Physics 110: Homework #2 Solutions

2.1

Parallax arises from the annual motion of the Earth around the Sun, while proper motion comes from the actual motion of stars through space. Parallax shifts the direction of a star back and forth. Proper motion moves the star progressively farther with time. One could observe the star at the exact same day of the year over the course of several years to determine its proper motion (doing the observation on the same day eliminates the parallax effect). Once the proper motion is known, one can remove it from the parallax measurements done over a year.

2.2

The emission and absorption lines correspond to exactly the same changes in atomic energy levels. During the emission process an electron drops from a higher energy level (say, A) to a lower one (say, B) emitting a photon. For the corresponding absorption line the electron in the exact same lower energy level (B) jumps to the exact same higher energy level (A) by absorbing a photon of the appropriate energy. One would need to completely ionize the atoms of the thin gas, in order to eliminate the absorption line spectrum.

2.3

The surface temperature of a star determines the level of ionization of the gas as well as the manner in which the atomic energy levels in the constituent atoms and ions are populated. Higher temperatures cause higher levels of ionization and result in the atoms and ions of the gas being in higher energy levels and vice versus for lower surface temperatures. Since absorption line come from transitions between atomic energy levels in atoms or ions, the particular pattern of lines seen in a stellar spectrum depends on the precise mix of ions and atoms in the gas as well as the specific energy levels that are populated.

2.4

This is significant because it gives us information on the evolution of stars: well-populated regions of the H-R diagram represent long-lived stages of evolution, while poorly populated regions correspond to evolutionary stages where few stars spend much time. Most stars fall on the main sequence, which suggests that stars spend most of their lives there. Stars of different luminosity class differ in their luminosities! More fundamentally, the higher luminosity stars are bigger in size and generally more massive than the lower luminosity ones.

2.5

The following information can be deduced from the analysis of light from a distant object: temperature, spectral class (for stars), luminosity class (for stars), chemical abundances, motions relative to the Earth, internal motions (e.g., rotation), and size (if the distance is known).

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