Saturn’s rings consists of tiny ice particles, each of them moving in the circular orbit about the planet. all answers in this problem should be given in hours. (a) find the orbital period of particles in the innermost part of the d-ring. (b) find the orbital period of particles in the outermost part of the f-ring. (c) find the orbital period of particles that would orbit in the position of the cassini gap. compare that value to the period of saturn’s moon mimas. how do you comment on that result?

Some material consisting of a collection of microscopic objects is kept at a high temperature. a photon detector capable of detecting photon energies from infrared through ultraviolet observes photons emitted with energies of 0.3 ev, 0.5 ev, 0.8 ev, 2.0ev, 2.5ev, and 2.8ev. these are the only photon energies observed. (a) draw and label a possible energy-level diagram for one of the microscopic objects, which has four bound states. on the diagram, indicate the transitions corresponding to the emitted photons. explain briefly. (b) would a spring–mass model be a good model for these microscopic objects? why or why not? (c) the material is now cooled down to a very low temperature, and the photon detector stops detecting photon emissions. next, a beam of light with a continuous range of energies from infrared through ultraviolet shines on the material, and the photon detector observes the beam of light after it passes through the material. what photon energies in this beam of light are observed to be significantly reduced in intensity (“dark absorption lines”)? explain briefly.