Re: Do the elements have calculable/specific vibratory rates?

Before I answer your question, allow me to try to rephrase it to make sure I am answering the right question. The question I see is, "If we know what the planet is made of, can we predict what sort of light (electromagnetic radiation) we will see?"

The answer is yes, more or less. If you start with anything but the best telescopes and the best instruments, you do not learn much about the surface of the planet. For a solid planet whose surface we can see, the overall spectrum is easy to predict: it's a blackbody, just likes stars or you and I are. The temperature of the surface tells us almost everything we can want to know about a blackbody spectrum, whereas the actually composition of the body is almost completely irrelevant. On top of the blackbody curve, we also get some light being absorbed in places. This is due not to the solid planet, but due to the atmosphere. This absorption does depend on what is in the atmosphere.

For a planet whose surface (if any) we cannot see, there is still a blackbody curve in there, but the absorption due to the gases in the atmosphere tends to be more important than in the solid-surface case.

For example, Jupiter's spectrum in the infrared as measured by the Infrared Space Observatory is shown above. The absorption (or dips in the spectrum) is due to gases in the atmosphere. Even if Jupiter had a surface, at this level, we would not be able to determine its composition.

We can actually do a bit better than this, but it requires really good spectra of their surfaces. With really good spectra, you can figure out what the surface is made of. For example, there are a number of groups who have tried to work out what is on the surface of Jupiter's moon Europa from spectra taken by the Galileo spacecraft, currently in orbit around Jupiter. This technique is relatively young and hard to do, however. Hopefully, as we have time to refine the technique, we will do better at it. Also, the only we learn from this is what is on the surface of the planet, not what is inside. (Note: if you bounce radio waves off the planet, you can get some idea of what is up to a few meters below the surface, but that is just scratching the surface of these bodies.)

As it turns out, we seldom get a change to predict the composition of a planet's atmosphere in this way. Usually, people look at the spectra we get and then try to match them with spectra of samples taken in a laboratory somewhere. So instead of using this is a predictive tool, we use it as a way to determining what is on the surface of planets without actually having to land there.

[Some recent spacecraft have begun flying gamma-ray spectrometers on them. These offer the possibility of measuring the surface composition as well, but again, only from the very surface of the object. Moderator]