1)I’ve never seen in books an explanation of why only 2 electrons can be in the first orbit but 8 in the second, and I forget the rest, but there is a certain number sequence.
What is the significance of this number sequence in mathematics or physics? 2) Also, this brings up why is there never more than one planet or moon in an orbit? One would think that there could be as many as were blown or formed there, provided they weren’t too close to each other.
3)Planets orbit the stars, satellites orbit planets, so are there any satellites of satellites? If so, how far can such recursiveness go? (I know there is an asteroid with a satellite, but what about a moon with its own moon(s)?

I can’t answer #1 at all but I can take a WAG at 2 & 3 from a strictly guessing point of view (no math from me).

  1. My guess is that any planet in orbit would sooner or later catch up to and absorb anything else in it’s orbit unless by some freak of nature two planets happened to orbit exactly opposite of one another. Even then I’d suppose something would eventually perturb on or the other’s orbit enough to throw that particular delicate balance out of whack (think Chaos theory…a small, tiny change today eventually adds up to a big change in the future). Sooner or later the balance would be unstable and the two planets would collide.

I have heard that we, as humans, are lucky to have Jupiter hanging in our solar system. It basically acted like a big sweeper/vacuum that sucked up a great deal of debris in the early solar system. Without this our planet would probably have been peppered by so many meteor impacts that life would never have existed long enough to evolve before being wiped out by relatively frequent meteor/asteroid impacts.

  1. Again, I’m not a mathematician but I think a satellite with a satellite with a satellite would be inherently unstable. Say our moon had its own moon. As it swept between the earth and the moon it would have very different gravitational forces acting on it than when it was on the far side of the moon. Sooner or later this would add up to the second moon spiraling off into the earth, the moon or the rest of the solar system.

Now that I think about it scratch my answer to #3. Basically we have that situation with the sun/earth/moon and obviously the moon doesn’t show any signs of an unstable orbit.

The only caveat I can think of to that is the proximity of the moon to the earth compared to their proximity to the sun. Perhaps being much closer to the earth would make a sustantial difference in destabilizing everything but the flip side is the sun has a much stronger gravitational pull.

Short answer: I have no idea what I’m talking about.

The planetary model of the atom (a la Lord Rutherford) is dead. Any resemblance of actual electron energy levels to planetary orbits is merely coincidental.

Planetary orbits are determined by speed and mass. For there to be two satellites in the same orbit, they would have to have the same angular momentum (result of mass and velocity). <damn, I’ve been using this angular velocity thing a bit today.>

On to the electrons.

There is no magic sequence to electrons. Sorry, no Fibbonachi here. In a newtonial view, it has to do with space; there ain’t much close to the nucleus, while there’s more further away.

This view is not really sufficient.

Electrons exist through the probabilistic model <i swear I did this earlier, oh yeah, in the exploding electrons thread>. the result is that there is one big honkin’ equation that predicts the probability of electron “existance” based on energy (Heisenberg uncertainty principle states that you can be sure of it’ position or energy, not both. It’s a heck of a lot easier to know it’s energy so we go with that). This is quite freaky and involves (psi)^2, the greek letter. Nuff said.

Rest assured, that the number of electrons at any n level of energy (formerly called energy shells) is dermined by the roots of that ugly equation.

Atkins has a good Physical Chemistry text book that outlines this.

Okay, someone’s likely to come along who can give more information, but here’s a brief answer to #1 (Electron orbits).

I can’t be entirely sure, but the association of this question with the ones about planets makes me think you may be dealing with the older Bohr model of the atom. This is the one in which electrons are usually shown orbiting the nucleus in the same way as planets orbit a star. The present understanding, using quantum mechanics, is somewhat different.

There’s a more detailed description, but the quick & dirty one is this :
The electrons don’t all orbit in circles like planets, but can be in spherical or somewhat elliptical or other orientations. The different orbits correspond to different energy levels – and only one electron is allowed at each energy level. Actually, two are allowed (I think they are of opposite spin[sup]*[/sup]). So only two in a particular kind of orbit. You get more electrons as you go out farther because there’s more potential orbits the further out you go.

The first two are in a spherical orbit. Then the next two are in a larger spherical orbit, then two in a sort of elliptical/dumbbell-shaped orbit at about the same distance. There’s three of these types of orbit at this distance, which is why the Bohr model had 8 electrons in the second shell (2 spherical, 6 in the other). After that, you add another type of orbit, and so on.

Side note on electrons in orbit : the Bohr model visualized electrons as little solid balls. Quantum mechanics has found that you don’t know where the electron really is when it’s orbiting, there’s just a probability for it to be at any particular point in space. So the model is usually visualized as a fuzzy cloud, the denser part being where the electron is more likely to be.

[sup]*[/sup]spin is just a property that particles like electrons can have. This just means that I can’t explain it.
Jedenfalls bin ich ueberzeugt, dass der nicht wuerfelt. – A. Einstein

don willard asked:

It is rather hard for multiple bodies to get into the same orbit but at different locations, and stabilize. It is theorized that formation of planets sweep all the matter in that particular orbit into one body. It is possible mathematically, I think, to have two planets 180 deg out, or 3 in a 135/215 deg pattern (three equadistant planets, trojan points), but not practical to get there.

However, the Earth does appear to have an asteroid trapped in the same orbit, but we will never meet.

A Companion to the Earth?

Jeff_42 is correct when he assumes those configurations would be unstable. It really depends on the masses and distances of the bodies involved. The obvious problem is that the gravity force from the largest object would interfere with the orbit around the secondary object. Consider the Earth/Moon pair. The two bodies are essentially a dual planet system - the center of gravity of the two bodies is very close to the Earth’s surface rather than near the Earth’s center. Relating to the sun, both are essentially the same distance from the sun, so there is not a large solar gravity fluctuation on the Moon, and Earth’s gravity and its own keep it in stable config. But if you tried to put a smaller body orbiting the Moon, it would experience fluctuating drag from Earth, as it moved nearer and farther away. This is one reason why artificial satellites around Earth have to have propulsion packages to keep them stable. There might be some arrangements that would work, if the primary satellite was some distance from the planet such that the secondary satellite didn’t see strong fluctuations and was dominated by the primary. Perhaps some of Jupiter’s moons would fit the bill.

  1. There is more detail in this thread, but the sequence can be summarized as follows:
  • Each electron is in a “state”.
  • It takes four integers to specifiy a state. Call these numbers n, l, m, s. The notation (2,1,0,1) means “the state with n=2, l=1, m=0, s=1.”
  • Quantum mechanics requires that a valid state has numbers satisfying the following rules: i) n > l, ii)l >= 0, iii) m >= -l and m <= l, iv) s=1 or s=-1.
  • A given state has a given energy. States with the same value for n (but different values for the other numbers) have close (but not equal) energies. That is, state (2,1,0,1) has nearly the same energy as state (2,1,0,-1), state (2,1,-1,1), etc.

Your magic number sequence, then, comes from counting the number of state with a given value for n:

n=1 (first shell)
Rules (i) & (ii) require l=0. Rule (iii) requires m=0. Rule (iv) requires s=1 or s=-1. Thus, there are two possible states with n=1: (1,0,0,1) and (1,0,0,-1). There’s your first shell.

n=2 (second shell)
Rules (i) & (ii) require l=0 or l=1. If l=0, rule (iii) gives m=0; but if l=1, rule (iii) gives m=-1, 0, or 1. Rule (iv), as always, requires s=1 or s=-1. Thus, there are eight states with n=2. The list (where s=-1 or s=1): (2,0,0,s), (2,1,-1,s), (2,1,0,s), (2,1,1,s) ==> eight states.

  1. Two of Saturn’s moons, Janus and Epimetheus, are in the same orbit. Actually, they switch periodically between orbits. If one is a tiny bit closer to Saturn, it’ll be moving faster. It will eventually go all the way around and catch up to the other one. The gravity between them will slow down the farther (from Saturn) one, making it fall into a lower and faster orbit. The previously lower one will gain some energy and will rise into a higher, slower orbit. The cycle repeats.

Also, if you’ll accept smaller bodies, planetary rings are full of bits that have the same orbit.

  1. Like Jeff_42 said, depending on the relative distances and masses involved, more than a couple recursions will probably lead to orbits that are just barely stable. If something was shooting towards the earth/moon system, it would have to have a pretty precise trajectory to be caught by the weak little moon and not by the strong earth. (NASA has had plenty of stuff orbit the moon, but they had rockets and things with which to aim their satellite…)

In the interest of numbers, though, I can think of a system with 5 levels: Apollo around the moon around the earth around the sun around the galactic center.

To sum up the quantum stuff: For any value of n, there can be up to 2*n[sup]2[/sup] electrons. This does not, however, correspond directly to the Periodic Table, becuase n isn’t the only thing that determines the energy of the state.

Quantum mechanical effects have nothing to do with planets. We have no idea if or how gravity is even quantized in the first place, and even if it is, the spacing between allowed orbits would be minimal (as in, much much smaller than we can even measure). You can have two planets in exactly the same orbit only if the separation between them is 60 (stable) or 180 (unstable) degrees. If they’re at any other separation, they’ll tend to attract each other and go into some other slightly different orbits. If the orbits are close enough, they can do the swapping thing like Janus and Epimetheus, or the Earth and that asteroid (what’s its name again?), so the average orbits are the same, but they’ll always be in different orbits from each other.

Pauli’s Exclusion Principle states that no two electrons may exist in the same state in an atomic structure. Pasta’s answer basically gives the rules for specifying the state of an electron.

In the first principle quantum level in an atom, n=1, the only orbital is a spherical “shell” (s-orbital) which can be populated by up to two electrons, one with spin +1/2 and the other with spin -1/2. For n=2, there is another spherical orbital which can again be populated by two electrons. This orbital is larger than the one for n=1, so the electrons in this orbital, on average, are located farther from the nucleus than n=1 electrons. However, for n=2, there exist three other other orbitals, p-orbitals. Each of these orbitals can hold two electrons. So, at most, 8 electrons can have a state of n=2. Taking this further, the n=3 level has one s-orbital, three p-orbitals, and 5 d-orbitals, for a total of 18 electrons.

As Chronos said, these sequences of orbitals do not correspond directly to energy levels. An electron will populate an n=4 s-orbital before an n=3 d-orbital, since the n=4 s-orbital is the lower-energy orbital.

The sequences are:

n=1, 1 s-orbital, 2 electrons max
n=2, 1 s-orbital 3 p-orbitals, 8 electrons max
n=3, 1 s-orbital 3 p-orbitals 5 d-orbitals, 18 electrons max
n=4, 1 s-orbital 3 p-orbitals 5 d-orbitals 7 f-orbitals, 32 electrons max
n=5, 1 s-orbital 3 p-orbitals 5 d-orbitals 7 f-orbitals 9 g-orbitals, 50 electrons max

and so on. n=6 has an additional 11 h-orbitals, n=7 has 13 i-orbitals, etc…

As to why the orbital progressions follow a 1,3,5… pattern, I’m not certain.

Very satisfactory replies! Now I’m wondering something else: The planet answers assume that if the moon, for instance, had a satellite it would be revolving in the same plane as the earth (and moon), thus getting between the earth and the moon periodically and thus making an unstable gravitational system. But what if the moon’s satellite were in an orbit at right angles to the plane of the orbit of the earth? Think of it coming fast from outer space and skimming by the “top” of the moon, which would bring it back around in an orbit that wouldn’t settle into the plane of the earth and moon orbits.

Caldazar-- there is nothing higher than the f-orbital. The g+ orbitals do not exist. s, p, d, and f are the only ones

Well, MO theory isn’t my strong point, and it’s been well covered.

Poogas - What do you mean there’s nothign beyond f? The f orbital electrons of atoms that have them are those most likely to be stimulated by a photon to jump to a higher energy level. If there’s no g, where do they go? The g orbital might not be filled in any stable atoms (or many ridiculously unstable atoms), that doesn’t mean it’s not there.

As for satellites having satellites, remember that gravity is a very weak force, in fact a force that diminishes with the square of the distance. The great distance between us and the sun compared to us and the moon means there is a far, far greater attraction between us and the moon. If the moon were to have a satellite, it would get sucked into either the earth or the moon very quickly, or else move in a very low orbit around the moon at a very high speed.

As for going at right angles, I believe that the solar system is all in one plain, with nothing orbiting the sun at any significant angle to it. This wouldn’t change for the satellite’s satellite. As for why a new object couldn’t come in at a right angle and get caught in a lunar orbit, I would think that the greater size of many other bodies would prevent this.

Check out the diagram at the bottom of this page, and you’ll see that the 5g orbitals would only be filled after the 8s orbitals–so you’d be looking at element number 181 or so. Extremely unstable. The outer electrons are the ones that get stripped off easiest. So, there may be a g orbital in theory, but not in our human experience.

Spherical harmonics.

So, I’d actually disagree with spritle, who said that there was no magic sequence to electrons. 1, 3, 5, … is as magic as any, and there is a very simple reason for the progression.

If you are familiar with the idea of Fourier harmonics, you realize that for every wave number n there are two wave functions, cos(n theta) and sin(n theta) which are just 90 degrees out of phase–and so are independent. Except for n=0, when there is just one function, the constant function–since cos(0 theta)=1 and sin(0 theta)=0, the sine function doesn’t contribute. So, for Fourier functions, the progression for increasing n goes 1, 2, 2, 2, 2, … At each step, as n increases, the number of waves over the interval increases by one, but there are two separate functions that are out-of-phase–they have zero correlation.

In spherical harmonics, an analogous thing develops. For n=0, the function is also constant over the sphere, so the first term of the sequence is also 1. Now imagine a cosine function of wavelength equal to the circumference wrapped around the sphere. You can do that in three independent directions, so the next term is 3.

Another way of looking at that (which will help the visualization of higher numbers), is to cut the sphere into a checkerboard using n slices. Cut it once in half horizontally, and the bottom of the sphere is low and the top high. It is rotationally symmetric. You can cut the sphere once vertically too, but then that wouldn’t be rotationally symmetric–you’d have a third possibility that was 90 degrees out of phase with it with the second one.

For n=2, we get to slice the sphere twice. If both slices are horizontal, it is rotationally symmetric so we only have one harmonic. There are three regions, one high, one low, and the last high. One vertical slice and a horizontal slice, plus its out-of-phase partner gives us two more, and two vertical slices and an out-of-phase partner give us five total.

I think you can see the progression: 1, 3, 5, … Each step up we get to carve up the sphere with one more slice, and we have a few more undulations in the surface of the sphere–the spherical analogue of the fourier waves. Each separate entity has zero correlation with any of the others.

Of course, the electron cloud is related to the square of these wave functions, so the weird shapes you see in the text books are harder to visualize. But just imagine a tiny sphere chopped up into a checkboard of highs and lows–and then each high and low corresponds to a place of high probability.

So, for n=0, the orbital is just a single bulb. For n=1, all three orbitals consist of two bulbs, one vertically oriented, one horizontally, and the third 90 degrees out of phase with the horizontal one.

For n=2, the first “checkerboard” is just a polar high, an equitorial low, and another polar high. A bulb on each pole, and a spare tire around the middle. The remaining checkerboards are all similar, but the derivation is slightly different. Slicing a sphere horizontally, and then vertically produces the same sort of pattern as two vertical slices–a high, low, high, low pattern, four bulbs arranged in a wheel. And that is the basic shape of the other four n=2 orbitals.

Anyway, that’s the way I visualize them.

Can’t happen. The orbital plane of the satellite, being at right angles to the orbital plane of the moon, would stay in the same plane, but the moon moves. So, as the moon orbits, the orbital plane of the satellite would gradually become lined up with the earth, and then gradually become perpendicular again as the moon orbits the earth.

Think of it this way - you are looking at the earth moon system from above the North Pole. The earth is at the center, the moon at the right, and the satellite is orbiting from top to bottom around the moon.

The moon moves up and to the left until it is at the top of the page, and the satellite still orbits from top to bottom. Now, it passes between earth and moon.

The moon moves down and to the left until it is at the left of the page, and now the satellite’s orbit is once again perpendicular to the earth-moon axis.

At two points per lunar orbit, the satellite’s orbit passes between the earth and moon.

Another point with captured satellites is that no single body can capture things by itself (neglecting things like General Relativity and friction). If you just have one body and a rock flying past near it, it’ll end up flying away with the same speed as it approached, relative to the main body. If you have two bodies, though, like the Earth-Moon system, and an incoming object interacts with both, then it can get captured. This leads to some bias towards captured objects being near the same plane.