the barycenter of the Sun-Jupiter system, it is, in fact, outside of the Sun.  So, the Sun does more than wobble in this case, it actually orbits around a point in space outside of itself.  If Jupiter would have accreted more mass (about 8 times more, in fact), nuclear fusion would have ignited it into a second star and it and the Sun would have been a binary star system.

Earth would have sucked about as much as Tatooine as well...
Earth would have sucked about as much as Tatooine as well…

As it stands now, it still almost is as the dynamics of the solar system are ruled by the Sun-Jupiter system; the other planets and objects are along for the ride.  It also illustrates why most of the exoplanets we find are giant Jupiter-like planets.  The more massive they are, the further between them the barycenter is and the larger the observed wobble in the star.  Earth-like planets, as I mentioned before, do it as well, but it’s way harder to detect.  We’re getting pretty good at it; as of right now, we’ve discovered about 3,500 exoplanets  in about 2,600 different planetary systems.

Pluto, by the way,  got kicked out of the planet club because it doesn’t gravitationally “rule” it’s neighborhood; it’s moons are so massive that the barycenter around which they all orbit is well outside any of the bodies and they all kind of orbit each other.  Not very planet-like.  As opposed to Jupiter that regularly tosses objects out of the solar system.

Planet 9 From Outer Space

As you can imagine, having more than two objects in the solar system makes their movements…complex.  All of the planets pull on each other really make a mess of things.  Jupiter, for instance, pulls on the Earth just as the Sun does, making your path through space a bit more spirographic than you might initially imagine.  It’s really amazing that the Jiffy Pop apes got to the Moon at all.

Both Uranus and Neptune were discovered due to their gravitational pull on the other planets, not direct observation.  In fact, you can’t see either of them with an unaided eye; you need a telescope.

...uhm, guys.
…uhm, guys.

Astronomers figured out where these planets were and where to look for them in the sky by “reverse-engineering” the orbital data of the planets they could see.  Jupiter and Saturn just didn’t quite move the way they should have.  It’s really a testament to the “Clockwork Universe” idea that Newton ushered in.

Well, now that we have ridiculous technology and can see so many things that we could see before, such as small, icy objects causing around the Kuiper belt beyond Neptune, there’s growing evidence that there might be yet another planet out there.  A massive one, none of this Pluto-sized crap.  We’re talking 10 times the mass of the Earth and about the size of Neptune.  Now, it’s still theoretical…honestly we’ve been talking about a Planet X for a long time.  It’s existence helps to explain the observed orbits of a slew of Kuiper belt objects, orbits that would be extremely improbable without a gravitational shepard.  More recently, people have conjectured that the fact that the rest of the planets are not on the equatorial plane of the Sun could be explained with a magic Planet 9.  The problem is that space is, well, big, and it’s really hard to find small, dark objects when you don’t know where to look.  Current estimates place it on an orbital plane that is about 24º or so off the ecliptic, the plane the Earth orbits the Sun on, and has an orbital period of at least 10,000 years.  If it does exist, it probably has a very eccentric orbit that ranges from 200 to 1,200 times the distance from the Earth to the Sun, almost 20 times further out than Neptune.  So, changes it will make to the rest of the system are weak and hard to detect; remember that gravitation force weakens as the square of the distance.  Plus, we have to detect them for a while to figure out where in that ridiculous orbit it might be before we can find it.  If it doesn’t find us first…

King_ghidorah_1965_01

It would be super awesome to actually see a new planet in my lifetime, though I’m not holding my breath.  If we found it today, it would take something like 20 years to get a probe there.  I’m pretty sure New Horizon’s images of Pluto are the last huzzah I’m going to get.  But who knows.  It would be amazing.  Who knows how it would change our idea of the solar system.  Was it formed with the rest of the planets and tossed out (probably by that fat kid, Jupiter) or was it a rouge planet cruising through space and get captured by the gravity of the Sun?  So many questions.

Anyway, I guess the final take home message is titles of popular science articles are stupid.  Then again, “Jupiter’s so damn BIG, it and the Sun orbit each other!!” is probably more interesting to the average person than “No surprise that the barycenter of the Sun-Jupiter system is 1.07 solar radii from the Sun’s center of mass”.  At least people are reading about science…

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