The Small Angle Approx-imation. The 2 p shows the fact that the natural units for angle here are “radians”; 2 p of them for a full circle (so 57.3 degrees per radian). Measuring distance with triangulation. Parallax – direct distances to the stars.
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The 2p shows the fact that the natural units for angle here are “radians”;
2p of them for a full circle
(so 57.3 degrees per radian).
d(parsec) = 1/p(arcsec) ; 1 parsec = 3.26 light years
The intrinsic luminosity of a star depends on its temperature (because blackbody radiation goes like T4 per unit area, and its size (to account for its total area ~R2) :
The apparent brightness of a source goes down like the square of the distance to the source (and depends on the intrinsic luminosity of the source :
We can think of an atom as consisting of a positive nucleus (protons and neutrons) surrounded by negative electrons. The electrons can be thought of as “orbiting” the nucleus, but are only allowed in certain orbits (or energy levels).
A photon with exactly the right energy can excite the electron from one level to another. The electron will drop back to the “ground state”, and emit photons with specific energies as it does so.
The energy of photon that can interact with a level jump just depends on the energy difference between the levels. Levels can be skipped.
Each atom has a specific set of energy levels, and thus a unique set of photon wavelengths with which it can interact.
The spectra from two different atoms are observed. A spectral line in the first atom has exactly one-half the wavelength of a spectral line in the second atom. Which of the below is TRUE?
A spectrometer makes an image (usually of its entrance slit) at every wavelength. A telescope illuminates the slit with starlight.
Very fine facets or grooves will act like many little slits and produce an interference pattern that spreads wavelengths.
far infrared grating
Hydrogen is particularly important and distinctive. The “H-alpha” line is the one from levels 2-3; the Balmer series from level 2 is in the visible. The Lyman series lines are all ultraviolet.
Different stars show different spectral lines, or different line strengths. They were sorted by this appearance (Annie Jump Cannon).
The reasons why spectra change were a bit subtle, so the ordering of the letters got scrambled when the temperature sequence was determined.
Most stars will be in their stable hydrogen-burning phase, called the “main sequence”. For these, the spectral type has a simple relation to the star’s properties. Note that luminosity has a large variation.
Hertzsprung and Russell had the idea of plotting the luminosity of a star against its spectral type. This works best for a cluster, where you know the stars are all at the same distance. Then apparent brightness vs spectral type is basically the same as luminosity vs temperature. They found that stars only appear in certain parts of the diagram.
Hot stars are very bright but very rare. They can affect the light, but not the mass of the Galaxy. Red supergiants are more common.