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- https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Supplemental_Modules_(Astronomy_and_Cosmology)/Cosmology/Astrophysics_(Richmond)/07%3A_Astronomical_Spectra%2C_Filters_and_MagnitudesThe u and v passbands, for example, lie just to the left and to the right of the strong break in the stellar spectrum (the "Balmer jump"); the ratio of the light gathered through these two passbands i...The u and v passbands, for example, lie just to the left and to the right of the strong break in the stellar spectrum (the "Balmer jump"); the ratio of the light gathered through these two passbands is a good diagnostic of stellar temperature. Note that the peak of the convolved spectrum lies to the blue of the filter transmission curve, because the stellar spectrum is "tilted" towards the blue.
- https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Supplemental_Modules_(Astronomy_and_Cosmology)/Cosmology/Astrophysics_(Richmond)/19%3A_Digression_-_the_Lagrange_Points_in_the_3-Body_ProblemAlong the line joining the two masses Two bodies, no rotation. One body, with rotation. Two bodies, with rotation. Zoom in closer, two bodies with rotation. Lagrange points in action The SOHO satellit...Along the line joining the two masses Two bodies, no rotation. One body, with rotation. Two bodies, with rotation. Zoom in closer, two bodies with rotation. Lagrange points in action The SOHO satellite is close to the Earth-Sun L1 point. A discussion of the Lagrange Points from SOHO's web site. Technical derivation and analysis of the Lagrange Points, again by Neil Cornish. John Baez's page on the Lagrange Points (John is a mathematical physicist at UC Riverside)
- https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Supplemental_Modules_(Astronomy_and_Cosmology)/Cosmology/Astrophysics_(Richmond)/22%3A_The_Boltzmann_EquationWhen an atom absorbs a photon, it jumps up to a higher level; the difference in energy of the two levels must be equal to the energy of the photon. "H-alpha" refers to the n=2 to n=3 transition, "H-be...When an atom absorbs a photon, it jumps up to a higher level; the difference in energy of the two levels must be equal to the energy of the photon. "H-alpha" refers to the n=2 to n=3 transition, "H-beta" to the n=2 to n=4 transition, "H-gamma" to the n=2 to n=5 transition, and so on. The second factor on the right-hand side depends on two quantities: the difference in energy between the two states, and the temperature T of the gas within which the atom sits.
- https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Supplemental_Modules_(Astronomy_and_Cosmology)/Cosmology/Astrophysics_(Richmond)/06%3A_Blackbody_RadiationAt the turn of the twentieth century, German physicist Max Planck figured out a mathematical expression for the spectrum of radiation emitted from a blackbody, a (fictional) object which absorbs all i...At the turn of the twentieth century, German physicist Max Planck figured out a mathematical expression for the spectrum of radiation emitted from a blackbody, a (fictional) object which absorbs all incident radiation.
- https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Supplemental_Modules_(Astronomy_and_Cosmology)/Cosmology/Astrophysics_(Richmond)/21%3A_Spectral_Classificationthen we can measure the "strength" of a line by measuring the "area under the curve". The top of the area is supposed to be the level of the surrounding continuum, but it can be hard to find the conti...then we can measure the "strength" of a line by measuring the "area under the curve". The top of the area is supposed to be the level of the surrounding continuum, but it can be hard to find the continuum in some cases. Now, the equivalent width of a line is simply the width of a perfectly rectangular line of the SAME AREA which would run from the continuum all the way down to zero (that is, no light at all).
- https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Supplemental_Modules_(Astronomy_and_Cosmology)/Cosmology/Astrophysics_(Richmond)Thumbnail: Public Domain; Image was created, authored, and/or prepared for NASA under Contract NAS5-26555.
- https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Supplemental_Modules_(Astronomy_and_Cosmology)/Cosmology/Astrophysics_(Richmond)/04%3A_Bias_in_Parallax_MeasurementsWell, let's qualify that claim just a bit: the errors in the result are actually pretty symmetric when the fractional error in the measurement is very small; it's only when the fractional error in the...Well, let's qualify that claim just a bit: the errors in the result are actually pretty symmetric when the fractional error in the measurement is very small; it's only when the fractional error in the measurement becomes large that the asymmetric mistake in result becomes obvious. In other words, when the uncertainty in a measured parallax becomes a significant fraction of the measurement itself, the chances are that the ACTUAL distance to the star is larger than the calculated distance.
- https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Supplemental_Modules_(Astronomy_and_Cosmology)/Cosmology/Astrophysics_(Richmond)/23%3A_The_Saha_EquationIf we can form the partition function of all hydrogen atoms in the neutral stage -- call that \(\mathbf{Z_I}\) -- and the partition function of all hydrogen atoms in the ionized stage -- call that \(\...If we can form the partition function of all hydrogen atoms in the neutral stage -- call that \(\mathbf{Z_I}\) -- and the partition function of all hydrogen atoms in the ionized stage -- call that \(\mathbf{Z_{II}}\) -- then we can use the Saha equation to compute the relative number of atoms in each ionization stage. Call the number of neutral atoms in the n=1 state \(\mathbf{N_1}\), the number of neutral atoms in the n=2 state \(\mathbf{N_2}\), and the number of ionized atoms \(\mathbf{N_i}\).
- https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Supplemental_Modules_(Astronomy_and_Cosmology)/Cosmology/Astrophysics_(Richmond)/14%3A_Integrals_of_Motion_and_Kepler's_Third_Law_(Again)Note that the ratio of KE to total energy (shown above in light purple) does change over the course of the orbit: the fraction of the total which is kinetic energy rises when the planet is near perihe...Note that the ratio of KE to total energy (shown above in light purple) does change over the course of the orbit: the fraction of the total which is kinetic energy rises when the planet is near perihelion, and falls below the average near aphelion. That means that the velocity of a planet in a circular orbit goes like its distance from the Sun to the negative one-half power: planets close to the Sun should orbit quickly, and planets far from the Sun should orbit slowly.
- https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Supplemental_Modules_(Astronomy_and_Cosmology)/Cosmology/Astrophysics_(Richmond)/15%3A_The_Effect_of_a_Tilt_of_the_Orbital_PlaneIf we tilt it A LOT around its minor axis (by 60 degrees in the example below), we not only make it fatter, we rotate the apparent major axis by 90 degrees: what APPEARS to be the major axis is actual...If we tilt it A LOT around its minor axis (by 60 degrees in the example below), we not only make it fatter, we rotate the apparent major axis by 90 degrees: what APPEARS to be the major axis is actually along the true orbit's minor axis. The big question is: can we come up with some simple rules, based upon the location of the primary star in the apparent orbit, which tell us how to un-tilt the apparent orbit to recover the original ellipse?
- https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Supplemental_Modules_(Astronomy_and_Cosmology)/Cosmology/Astrophysics_(Richmond)/27%3A_(Local)_Thermodynamic_EquilibriumIf we are trying to understand the detailed interaction of light and matter inside a star, it would be very, very convenient if we could use a single value, T, to predict the speed of gas molecules, t...If we are trying to understand the detailed interaction of light and matter inside a star, it would be very, very convenient if we could use a single value, T, to predict the speed of gas molecules, the excitation of atoms, the spectrum of radiation, etc. On the other hand, if the mean free path of the atom is very small compared to the distance over which the temperature changes,
