OK, one more thing about planets and such. In my original article, I screwed up my math (that’s what you get for writing in a hurry under deadline pressure when your server has crashed and you think it’s hacked and you’ll be out hundreds of bucks to fix it and also have to use backups from two weeks ago because you forgot to do them more recently and haven’t written a script to do it automatically, but that’s no excuse).
I said that the barycenter of the Earth-Moon system is about 1700 kilometers underneath the Earth’s surface, which is correct. Since the Moon is moving away from the Earth by 4 centimeters a year, I said that the barycenter will then be above the Earth’s surface in about 40 million years (1700 km/4 cm/yr).
Bzzzzt. I was wrong. The barycenter moves outward from the center of the Earth more slowly than the Moon does, by the ratio of masses of the Moon and the Earth. So for every kilometer the Moon moves out, the barycenter moves out 1/81 of that or so. I redid the math, and I get that the barycenter will reach the Earth’s surface when the Moon is about 524,000 kilometers away. At 4cm/yr, that’s more like 3 billion years from now. That’s a long time, so I guess we don’t have to worry so much about the Moon having to be called a planet any time soon.
I should also note, as a few people in the comments and via email have pointed out, the Moon’s recession changes with time. Its current rate of 4 cm/yr is likely to be higher than normal due to some complicated physics with how the Moon and Earth interact (and the speed of the ocean tides and shape of the continents). So in the future the recession rate will likely be lower than 4 cm, meaning the Moon will be a moon for even longer than 3 billion years.
So there you go. I sometimes have to debunk myself. Anyway, I corrected my original entry and linked it to here for all to see my off-centered correction.
August 18th, 2006 at 1:34 pm
Hey, at least you’re among the people that admit their mistakes.
August 18th, 2006 at 1:43 pm
You messed up on your World Jump Day math too
August 18th, 2006 at 2:10 pm
I’m curious – what do you think of this definition? http://www.contracheck.com/nika/?p=1241
August 18th, 2006 at 2:13 pm
Hey man, so, if Jupiter’s barycenter is outside the sun (I think I read that somewhere cool) wouldn’t it be like a proto-star? Or, no, check this out: it’s a pre-fussion, super-planetoid!
Let’s call the whole thing off.
August 18th, 2006 at 2:31 pm
At the IAU meeting there is a new model for “what is a planet”.
I found it here:
http://www.newscientistspace.com/article/dn9797-pluto-may-yet-lose-planet-status.html
It´s going to be really interesiting next week when thay want to make the decision and how many other proposals will be there to be voted
August 18th, 2006 at 2:59 pm
Suppose one would desire to push the moon into a collision with earth. How many 5oz CO2 bottles would be required to do this?
Mwahahahahahah
August 18th, 2006 at 4:30 pm
You made a mistake? You admited your mistake? We should have more people in the world like you, it’s a great gift to be able to admit mistakes… I wish my dad did that.
August 18th, 2006 at 4:59 pm
BA has inadvertantly displayed the great power of the scientific method – everyone carefully checks and rechecks so the occasional, inevitable mistake is found and corrected. Science works because it constantly self-corrects its model of the universe, in distinction to some belief systems that try to hide errors or back-pedal on their claims when shown to be wrong.
August 18th, 2006 at 5:25 pm
Gary, just a point here: it was not inadvertant at all. I admit my mistakes (when they are important) on purpose, for the very reasons you’ve stated. You can find where I talk about that on my site and on the bulletin board. See if Hoagland, Lieder, Sibrel, et al. ever do that.
August 18th, 2006 at 6:13 pm
Dr. Evil Says:
> Suppose one would desire to push the moon into a
> collision with earth. How many 5oz CO2 bottles would
> be required to do this?
>
> Mwahahahahahah
Or how many liter bottles of Pepsi and packs of Mentos?
August 18th, 2006 at 8:46 pm
I don’t really think it matters when it happens. Your point was that eventually our moon will (under these new guidelins) be a planet.
August 18th, 2006 at 11:24 pm
Just one more voice chiming in to say what a great system the BA has to identify mistakes- in which he explicitly shows where he has (very infrequently) messed up.
Scientists don’t find it easier than anyone else to admit that they’ve made a boo-boo. Of course- admitting you’ve got it wrong ought to be part and parcel of being a scientist- but in practice, it also requires a humble personality- a quality which is not shared by all scientists.
Also- you don’t have to be a scientist to follow the BA’s example- and I’m sure that politicians will any day now be admitting where they got it wrong (sarcasm).
August 19th, 2006 at 12:07 am
Well, BA, I also think better of you for the way in which you ‘fess up to mistakes. None of us is perfect, and we all make mistakes.
I work in biopharmaceuticals, where it is really important to highlight mistakes and assess their impact on the product. After all, when your final product is going to be injected into people, it gives you a clearer perspective on the difference between (a) looking stupid ’cause you got something wrong and (b) being hideously, nay egregiously, incompetent because you failed to point out that you got something wrong.
August 19th, 2006 at 12:08 am
Hmm. “-i” tag didn’t seem to work. I only intended for one word to be italicised. Maybe I made a mistake.
August 19th, 2006 at 2:18 am
According to Randi that seems to rule out your possession of a PhD. People with PhDs lose the ability say two things: “I don’t know” and “I was wrong”.
Heehee…
August 19th, 2006 at 4:16 am
I would say the acquisition of a PhD involves learning how to say “I don’t know”, and “I was wrong”.
August 19th, 2006 at 6:00 am
Phil, I bet your eraser has only one little corner worn down a bit. As opposed to others’ either all worn round, or not at all. It’s nice to be in that middle ground.
Ivan.
August 19th, 2006 at 6:48 am
PK said:
“I would say the acquisition of a PhD involves learning how to say “I don’t knowâ€, and “I was wrongâ€. ”
Usually followed by “Go away! Leave me alone!!!”
August 19th, 2006 at 10:28 am
Geez, it was more a nit than something needing debunking. The math may have been wrong, but the intent of the message was unchanged – moons can become planets given enough time.
August 19th, 2006 at 10:35 am
Phil, may I know the formula you use to calculate the barycenter of the Earth-Moon system?
August 19th, 2006 at 11:39 am
Kim– you can find it on wikipedia, but I derived it myself:
Assume two masses, M1 and M2, each a certain distance from the barycenter, R1 and R2, respectively. Then you can fool around with all sorts of equations to get to this, but it also just kinda makes sense:
M1 * R1 = M2 * R2
If you increase the mass of one object, then its distance from the barycenter will decrease, and vice-versa.
Let the distance between the centers of the objects be R. Then
R1 + R2 = R
or
R2 = R – R1.
Substitute that into the equation above and solve for R1.
M1 * R1 = M2 * (R – R1)
R1 = M2/M1 * (R – R1)
R1 + M2/M1 R1 = M2/M1 * R
R1 * (1+ M2/M1) = M2/M1 * R
R1 = M2/M1 * R / (1+M2/M1)
R1 = M2/M1 * R / ( (M1+M2)/M1)
Lessee, the M1s cancel and you can rearrange to get
R1 = R * M2/(M1 + M2)
If M1 is a lot bigger than M2 you can simplify this to
R1 = R * M2/M1
We know that the Moon/Earth mass ratio is about 81, so you can see that as the Moon moves away from the Earth (R gets bigger), R1 (the distance of the barycenter from the Earth’s center) gets farther out by a factor of 1/81.
Thus ends the algebra lesson for today. If someone wants to derive that first equation, be my guest.
August 19th, 2006 at 11:41 am
Oh, and Shawn: Randi’s just jealous.
No, I’m kidding. We’ve talked about that; he’s kidding, sortof. A lot of people with higher degrees get rigid in their thinking, but I think a majority, at least in my field, love to say “I don’t know”. That means there’s a mystery afoot, and that’s why we’re in this!
August 19th, 2006 at 2:03 pm
,,,ooooh! A mistook. I guess that means scientists are human after all,,,and it takes some really BIG cahones to admit it. Congratulations. You’ve just proved big brains and big reproductive potential are NOT incompatible.
GAry 7
August 19th, 2006 at 10:58 pm
Another question:
Will the moon continue retreat until the earth becomes tidally locked, or will the orbital diameter exceed the sun/earth lagrange point before the earth spins down? (my physics is a bit rusty…).
Assume the solar system lasts long enough for the earth-moon system to reach equilibrium.
August 19th, 2006 at 11:52 pm
Lab Lemming, as I understand it, the Moon’s orbit will stop expanding once the Earth is tidally locked with the Moon. This is because the mechanism that transfers Earth’s rotational energy to the Moon is tidal (having to do with the frictional forces between the oceans and the Earth’s crust and the impact this has on the distribution of water over Earth’s surface in response to the tidal attraction of the Moon).
See here for more detail:
http://www.astronomynotes.com/gravappl/s10.htm#A9
August 20th, 2006 at 11:11 am
There’s fellow named Zim Olsen who seems to be an expert in…um…new math. He offers an exam which, if you pass, could earn you a certificate. Good luck!
I wonder if Zim Olsen makes mistakes.
August 20th, 2006 at 11:56 am
Also to be thrown into the mix is the question of when the Moon’s orbit – as a fraction of the Earth’s Hill sphere radius – will become unstable due to solar tides. Innanen in an article from 1979 in Astron. J. (v. 84, p. 960) estimates it at about 1 million km.
August 21st, 2006 at 6:26 am
[...] Why Pluto-Charon when our own Moon is larger than both Pluto and Charon? Because the barycenter of the Pluto-Charon system is outside Pluto, while, for the Earth-Moon system it is 1700 km below the surface of the Earth. Phil points out that, with the Moon receding from Earth at 4 cm per year, in about 40 million years [correction: make that about 3 billion years] the Earth-Moon barycenter will be outside the Earth and the Moon will then be designated a planet (that is, if the IAU doesn’t redefine planet before then). [...]
August 21st, 2006 at 7:42 am
Concerning that blog archive post: One has to love the Internet. Its error propagation rate is PHENOMINAL. And it’s all your fault, Dr. Plait. *wags finger* Ah well. We, your loyal fans, forgive you–not like it’s the first time, neh?
Like Neil above, engineering is like biopharmaceuticals in where error-checking and admitting mistakes is really important. Think about it next time you’re seven miles off the ground in an aluminum tube maybe one or two millimeters thick (of course not counting frames and longerons and any of the -real- structure in a semimonocoque aircraft… damnit… engineers and technicalities, go figure). So good on ya, man.
Still, if we were to put the world’s combined nuclear arsenal on the dark side of the moon with a bunch of nuclear waste and detonate it all in a tragic “accident,” could we make the Moon go superluminal?
There is no need to point out everything wrong in that last sentence, Citizens.
August 25th, 2006 at 11:54 am
Here’s a thought: How far away can the moon get from the earth before outside forces really start to distort the moon’s orbit (possibly throwing it from earth, or crashing it back down I suppose)? Is that anywhere close to where/when the barycenter crosses earth’s surface?
June 21st, 2009 at 12:54 am
Let’s blow up Ceres into many small asteroids. It’ll make the whole debate just a little simpler.