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The actual spectral form for thermal bremsstrahlung is not a pure exponential. The Gaunt factor causes the flat portion of the log-log plot to decrease slowly with increasing frequency. Also the several atomic elements in cosmic plasmas lead to strong emission lines superposed on the quasi exponential continuum. A theo... | {
"Header 1": "*Radiation from a hot plasma*",
"Header 3": "Shocks in supernova remnants, stellar coronae, H II regions",
"token_count": 739,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
A mechanism that can give rise to a spectrum of very different shape is *synchrotron* radiation. This occurs when very high energy (relativistic) electrons spiral around magnetic field lines due to the $qv \times B$ force on an electric charge q moving with velocity v in a magnetic field B. The electrons emit electro... | {
"Header 1": "*Radiation from a hot plasma*",
"Header 3": "Synchrotron radiation",
"token_count": 1124,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
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**Spectrum**
An emitting body can be *optically thick*. The conditions are such that the photons scatter, or are absorbed and re-emitted, many times prior to being emitted from the surface. In this case one obtains a spectral shape known as the *blackbody spectrum*. The spectrum depends upon the temperature of the em... | {
"Header 1": "*Radiation from a hot plasma*",
"Header 3": "Blackbody radiation",
"token_count": 763,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
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At frequencies significantly less than that of the peak frequency, the blackbody function varies linearly with the temperature and quadratically with frequency:
$$I(\nu,T) \approx \frac{2\nu^2 kT}{c^2} \propto \nu^2 T \qquad \text{(Rayleigh–Jeans law)} \qquad (11.24)$$
This expression follows from an expansion of t... | {
"Header 1": "*Radiation from a hot plasma*",
"Header 3": "Radio spectra and antenna temperature",
"token_count": 837,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
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A beautiful example of blackbody radiation is the remnant radiation from the early hot, dense universe. The cosmic background radiation (CMB) would have had a blackbody spectrum of temperature *T* ≈ 4000 K when the cooling and expanding universe first became optically thin to this radiation. This occurred when protons ... | {
"Header 1": "*Cosmic microwave background*",
"token_count": 616,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
The overall shape of the spectra of many stars approximates that of a blackbody, and blackbody formulae are often adopted to describe their energy output. Nevertheless the spectrum is substantially distorted by absorption lines and by the effect of the temperature variation with depth in the stellar atmosphere. In the ... | {
"Header 1": "*Cosmic microwave background*",
"Header 3": "*Stars*",
"token_count": 397,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
Figure 11.10. Examples of absorption and emission lines in sketches by the spectroscopist, Lawrence Aller. (a) Spectrum of starαCarinae (Canopus), a star of Type F0, not unlike our sun (Type G2), showing absorption lines. The vertical and horizontal scales are changed leftward of 500 nm. ... | {
"Header 1": "*Cosmic microwave background*",
"Header 3": "(b) Carinae",
"token_count": 911,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
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Spectral lines arise from atoms or molecules undergoing transitions between two energy states differing in energy by $\Delta E$ . Such transitions in the hydrogen atom are shown as arrows in Fig. 10.1. If the atom is going from a high (excited) energy state to a lower energy state, the excess energy is emitted as a ph... | {
"Header 1": "11.4 Spectral lines",
"Header 2": "Absorption and emission lines",
"token_count": 373,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
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Figure 11 shows how the emission and absorption lines arise. A hot incandescent lamp emitting a continuum spectrum illuminates a cool cloud containing sodium (Na) atoms. Three observers analyze the light with a prism; each has a different perspective, and each sees a different spectrum. Each can choose to observe the l... | {
"Header 1": "Origin of spectral lines",
"token_count": 652,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
Radiation from stars exhibits both absorption and emission lines (Fig. 12). When the star is viewed directly, the decreasing temperature with increasing radius in the photosphere results in the production of absorption lines (observer C ). These are known as *Fraunhofer lines* after the discoverer of such lines in the ... | {
"Header 1": "Origin of spectral lines",
"Header 3": "*Stars and nebulae*",
"token_count": 501,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
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Emission lines that arise from *allowed transitions* are called *permitted lines*. The selection rules of quantum mechanics allow these transitions to occur rapidly. The emitted radiation is *electric-dipole radiation*. If the atom is in an upper state of a permitted transition, the transition will occur after a very s... | {
"Header 1": "Origin of spectral lines",
"Header 3": "Permitted and forbidden lines",
"token_count": 668,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
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Spectral lines are studied in all bands from the radio through gamma-ray. In radio astronomy, the study of line emission and the Doppler shifts in frequency of these lines has provided valuable information about the existence of molecules in space (Fig. 13) which are the building blocks of life. The Doppler shifts of "... | {
"Header 1": "Origin of spectral lines",
"Header 3": "*Spectral lines at non-optical frequencies*",
"token_count": 222,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
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A typical spectral line will have a *profile* that may be more or less Gaussian in shape and which can be severely distorted under certain conditions (Fig. 14). The total (integrated) area of an absorption or emission line in the observed spectrum is the measure of its strength or total power. The irregular shape of so... | {
"Header 1": "*Equivalent width*",
"token_count": 542,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
The profile of a spectral line from a sample of unperturbed gas has a shape governed primarily by two factors. First, the atoms in the gas will have a thermal spectrum governed by the Maxwell–Boltzmann (M-B) velocity distribution. The atoms are receding from and approaching the observer; radiation emitted or absorbed b... | {
"Header 1": "*Damping and thermal profiles*",
"token_count": 1395,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
Lines can also be Doppler broadened by rapid motions of clouds of emitting or absorbing atoms; this is known as *bulk turbulent motion*. The velocities of the several clouds are not necessarily thermally distributed so the shape of the line may differ from that quoted above. Bulk motion will significantly affect the li... | {
"Header 1": "*Damping and thermal profiles*",
"Header 3": "Turbulent motions and collisional broadening",
"token_count": 367,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
The *curve of growth* (Fig. 16) of a spectral line describes the measured strength (equivalent width, EW) as a function of the number N of absorbing (or emitting) atoms along the line of sight (atoms/ $m^2$ ). Consider the absorption case (Figs. 14a,c,e). When the strength of the line is weak (Fig. 14a), the atoms alon... | {
"Header 1": "Saturation and the curve of growth",
"token_count": 475,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
The differential equation that governs the absorption and emission in a layer of gas follows from the geometry of Fig. 17. A uniform cloud ("source") of temperature *T*s, depth Λ, and optical depth τ<sup>Λ</sup> lies between the observer and a background source at some other temperature *T*0.
![](_page_391_Picture_2.... | {
"Header 1": "*Radiative transfer equation (RTE)*",
"token_count": 445,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
Consider a beam of photons moving in the direction of an observer at some location in the cloud. The differential equation that describes absorption of the photons in a differential path length dx is, from (10.17), $dN/N = -\sigma n \, dx$ , where dN/N is the fractional change in the number of photons in the beam, $\... | {
"Header 1": "Intensity differentials",
"token_count": 1587,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
If the gas of the cloud were in *complete thermodynamic equilibrium*, the radiation and matter would all be in thermal equilibrium at some temperature T; the specific intensity $I(\tau)$ would not vary throughout the cloud. In this case, the derivative in (39) equals zero, $dI/d\tau = 0$ , and the observed intensity... | {
"Header 1": "Local thermodynamic equilibrium",
"token_count": 517,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
Insight into the behavior of $I(\tau)$ according to the radiative transfer equation (39) can be gained simply from knowledge of the relative magnitudes of $I(\tau)$ and $I_s$ . If $I(\tau) < I_s$ at some depth $\tau$ , the derivative in (39) is positive which tells us that $I(\tau)$ increases with optical dep... | {
"Header 1": "Solution of the RTE",
"token_count": 843,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
The solution (44) readily illustrates the formation of spectral lines if we consider the variation of $\tau$ (and also $I_0$ and $I_s$ ) with frequency. There are four cases to consider, one of which has two possibilities:
$I_0 = 0$ : there is no background radiation illuminating the cloud
(i) $\tau \ll 1$ : ... | {
"Header 1": "Solution of the RTE",
"Header 3": "Limiting cases",
"token_count": 2059,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
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18b), the increase in opacity again moves the observer from A to B, but in this case it yields a decrease in intensity, or an absorption line.
If the functions *I*<sup>0</sup> and *I*<sup>s</sup> are each blackbody spectra, the one with the higher temperature will have the greater intensity at any frequency (Fig. 8).... | {
"Header 1": "Solution of the RTE",
"Header 3": "Limiting cases",
"token_count": 692,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
*Problem 11.21.* (a) The spectral flux density in wavelength units of some source varies as the inverse fourth power of the wavelength, *<sup>S</sup>*<sup>λ</sup> <sup>=</sup> *<sup>K</sup>*λ−4, where *<sup>K</sup>* is a constant. What is *S*<sup>ν</sup> , expressed as a function of ν? See if you can do this from first... | {
"Header 1": "*11.2 Plots of spectra*",
"token_count": 494,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
*Problem 11.31.* Consider the sketches of thermal bremsstrahlung spectra on a log-log plot in Fig. 3c. The curves are for two identical plasmas, with constant identical Gaunt factors, except that their temperatures differ. Suppose that one is three times hotter than the other, *T*<sup>2</sup> = 3*T*1. (a) At what photo... | {
"Header 1": "*11.3 Continuum spectra*",
"token_count": 722,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
*Problem 11.41.* (a) What is the approximate equivalent width (in units of nm) of the prominent absorption line shown at $\lambda \approx 485$ nm toward the left in Fig. 10a? (b) Estimate the equivalent width (in eV) of the Ne X emission line at $\sim 1022$ eV in the Capella spectrum of Fig. 5. [Ans. $\sim 1$ nm;... | {
"Header 1": "11.4 Spectral lines",
"token_count": 680,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
Problem 11.51. Consider a stellar atmosphere where $I_s$ varies with depth in the cloud as $I_s = a + b\tau$ where a is a positive constant and b is a constant that can be positive or negative. (In the text, we took $I_s$ to be constant throughout the cloud.) Assume that conditions of local thermodynamic equilibr... | {
"Header 1": "11.4 Spectral lines",
"Header 3": "11.5 Formation of spectral lines (radiative transfer)",
"token_count": 334,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
Major new facilities that detect signals from the cosmos other than electromagnetic radiation are bringing new fields into the forefront of astronomy. **Neutrino observatories** study the energy-producing thermonuclear reactions at the center of the sun with detectors utilizing **chlorine**, **gallium**, and **pure wat... | {
"Header 1": "**What we learn in this chapter**",
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"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
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Astronomers and physicists now observe the sky with instruments that are sensitive to signals that are not a form of Maxwell's electromagnetic waves or their equivalent, photons. These "telescopes" have been designed to detect (*i*) neutrinos from the sun, supernova explosions and nuclear interactions in the earth's at... | {
"Header 1": "**12.1 Introduction**",
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"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
*Electron neutrinos* <sup>e</sup> are emitted in the power-generating nuclear interactions that occur at the center of stars such as the sun. There are two other *flavors* of neutrinos, the *muon neutrino* and the *tau neutrino* but these are not emitted in the nuclear reactions within the sun. (Each of the three flav... | {
"Header 1": "*Neutrinos from the sun*",
"token_count": 1365,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
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The original experiment to detect solar neutrinos was carried out by Ray Davis with much encouragement from John Bahcall whose calculations showed the solar flux of neutrinos was indeed sufficient for detection by this experiment. He and others over the years continuously refined the theoretical model while experimenta... | {
"Header 1": "*Neutrinos from the sun*",
"Header 3": "Homestake mine experiment",
"token_count": 651,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
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The incoming flux of neutrinos steadily produces $^{37}$ Ar atoms which accumulate in the tank. However, the $^{37}$ Ar is radioactive with a *half-life* of 35 days. In 35 days, 1/2 of an isolated sample of atoms will have converted back to $^{37}$ Cl by the process called *electron capture*, or *K-shell capture*, w... | {
"Header 1": "*Neutrinos from the sun*",
"Header 3": "Argon decay",
"token_count": 748,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
The number of 37Ar atoms in the tank is determined as follows. Helium gas is pumped through the tank; it collects ("sweeps up") the individual 37Ar atoms and thereby removes (purges) them from the liquid. This is done about every 100 days. The 37Ar atoms are removed from the helium by trapping them in a charcoal filter... | {
"Header 1": "*Sweeping for argon atoms*",
"token_count": 246,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
The low rates of neutrino detection are described with the "SNU" the *solar neutrino unit*.
$$1 \text{ SNU} = 10^{-36} \text{ captures s}^{-1} (\text{target atom})^{-1}$$
(12.4)
The expected value from the sun depends upon assumptions about conditions in the sun, but for the standard solar model, it is about 8 SNU ... | {
"Header 1": "*Solar neutrino problem*",
"token_count": 410,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
#### Gallium detectors
A second generation of solar neutrino experiments were carried out in the 1990s to search for the more abundant low energy pp neutrinos. They were located in the former Soviet Union (SAGE) and in Italy (GALLEX). They used gallium as an absorber, with a total mass of 60 Mg and 30 Mg (60 and 30 m... | {
"Header 1": "*Solar neutrino problem*",
"Header 3": "Second generation experiments",
"token_count": 295,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
Super-Kamiokande (SK) is a much enlarged version of the original Kamiokande experiment. It is located 1000 m underground in the Japanese Alps, in a mine of the Kamioka mining company. Beginning in 1996, it has monitored the energetic $^8B$ neutrinos from the sun. It is a huge (40 m diameter and 40 m tall $\rightarro... | {
"Header 1": "*Solar neutrino problem*",
"Header 3": "Super-Kamiokande",
"token_count": 1098,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
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The puzzling deficiency of neutrinos from the sun could be resolved through the decay or the transformation of the neutrinos en route to the earth. Although the neutrino has long been considered to be a zero-mass particle (like the photon), particle theories can easily accommodate neutrinos with small masses. In this c... | {
"Header 1": "*Solar neutrino problem*",
"Header 3": "*Neutrino oscillations and more*",
"token_count": 575,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
The term *cosmic rays* sounds like a grand term to describe all radiation from the cosmos. In fact, it has taken on a specific and restricted meaning. It refers, for the most part, to high energy charged particles (mostly protons) that travel through the Galaxy, some of which arrive at the earth. It also refers to the ... | {
"Header 1": "*Solar neutrino problem*",
"Header 3": "**12.3 Cosmic ray observatories**",
"token_count": 345,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
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Storage in the Galaxy
The general picture that emerged from subsequent research is that charged particles (protons with an admixture of heavier atomic nuclei), are accelerated to high energies by processes not yet well determined, but probably in part in supernovae and the shock waves of their aftermath. They then tr... | {
"Header 1": "*Solar neutrino problem*",
"Header 3": "Primary and secondary fluxes",
"token_count": 576,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
The primary protons (and heavier nuclei) find the atmosphere to be quite opaque. High in the atmosphere, they undergo nuclear collisions with the nuclei of nitrogen and oxygen nuclei. Many lower energy particles, the *secondary cosmic rays*, are produced in these interactions. The average amount of atmospheric matter t... | {
"Header 1": "Nuclear component",
"token_count": 491,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
The muons from the <sup>+</sup> and <sup>−</sup> decays are essentially heavy electrons with mass 207 times that of the electron (*mc*<sup>2</sup> <sup>=</sup> 106 MeV). A muon decays to an electron
Figure 12.3. Sketch showing a high energy primary cosmic proton entering the atmosphere,... | {
"Header 1": "*Muon component*",
"token_count": 392,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
Cosmic rays are not the ideal tool for doing astronomy because the particles, being charged, are deviated from their initial directions of travel by the magnetic fields of the Galaxy and the earth. Thus cosmic rays from many different sources will be mixed together when they arrive at the observer. In fact, they arrive... | {
"Header 1": "*Muon component*",
"Header 3": "Cosmic ray astronomy",
"token_count": 774,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
The nuclear components (protons, neutrons, etc.) near the center of the EAS are continuously undergoing new interactions with the atmospheric nuclei and thereby continuously feeding energy into the spreading electron/photon component. The mechanism for this is, as described just above, the production of <sup>0</sup> me... | {
"Header 1": "*Growth and decay*",
"token_count": 352,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
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EAS may be detected in two other ways. The relativistic electrons passing through the atmosphere travel faster than the speed of light in air and thus emit visible *Cerenkov radiation* (Section 2). Most of the electrons travel in the downward direction, but with some scattering in their directions of travel. Since the ... | {
"Header 1": "*Cerenkov radiation and fluorescence*",
"token_count": 359,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
The growing pancake of electrons and gamma rays, 100 m in diameter, makes possible the study of the relatively rare high energy primaries. In effect, the atmosphere "develops" the primary proton to a large size so that it can be detected and located with relatively few detectors (e.g., large scintillation counters) spr... | {
"Header 1": "*Detection of EAS*",
"token_count": 1275,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
The extremely ambitious international *Pierre Auger project* for the detection and study of the EAS initiated by the UHECR is now under construction in Argentina (Fig. 5a) at an altitude of about 1400 m where these EAS reach their maximum development. When completed in 2005, construction will begin on a sister site in ... | {
"Header 1": "*Detection of EAS*",
"Header 3": "Auger project",
"token_count": 725,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
In contrast to charged particles, energetic gamma rays should travel along more or less straight lines in the Galaxy like other forms of electromagnetic radiation. For example, gamma rays are produced in collisions of the high energy cosmic ray protons with the gas in the plane of the Galaxy through the creation and de... | {
"Header 1": "*Gamma-ray primaries – TeV and EeV astronomy*",
"token_count": 858,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
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A *neutron star* is a possible end state of a star. Its nominal mass is $\sim 1.4~M_{\odot}$ and its radius $\sim 10~\rm km$ . This is an extremely compact object; a mass comparable to the mass of the sun is contained in an object the size of Manhattan. Neutron stars were first discovered in 1967 as *radio pulsars*.... | {
"Header 1": "*Gamma-ray primaries – TeV and EeV astronomy*",
"Header 3": "Orbiting neutron stars",
"token_count": 287,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
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The H-T binary pulsar was discovered in 1974; its coordinate name is PSR B1913 + 16 but it often called simply *the binary pulsar* because for many years it was the only one known. Its pulse (spin) period is P = 59 ms and its orbital period 7.75 h. It is distant about 16 000 LY. The Doppler variation of the pulsing fre... | {
"Header 1": "*Gamma-ray primaries – TeV and EeV astronomy*",
"Header 3": "Hulse-Taylor pulsar",
"token_count": 519,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
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This orbital decay is detectable because the very massive neutron stars are whipping around each other in a compact orbit (indicated by the short period). The masses are being highly accelerated and hence they emit sufficient gravitational radiation to bring about a detectable advance in the orbit phase. This detection... | {
"Header 1": "Energy loss rate",
"token_count": 751,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
In GR, gravity is considered a distortion of the space-time fabric. Light rays are bent when they pass near a massive object (e.g., the sun). We might be tempted to say that gravity exerts a force on the photons. However, it is more appropriate to say that space is warped, and that light rays define "straight" lines, k... | {
"Header 1": "Energy loss rate",
"Header 3": "Distortion of space",
"token_count": 388,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
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The gravitational radiation predicted by general relativity is *quadrupole* (or highermoment) *radiation*. This describes the angular distribution of the emitted radiation. It arises from a mass distribution with an accelerating quadrupole moment. Dipole radiation is not possible because, in part, there is only one sig... | {
"Header 1": "*Quadrupole radiation*",
"token_count": 988,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
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The quadrupole moment tensor at time t for this case is easily constructed from (8) if we approximate the mass distribution as two point masses each of mass m in a circular binary orbit of angular frequency $\omega$ (rad/s) in the x, y plane. Each mass is at a distance r from the origin (Fig. 8a); the origin is taken... | {
"Header 1": "*Quadrupole radiation*",
"Header 3": "Variable quadrupole moment",
"token_count": 1951,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
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Substitute the values for our system, namely $m = 1.4 M_{\odot}$ , $r = 1 \times 10^4$ m, $P_{\text{orb}} = 1 \times 10^{-3}$ s, $G/c^4 = 0.8 \times 10^{-44}$ (SI units), into (12) to obtain the result,
$$h_{+} = \frac{360}{R} \cos 2\omega t$$
(Strain for coalescing neutron stars; (12.14)
In our Galaxy, only... | {
"Header 1": "*Quadrupole radiation*",
"Header 2": "Detection in Virgo cluster",
"token_count": 327,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
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The first searches were carried out with large cylindrical bars (Fig. 9a) operated in isolated and sometimes cooled environments to shield them from vibrations and ambient disturbances. The natural resonant frequency of the bar is where it is most sensitive. The first such experiment was carried out in the 1960s. It ma... | {
"Header 1": "*Detectors*",
"Header 3": "*Resonant bars*",
"token_count": 725,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
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A gravitational signal may come in the form of a single brief pulse. Unwanted events due to local phenomena can be discarded if two detectors are operated independently and at a large distance from one another. A genuine gravitational pulse would be detected almost simultaneously in both whereas a spurious local pulse ... | {
"Header 1": "*Multiple antennas*",
"token_count": 539,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
Lower frequency studies (seconds to hours) will be carried out by the ambitious NASA/ESA Laser Interferometer Space Antenna (LISA) program to be launched in $\sim$ 2010. It will consist of three satellites that will define the legs of an interferometer. The separations will be huge $\sim$ 5 × 10<sup>9</sup> m, (3% of... | {
"Header 1": "*Multiple antennas*",
"Header 3": "Low frequency antenna in space",
"token_count": 1042,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
*Problem 12.31*. The principle of relativistic time dilation states that the mean life at rest, $\tau = 2.2 \,\mu s$ , of a fast moving muon will be extended to $\tau'$ according to
$$\tau' = \gamma \tau \qquad \gamma = \frac{E}{mc^2} \tag{12.17}$$
where E is the total energy (rest energy + kinetic energy), and ... | {
"Header 1": "*Multiple antennas*",
"Header 3": "12.3 Cosmic ray observatories",
"token_count": 2052,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
| · · · · · · · · · · · · · · · · · · · | |
|---------------------------------------|-----------------------------------------------------------------------------------------------------------|
| Universal ... | {
"Header 1": "Units, symbols, and values",
"Header 3": "Table A5. Physical constants<sup>a</sup>",
"token_count": 2046,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
At its original conception, this book was based on the structure, scope, and philosophy of a sophomore/ junior level course taught at M.I.T. by the author and Prof. Irwin I. Shapiro from 1969 to 1982. Although the content of that course varied greatly over the years in response to the vast new knowledge of the Solar Sy... | {
"Header 1": "Foreword",
"token_count": 2030,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
When asked in an interview to give his viewpoint on the frontiers of science, the famous physicist Victor Weisskopf commented that the most exciting prospects fell into two categories, the frontier of size and the frontier of complexity. A host of examples come to mind: cosmology, particle physics, and quantum field th... | {
"Header 1": "Nature and Scope of the Planetary Sciences",
"token_count": 2025,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
This book will begin with what little we presently know with confidence about the earliest history of the Universe, and trace the evolution of matter and its constructs up to the time of the takeover of regulatory processes on Earth by the biosphere. We introduce the essential contributions of the various sciences in... | {
"Header 1": "Nature and Scope of the Planetary Sciences",
"token_count": 381,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
It is difficult, as we have seen above, to draw a tidy line around a particular portion of the scientific literature and proclaim all that lies outside that line to be irrelevant. Still, there are certain journals that are more frequently used and cited by practitioners of planetary science. Every student should be awa... | {
"Header 1": "Guide to the Literature",
"token_count": 1051,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
It is assumed that all readers are familiar with scientific notation, which expresses numbers in the format n:nnnn 10<sup>x</sup>. This convention permits the compact representation of both extremely small and extremely large numbers and facilitates keeping track of the decimal place in hand calculations. Thus the numb... | {
"Header 1": "Numbers in Science",
"token_count": 2046,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
Solar System astronomers routinely use the astronomical unit and Earth's year as standard units, or janskys as a unit of flux. In the same vein, meteorologists diligently strive to describe hydrodynamic processes in terms of dimensionless parameter such as the Rayleigh, Reynolds, Richardson, and Rossby numbers and the ... | {
"Header 1": "Numbers in Science",
"token_count": 786,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
#### Introduction
We cannot study the Solar System without some knowledge of the Universe in which it resides, and of events that long predate the Solar System's existence, including the very origin of matter and of the Universe itself. We shall therefore begin by tracing the broad outlines of present understanding o... | {
"Header 1": "II. Astronomical Perspective",
"token_count": 2036,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
Another way of expressing this result is to say that, some 14 Ga ago, every other galaxy in the Universe was in the same place as our own. At that time, all the matter in the observable Universe must have been hurled outward from some very small volume of space at speeds up to
almost the speed of light. Direct evid... | {
"Header 1": "II. Astronomical Perspective",
"token_count": 1977,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
$$h = 6.625 \times 10^{-27} \,\mathrm{erg}\,\mathrm{s}$$
$c = 2.997 \times 10^{10} \,\mathrm{cm}\,\mathrm{s}^{-1}$
$k = 1.380 \times 10^{-16} \,\mathrm{erg}\,\mathrm{K}^{-1}$ .
It can be shown that a typical photon in this gas has an energy, $h\nu$ , which is related to the equilibrium temperature of the radiati... | {
"Header 1": "II. Astronomical Perspective",
"token_count": 1949,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
Other reactions which are important during this era include
$$p+p \rightarrow D + e^+ + \nu_e \hspace{1cm} (II.26)$$
$$D + n \rightarrow {}^{3}H + \gamma \tag{II.27}$$
$$D + p \rightarrow {}^{3}He + \gamma \tag{II.28}$$
$${}^{3}\text{He} + {}^{3}\text{He} \rightarrow {}^{4}\text{He} + 2p + \gamma,$$
(II.29) ... | {
"Header 1": "II. Astronomical Perspective",
"token_count": 1146,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
... what God originally created, that matter which, by dint of His volition, He first made from His Spirit or from nihility, could have been nothing but matter in its utmost conceivable state of—of what?—of simplicity?
Edgar Allen Poe Eureka
Reactions of elements heavier than hydrogen are strongly inhibited because... | {
"Header 1": "II. Astronomical Perspective",
"Header 2": "Limitations on Big Bang Nucleosynthesis",
"token_count": 2019,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
Small gas clouds with quite high densities and low angular momenta will produce first-generation stars with random masses, many of which will be much larger than normal stable stars. We must pursue further the evolution and classification of stars and stellar systems in order to appreciate fully the significance and ... | {
"Header 1": "II. Astronomical Perspective",
"Header 2": "Limitations on Big Bang Nucleosynthesis",
"token_count": 2042,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
The speed of the Sun relative to the *average* of the globular clusters is much higher, roughly 200 km s<sup>-1</sup>. Since the distribution and motion of the globular clusters are spherically symmetrical, they do not partake of the orderly rotation of the disk population of stars. As many are moving "forward" as ar... | {
"Header 1": "II. Astronomical Perspective",
"Header 2": "Limitations on Big Bang Nucleosynthesis",
"token_count": 2040,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
There are endless mnemonics to assist in keeping this sequence intact and in order: my favorite is "Oscar, Bring A Fully Grown Kangaroo: My Recipe Needs Some." (Certain other spectral classes, such as C, are often encountered in the astronomical literature but rarely seen in space.) Thus O and B stars are very strong u... | {
"Header 1": "II. Astronomical Perspective",
"Header 2": "Limitations on Big Bang Nucleosynthesis",
"token_count": 2042,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
and for $M_2$ ,
$$\frac{GM_1M_2}{R^2} = \frac{M_2V_2^2}{R_2}; \quad \frac{GM_1}{R_2} = \frac{V_2^2}{R_2}.$$
(II.55)
The orbital periods are
$$P_1 = \frac{2\pi R_1}{V_1}$$
$P_2 = \frac{2\pi R_2}{V_2} = P_1 = P.$ (II.56)
Substituting for $V_1$ and $V_2$ in Eqs. (II.54) and (II.55) and adding
$$\frac{GM_... | {
"Header 1": "II. Astronomical Perspective",
"Header 2": "Limitations on Big Bang Nucleosynthesis",
"token_count": 2041,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
Such stars are so faint that the census surely missed many of them. It is therefore very probable that the resulting luminosity function is incomplete on the faint end. It should be recalled that such undetected stars would contribute mass but almost no luminosity to the totals, and their hypothetical presence would sh... | {
"Header 1": "II. Astronomical Perspective",
"Header 2": "Limitations on Big Bang Nucleosynthesis",
"token_count": 1942,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
The principal nuclear reactions producing energy in a Pop II star involve the fusion of hydrogen to helium by the proton–proton chain,
$$2(p + p \rightarrow {}^{2}D + e^{+} + \nu_{e})$$
(II.63)
$$2(^{2}D + p \rightarrow {}^{3}He + \gamma) \tag{II.64}$$
$$^{3}\text{He} + {^{3}\text{He}} \rightarrow {^{4}\text{He... | {
"Header 1": "II. Astronomical Perspective",
"Header 2": "Limitations on Big Bang Nucleosynthesis",
"token_count": 2008,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
Ignition of helium burning causes a "helium flash," after which the star settles down for about 108 years on the "helium burning main sequence" as a giant. At an advanced stage of helium burning, the star again flares up as a Wolf-Rayet star, this time violently enough to expel much of the hydrogen-bearing outer envelo... | {
"Header 1": "II. Astronomical Perspective",
"Header 2": "Limitations on Big Bang Nucleosynthesis",
"token_count": 2040,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
Stellar Origins 29
Alternatively, we could note that the large majority of the present angular momentum in the Solar System resides in the orbital motions of the planets, not the rotation of the Sun. It has been suggested that the presence of planets provides an angular momentum sink and that slowly rotating stars ... | {
"Header 1": "II. Astronomical Perspective",
"Header 2": "Limitations on Big Bang Nucleosynthesis",
"token_count": 2006,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
According to the H-R diagram, this star has a surface temperature about four times that of a G0 star, and, because $L \propto R^2 T^4$ , the radius of the star must be $L^{0.5}/T^2 = 200 R_{\odot}$ ( = 1 AU). The collapse energy of the star is $GM^2/R$ , or 50 times that of the Sun, roughly $2 \times 10^{50}$ erg... | {
"Header 1": "II. Astronomical Perspective",
"Header 2": "Limitations on Big Bang Nucleosynthesis",
"token_count": 1773,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
Astronomical Perspective
Table II.3 Interstellar Molecules
#### Inorganio
$\rm H_2, \, H_3^+, \, OH, \, H_2O, \, SiO, \, SiS, \, SiN, \, SiH_4, \, SO, \, SO^+, \, SO_2, \, NS, \, HS, \, H_2S, \, NH, \, NH_2, \, NH_3, \, NO, \, N_2O, \, N_2, \, N_2H^+, \, H^+, \, H_3O^+, \, H_2D^+, \, HNO, \, O_3, \, HCl, \, PN, \... | {
"Header 1": "II. Astronomical Perspective",
"Header 2": "Limitations on Big Bang Nucleosynthesis",
"token_count": 2031,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
The line is the locus of solutions for temperature and pressure as a function of density for steady-state dynamic balance of the energy sources and loss mechanisms in the ISM. Coronal and HII regions are source phenomena, not steady-state solutions. The stability of GMCs is due to a new factor that has negligible influ... | {
"Header 1": "II. Astronomical Perspective",
"Header 2": "Limitations on Big Bang Nucleosynthesis",
"token_count": 376,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
The Infrared Astronomy Satellite (IRAS) has found several thousand dense, warm globules or disks in giant molecular cloud (GMC) complexes where star formation is known to be occurring. There is good reason to believe that these bodies are in fact prestellar disks, detectable in the infrared, but so heavily shrouded in ... | {
"Header 1": "Outline of Star Formation",
"token_count": 1735,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
The reactions involved are
$$^{12}\text{C} + \text{H} \rightarrow ^{13}\text{N} + 1.95 \,\text{MeV}$$
(II.74)
$^{13}\text{N} \rightarrow ^{13}\text{C} + \beta^{+} + \nu_{\text{e}} + 1.50 \,\text{MeV}$ (II.75)
$$^{13}N \rightarrow ^{13}C + \beta^{+} + \nu_{e} + 1.50 \,\text{MeV} \quad (\text{II.75})$$
$$^{13}C+H\... | {
"Header 1": "Outline of Star Formation",
"token_count": 1933,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
The series of products made by successive additions of alpha particles is
$$^{12}\text{C} + ^{4}\text{He} \rightarrow ^{16}\text{O} + \gamma$$
(II.95)
$$^{16}\text{O} + ^{4}\text{He} \rightarrow ^{20}\text{Ne} + \gamma$$
(II.96)
$$^{20}$$
Ne + $^{4}$ He $\rightarrow$ $^{24}$ Mg + $\gamma$ (II.97)
and so o... | {
"Header 1": "Outline of Star Formation",
"token_count": 2047,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
The pairs of abundance peaks at high A are discussed in the text. The even-odd nuclide <sup>9</sup>Be clusters with the other unstable isotopes of lithium and boron.
The rates of these reactions are roughly proportional to the temperature to the 30th power! Near the equilibrium stability maximum at <sup>56</sup>Fe th... | {
"Header 1": "Outline of Star Formation",
"token_count": 2028,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
Each successive n-addition product is farther from the original stable nuclide and less stable, and each has a shorter lifetime than the previous product.
About 50 years ago the element technetium (Tc), with Z=43, was discovered for the first time in nature in the spectra of S-type stars (and, by a strange coincidenc... | {
"Header 1": "Outline of Star Formation",
"token_count": 2029,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
A much more serious instability is believed to occur in the interiors of very highly evolved red giant stars that have very high core temperatures. In their cores, the pressures and temperatures are so large that nuclear equilibrium has largely been attained. Reactions have progressed through hydrogen and helium burn... | {
"Header 1": "Outline of Star Formation",
"token_count": 2037,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
They have shown that burning at $T_9 = 4.5$ for no more than 1 second produces excellent agreement with observed elemental abundances up to A = 59.
There still remains the question of how nuclides much heavier than these are produced in stellar explosions. A clue to the nature of this process is the observation tha... | {
"Header 1": "Outline of Star Formation",
"token_count": 2048,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
This Main Sequence stage is followed by a briefer interlude about 10<sup>8</sup> years in duration, during which the principal heat source in the star is helium burning and the ensuing alpha process. Then comes about 10<sup>4</sup> years of the s-process in parallel with the changeover to a roughly 10<sup>7</sup>-year ... | {
"Header 1": "Outline of Star Formation",
"token_count": 1994,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
If we have an accurate theoretical estimate of the initial ${}^{87}\mathrm{Sr}$ : ${}^{86}\mathrm{Sr}$ ratio from nucleosynthesis models, a meteorite that is almost totally devoid of rubidium, or a meteorite that has never been subjected to melting and isotopic homogenization, then we can date the time since the end ... | {
"Header 1": "Outline of Star Formation",
"token_count": 2024,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
What is the temperature of the gas?
- II.4 A gas in equilibrium with a Planckian radiation field is hot enough so that only one photon in a million has enough energy to make an electron. Compare the rate of pair production to that in Problem II.3.
48 II. Astronomical Perspective
II.5 A nuclear explosion in space pr... | {
"Header 1": "Outline of Star Formation",
"token_count": 1148,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
II.18 Equation (II.84) shows that the CC process generates positrons. These positrons must
Exercises 49
- annihilate upon collision with electrons, giving an additional source of energy. What fraction of the total energy output from the CC cycle is contributed by these annihilation reactions?
- II.19 What fraction ... | {
"Header 1": "Outline of Star Formation",
"Header 2": "Stellar Explosions and Nucleosynthesis",
"token_count": 843,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
The Sun,which makes up about 99.9% of the mass of our planetary system,is a typical stable Main Sequence dwarf star of spectral class G2. It pursues an orbit about the center of the Galaxy with a radius of roughly 8 kpc and a period of about 200 million years.
The Sun rotates approximately every 26 days around an axi... | {
"Header 1": "The Sun",
"token_count": 2039,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
The laws of planetary motion as laid out by Johannes Kepler are:
- I. Each planet executes a planar elliptical orbit about the Sun, with the Sun at one focus of the ellipse.
- II. The area swept out by the radius vector from the Sun to the planet per unit time is a constant.
- III. The square of the orbital period ... | {
"Header 1": "The Sun",
"token_count": 2048,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
This behavior is illustrated in the hodograph in Fig. III.3b.
Figure III.3 Hodograph for elliptical motion. See the text for explanation.
Orbits of the Planets 55
The total kinetic energy per unit mass can, with the help of Fig. III.3, be resolved into components due to motion in t... | {
"Header 1": "The Sun",
"token_count": 2048,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
C. Adams of England and U. J. J. Leverrier of France independently calculated the position and mass of this undiscovered planet,using the assumption that it obeyed Bode's Law. When telescopes were turned to the predicted position the planet known to us as Neptune was quickly discovered. Neptune had,in effect,been disco... | {
"Header 1": "The Sun",
"token_count": 404,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
The basic theory of orbital motion outlined earlier is appropriate for use when the gravitational force is exerted by a mass point or a perfectly homogeneous, spherically symmetrical mass. It also does not,in this form,take into account other forces,such as additional gravitating bodies,rocket propulsion,atmospheric dr... | {
"Header 1": "Changes in Orbital Motion",
"token_count": 1722,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
Particularly noteworthy are the very long rotation period of Mercury, the slow retrograde rotation of Venus, the near
**Table III.2** Rotation of the Planets
| | | | Nort | h pole | |
|---------|-----------------|-------------------|--------|--------|---... | {
"Header 1": "Changes in Orbital Motion",
"token_count": 2043,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
In surveying the general properties of the Solar System,we have seen that certain commodities,such as total mass,gas abundances,and angular momentum,seem to be distributed very inequitably. We of course note that
Figure III.6 Visual appearance of the planets. a is a mosaic of Mariner 10 ... | {
"Header 1": "Mass and Angular Momentum Distribution",
"token_count": 1028,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
Since Galileo Galilei first turned his telescope on the planets in the early 17th century,it has been clear that a number of other sizeable bodies can be found in the Solar System. In fact,the largest satellites of Earth, Jupiter,Saturn,and Neptune are all of planetary dimensions. Modern observational techniques,culmin... | {
"Header 1": "Satellites",
"token_count": 371,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
would not have survived over the age of the Solar System.
Earth's moon has an appearance strikingly similar to Mercury, but a density some 40% lower than Mercury's. It is also enormously more conveniently situated for observation and has been the object of dozens of spacecraft missions in the Soviet Luna, Zond, and... | {
"Header 1": "Satellites",
"token_count": 1190,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Lewis_2004.pdf"
} |
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