page_content stringlengths 12 2.63M | metadata unknown |
|---|---|
The pulsar at the center of the Crab Nebula has a period P=0.033326 s and a period increase of $dP/dt=\dot{P}=4.213\times 10^{-13}$ s s<sup>-1</sup>. Assuming that this pulsar has a mass equal to the mass of a neutron with a mass $M=M_{NS}\approx 1.4~M_{\odot}$ , where the Sun's mass $M_{\odot}=1.989\times 10^{30}$... | {
"Header 1": "Essential Astrophysics",
"Header 2": "Example: Energy loss and magnetic field strength of the Crab Nebula pulsar",
"token_count": 1135,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
Because x-rays are absorbed in our atmosphere, cosmic x-ray sources must be observed with instruments launched above the obscuring air, in rockets or satellites. By the mid-twentieth century brief, 5-minute rocket flights had shown that the Sun radiates detectable x-rays, and it was thought that lunar material also mig... | {
"Header 1": "Essential Astrophysics",
"Header 2": "13.7.3 X-ray Pulsars from Neutron Stars in Binary Star Systems",
"token_count": 680,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
M_{XP} = mass of x-ray pulsar = 1.05–1.87 M_{\odot} \approx (2.1-3.7) \times 10^{30} kg
```
anniversary of the independence of Kenya, the satellite was given the name *Uhuru*, the Swahili word for freedom.
After analyzing a year of observations of Centaurus X-3, the *Uhuru* scientists found a regular pattern of int... | {
"Header 1": "Essential Astrophysics",
"Header 2": "13.7.3 X-ray Pulsars from Neutron Stars in Binary Star Systems",
"token_count": 1873,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
10.1, Focus 10.1):
$$L_{Edd} = \frac{4\pi G m_p c M}{\sigma_T} \approx 6.3 M \text{ J s}^{-1},$$
(13.33)
or
$$L_{Edd} \approx 1.25 \times 10^{31} \frac{M}{M_{\odot}} \text{ J s}^{-1},$$
(13.34)
464 13 Stellar End States
where *M* is the mass of the compact accreting star, the Thomson scattering cross section ... | {
"Header 1": "Essential Astrophysics",
"Header 2": "13.7.3 X-ray Pulsars from Neutron Stars in Binary Star Systems",
"token_count": 677,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
The maximum mass transfer rate $\dot{M}_{Edd}$ onto a neutron star of radius $R_{NS}=10~{\rm km}=10^4~{\rm m}$ will be $\dot{M}_{Edd}=8\pi m_P c R_{NS}/\sigma_T\approx 2\times 10^{15}~{\rm kg~s}^{-1},$ where the proton mass $m_P=1.6726\times 10^{-27}~{\rm kg}$ , the speed of light $c=2.9979\times 10^8~{\rm m~s}... | {
"Header 1": "Essential Astrophysics",
"Header 2": "Example: Accretion luminosity and temperature from mass transfer to a neutron star",
"token_count": 1209,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
Since a black hole is invisible, and it does not absorb, emit, or reflect radiation, how do we know it is there? We detect a black hole by its gravitational effect on the motion of a visible star.
With remarkable foresight, the Reverend John Michell also speculated, in 1784, that the unseen star might betray its pres... | {
"Header 1": "Essential Astrophysics",
"Header 2": "13.8.2 Observing Stellar Black Holes",
"token_count": 1485,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
The outer edge of a black hole can be defined as the radius at which the escape velocity, required to escape from its gravitational pull, is equal to the speed of light, or when the kinetic energy of an object moving at this speed is equal to the gravitational potential energy of the mass holding it in. This radius is ... | {
"Header 1": "Essential Astrophysics",
"Header 2": "13.8.3 Describing Black Holes",
"token_count": 2047,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
470 13 Stellar End States
The Schwarzschild metric has a one over zero term, a singularity, which blows up at the Schwarzschild, or gravitational, radius $R_g = 2GM/c^2$ , which is the radius at which the escape velocity becomes equal to the speed of light. In 1963 the New Zealand mathematician Roy Kerr (1934–) de... | {
"Header 1": "Essential Astrophysics",
"Header 2": "13.8.3 Describing Black Holes",
"token_count": 582,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
On a clear, moonless night, we can look up and see a hazy, faintly luminous band of light that stretches across the sky from one horizon to the other; it is known as the Milky Way (Fig. [14.1\)](#page-488-0). According to ancient Greek myth, the goddess Hera, Queen of Heaven, spilled milk from her breast into the sky. ... | {
"Header 1": "Essential Astrophysics",
"Header 2": "14.1.1 A Fathomless Disk of Stars",
"token_count": 1348,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
The luminosity of some stars does not remain constant but instead fluctuates over regular periods. These stars do not only turn on and off, like a switched house light, but instead gradually vary from dimmer to brighter and then back to dimmer again with periods ranging from a few days to a few months.
The very lumin... | {
"Header 1": "Essential Astrophysics",
"Header 2": "14.1.2 The Sun is Not at the Center of Our Stellar System",
"Header 3": "Focus 14.1 Cepheid variable stars",
"token_count": 1987,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
(2007), for example, used the *Hubble Space Telescope* to obtain the parallax and distance of 10 nearby Cepheid variables, obtaining the relation:
$$M_V = -1.62 - 2.43 \log P, \tag{14.2}$$
where P is the period in days and the uncertainty in the absolute visual magnitude $M_V$ is $\pm 0.10$ . This is the period-... | {
"Header 1": "Essential Astrophysics",
"Header 2": "14.1.2 The Sun is Not at the Center of Our Stellar System",
"Header 3": "Focus 14.1 Cepheid variable stars",
"token_count": 1514,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
The physical parameters of the galactic disk are listed in Table [14.1.](#page-494-0)
**Table 14.1** Physical properties of the Milky Way disk
```
R_{disk} = radius of disk = 50,000 light-years \approx 15,000 \text{ pc} \approx 4.6 \times 10^{20} \text{ m}
L_{disk} = thickness of disk = 3,000 light-years \approx ... | {
"Header 1": "Essential Astrophysics",
"Header 2": "14.1.2 The Sun is Not at the Center of Our Stellar System",
"Header 3": "Focus 14.1 Cepheid variable stars",
"token_count": 1916,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
The period $P_{\odot}$ for one rotation of the Sun around the center is $P_{\odot} = 2\pi R_0/V_{\odot}$ $\approx 7.6 \times 10^{15} \text{ s} \approx 2.4 \times 10^8 \text{ years}$ , where 1 year = $3.1557 \times 10^7 \text{ sec}$ and $R_0 = D_{\odot} = 8.5 \text{ kpc} = 2.6 \times 10^{20} \text{ m} = 27,700... | {
"Header 1": "Essential Astrophysics",
"Header 2": "14.1.2 The Sun is Not at the Center of Our Stellar System",
"Header 3": "Focus 14.1 Cepheid variable stars",
"token_count": 2043,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
That is equivalent to about 100 billion solar masses, or $10^{11}$ $M_{\odot}$ , where the mass of the Sun is $M_{\odot} = 1.989 \times 10^{30}$ kg. So there is a mass equivalent to about 100 billion stars like the Sun within the Sun's galactic orbit. Fish and Tremaine (1991) have provided a review of the mass of ... | {
"Header 1": "Essential Astrophysics",
"Header 2": "14.1.2 The Sun is Not at the Center of Our Stellar System",
"Header 3": "Focus 14.1 Cepheid variable stars",
"token_count": 1364,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
Radio astronomers have looked right through interstellar dust and detected an exceptionally powerful and compact radio source at the center of the Milky Way. It is in the direction of the constellation Sagittarius, and therefore been named Sagittarius A\* (abbreviated Sgr A\* and pronounced ''Sag A'' star).
Radio int... | {
"Header 1": "Essential Astrophysics",
"Header 2": "14.1.5 A Central Super-Massive Black Hole",
"token_count": 2040,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
#### **Example: Mass of the dark halo**
We can infer the total mass, $M_G$ , of our stellar system under the assumption that distant, small companions are gravitationally bound to it. (Here we use the subscript G to denote our Galaxy, which is a term that is introduced later in the book.) The dwarf spheroid Leo I ... | {
"Header 1": "Essential Astrophysics",
"Header 2": "14.1.5 A Central Super-Massive Black Hole",
"token_count": 767,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
Long before the discovery of dark matter, Edwin Hubble (1889–1953), showed that the Milky Way does not contain everything there is, and settled an ongoing controversy about the nature of spiral nebulae. The issue was presented during the now-famous Shapley-Curtis debate over ''The Scale of the Universe'' during a meeti... | {
"Header 1": "Essential Astrophysics",
"Header 2": "14.2 The Discovery of Galaxies",
"token_count": 2037,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
The spectral characteristics of the light from the spirals are similar to that of our Sun, indicating stellar temperatures of thousands of K. If a spiral were filled with gas at this temperature throughout its enormous dimensions, the nebula would be more
than 1 billion, billion times more luminous than the Sun, ra... | {
"Header 1": "Essential Astrophysics",
"Header 2": "14.2 The Discovery of Galaxies",
"token_count": 949,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
At the time of their discovery in enormous numbers, most astronomers thought that the spiral nebulae were nascent planetary systems, not galaxies. The bright center was supposed to be a newborn star, and the spiral arms surrounding it were thought to be developing planets, whirling and rotating around the central star ... | {
"Header 1": "Essential Astrophysics",
"Header 2": "14.3 The Galaxies are Moving Away from us and from Each Other",
"token_count": 2029,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
However, there was a wide dispersion between the plotted points and only a mild tendency for velocity to increase with distance (Fig. 14.9). Nevertheless, his conclusion subsequently was confirmed by more comprehensive observations of a much greater number of galaxies.
The discovery of the expanding universe also exp... | {
"Header 1": "Essential Astrophysics",
"Header 2": "14.3 The Galaxies are Moving Away from us and from Each Other",
"token_count": 2004,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
The systematic uncertainties in $H_0$ have decreased as a result of observations with the *Hubble Space Telescope* and the *Spitzer Space Telescope* with recent determinations of $H_0 = 73.8 \pm 2.4$ km s<sup>-1</sup> Mpc<sup>-1</sup> (Reiss et al. 2011) and $H_0 = 74.3 \pm 2.1$ km s<sup>-1</sup> Mpc<sup>-1</sup>... | {
"Header 1": "Essential Astrophysics",
"Header 2": "14.3 The Galaxies are Moving Away from us and from Each Other",
"token_count": 1931,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
[1992\)](http://dx.doi.org/10.1007/978-3-642-35963-7_16#CR662):
$$N_g = 0.0552 h^3 \,\text{Mpc}^{-3} \approx 0.019 \,\text{Mpc}^{-3}$$
(14.39)
$$L_g \approx 2 \times 10^8 \, h \, L_{B\odot} \, \text{Mpc}^{-3} \approx 3 \times 10^{34} \, \text{J s}^{-1} \, \text{Mpc}^{-3},$$
(14.40)
where Hubble's constant $H_0 =... | {
"Header 1": "Essential Astrophysics",
"Header 2": "14.3 The Galaxies are Moving Away from us and from Each Other",
"token_count": 640,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
Throughout most of the past decades, it has been assumed that it is the mass of the universe that curves its shape, establishes its geometry, and determines its fate. Under this assumption, which ignores the more recent discovery of dark energy, the mass density of galaxies, $\rho_g$ , determines the ultimate destiny ... | {
"Header 1": "Essential Astrophysics",
"Header 2": "Example: Can visible or invisible matter stop the expansion of the universe?",
"token_count": 784,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
Astronomers have been mapping the distribution of galaxies for about a century, determining the shape and form of the larger universe. The first cosmic maps were two-dimensional, constructed from catalogues giving the celestial positions of the brightest nebulae. Although a foreground and background galaxy might someti... | {
"Header 1": "Essential Astrophysics",
"Header 2": "14.4.1 Clusters of Galaxies",
"token_count": 1246,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
Clusters of galaxies are bound together by gravity, even though the expansion of the universe is pulling the galaxies away from one another. We could think that the combined gravitational pull of the numerous galaxies might be sufficient to hold them together but, in 1937, Fritz Zwicky (1898–1974) showed that there mus... | {
"Header 1": "Essential Astrophysics",
"Header 2": "14.4.1 Clusters of Galaxies",
"Header 3": "14.4.2 Dark Matter in Clusters of Galaxies",
"token_count": 2048,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
14.12 and 14.13). As Zwicky proposed, the gravitational-lens effect provides information on both the visible and unseen matter. Moreover, the dark matter can act like a zoom lens, magnifying distant galaxies too faint to be seen and bringing them into view.
The presence of two galaxies along the same line of sight, o... | {
"Header 1": "Essential Astrophysics",
"Header 2": "14.4.1 Clusters of Galaxies",
"Header 3": "14.4.2 Dark Matter in Clusters of Galaxies",
"token_count": 2047,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
A distance of about 778 kpc currently separates the two galaxies, but they are set on an irrevocable collision course. They will meet in a possibly destructive encounter in a few billion years.
#### Example: When will Andromeda enter the Milky Way?
The distance of the Andromeda nebula from the Earth is $D=778~\rm ... | {
"Header 1": "Essential Astrophysics",
"Header 2": "14.4.1 Clusters of Galaxies",
"Header 3": "14.4.2 Dark Matter in Clusters of Galaxies",
"token_count": 1197,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
By determining the concentrations of galaxies in different directions and at various redshifts, or depths, astronomers located places where the collective force of gravity pulled galaxies together and locally reversed the uniform expanding motion. The three-dimensional maps reveal fascinating lace-like patterns that co... | {
"Header 1": "Essential Astrophysics",
"Header 2": "14.4.4 Galaxy Walls and Voids",
"token_count": 2002,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
Assuming that the density parameter $\Omega_0\approx 10^{-2}$ , then the look-back time for this galaxy is $t_L=0.83\,t_H=10.8$ billion years, and about 3 billion years after the big bang that occurred about 13.7 billion years ago.
The Hubble time is the approximate time when the expansion of the universe began. G... | {
"Header 1": "Essential Astrophysics",
"Header 2": "14.4.4 Galaxy Walls and Voids",
"token_count": 2046,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
So it was fortunate that Henrietta H. Swope (1902–1980), the daughter of the wealthy president of the General Electric Company, joined Baade to assist with the analysis of his excellent photographs. They used the results to propose a downward revision of the Hubble constant to a value of 100, in the usual units (Baade ... | {
"Header 1": "Essential Astrophysics",
"Header 2": "14.4.4 Galaxy Walls and Voids",
"token_count": 1301,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
Edwin Hubble (1889–1953) relied solely on the power of observation, preferring to avoid what he called "the dreamy realms of speculation" (Hubble 1936), most likely referring to theoretical physicists. Although an expanding universe was a possible consequence of Albert Einstein's (1879–1955) *General Theory of Relativi... | {
"Header 1": "Essential Astrophysics",
"Header 2": "14.6 Using Einstein's General Theory of Relativity to Explain the Expansion",
"token_count": 1965,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
Moreover, in the present matter-dominated era the pressure $P_0 = 0$ , the radiation energy density $\rho_r(t_0)$ can be omitted when compared to the mass density $\rho_m(t_0) = \rho_0$ , and the deceleration parameter is given by:
$$q_0 = q(t_0) = \frac{4\pi G}{3H_0^2}\rho_0 = \frac{\rho_0}{2\rho_C} \text{ for }... | {
"Header 1": "Essential Astrophysics",
"Header 2": "14.6 Using Einstein's General Theory of Relativity to Explain the Expansion",
"token_count": 965,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
Regardless of the direction in which we look out into space, almost all of the distant galaxies are flying apart, dispersing and moving away at speeds that increase with their distance, as if they had been ejected by a cosmic bomb. Astronomers call it the ''big bang.''
We can envision this early state by putting the ... | {
"Header 1": "Essential Astrophysics",
"Header 2": "15.1 Hotter Than Anything Else",
"token_count": 1888,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
$$T_r(t) = \left[ \frac{3c^2 M_r(t)}{4\pi a R^3(t)} \right]^{1/4} = \left[ \frac{3c^2}{8\pi G a} \right]^{1/4} \frac{1}{t^{1/2}} \approx 2.15 \times 10^{10} \frac{1}{t^{1/2}} \text{ K}, \tag{15.6}$$
where the time t is in seconds for the numerical approximation, or equivalently
$$t \approx 4.6 \times 10^{20} \fra... | {
"Header 1": "Essential Astrophysics",
"Header 2": "15.1 Hotter Than Anything Else",
"token_count": 319,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
The discovery of the faint afterglow of the big bang was a serendipitous event, involving a horn-reflector antenna that had been used at the Bell Telephone Laboratories in the first tests of a communication satellite. Arno Penzias (1933– ) and Robert Wilson (1936– ) were measuring the temperatures of noises in the horn... | {
"Header 1": "Essential Astrophysics",
"Header 2": "15.2.1 An Unexpected Source of Noise",
"token_count": 780,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
At the high temperatures during the early history of the expanding universe, the radiation and subatomic particles frequently interacted, achieving thermal equilibrium characterized by single temperature. Later, when the universe thinned out and cooled by expanding into a greater volume, the matter and radiation quit i... | {
"Header 1": "Essential Astrophysics",
"Header 2": "15.2.2 Blackbody Spectrum",
"token_count": 1353,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
What alerted astronomers to the importance of the background radiation was its equal brightness wherever one looked, indicating that it uniformly fills all of space (Wilson and Penzias [1967](http://dx.doi.org/10.1007/978-3-642-35963-7_16#CR1129)). This spatial isotropy satisfied one of the basic tenets of modern cosmo... | {
"Header 1": "Essential Astrophysics",
"Header 2": "15.2.3 As Smooth as Silk",
"token_count": 224,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
In 1992, George Smoot (1945– ) and his colleagues announced measurements of the temperature fluctuations in the cosmic microwave background radiation using four years of data gathered by COBE (Smoot et al. [1992;](http://dx.doi.org/10.1007/978-3-642-35963-7_16#CR979) Bennett et al. [1993,](http://dx.doi.org/10.1007/978... | {
"Header 1": "Essential Astrophysics",
"Header 2": "15.2.4 Cosmic Ripples",
"token_count": 1848,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
Definitive new
| Parameter | Name | Value |
|------------------|----------------------------------------------------------------------|-----------------------------------------------------------|... | {
"Header 1": "Essential Astrophysics",
"Header 2": "15.2.4 Cosmic Ripples",
"token_count": 797,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
#### 15.3.1 The First Three Minutes
George Gamow (1904–1968) and his colleagues proposed that the first elements were formed during the big bang that propelled the universe into expansion (Alpher et al.1948, Sect. 10.5). As they supposed, the lightest atomic nuclei were
<sup>&</sup>lt;sup>a</sup> Parameter values a... | {
"Header 1": "Essential Astrophysics",
"Header 2": "15.3 The Beginning of the Material Universe",
"token_count": 2043,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
Whole atoms were not formed until the expanding universe cooled enough for electrons to combine with protons and helium nuclei to form long-lived hydrogen and helium atoms. This recombination occurred about 400,000 years after the big bang, when the temperature had fallen to about 3,000 K. The rate of recombination was... | {
"Header 1": "Essential Astrophysics",
"Header 2": "15.3.2 Formation of the First Atoms, and the Amount of Invisible Dark Matter",
"token_count": 1992,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
The mass density, $\rho_m(t)$ , doesn't decrease as rapidly with increasing time and radius, since it thins out with increasing volume, or with
$$\rho_m(t) \propto \frac{1}{R^3(t)}.\tag{15.16}$$
Since
$$T_r(t) \propto \frac{1}{R(t)},\tag{15.17}$$
the ratio
$$\frac{\rho_m(t)T_r(t)}{\rho_r(t)} = T_r(t_{eq}) \t... | {
"Header 1": "Essential Astrophysics",
"Header 2": "15.3.2 Formation of the First Atoms, and the Amount of Invisible Dark Matter",
"token_count": 1965,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
This also marks the beginning of the dark ages of the expanding universe, for there were no sources of radiation other than the gradually cooling and darkening cosmic background radiation until stars and galaxies
| Time (after the big | Redshift, z | Temperature | Key events ... | {
"Header 1": "Essential Astrophysics",
"Header 2": "15.3.2 Formation of the First Atoms, and the Amount of Invisible Dark Matter",
"token_count": 1889,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
With the help of cold dark matter, the first stars and galaxies appeared more than 10 billion years ago. We can observe these embryonic galaxies when they were cosmic infants; the light now reaching us began its journey long before the Sun came into existence.
Bromm and Larson ([2004\)](http://dx.doi.org/10.1007/978-... | {
"Header 1": "Essential Astrophysics",
"Header 2": "15.4.2 When Stars Began to Shine",
"token_count": 2005,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
Salpeter (1924–2008), who showed that the number of stars with masses in the range M to M ? dM within a specified volume of space, is proportional to M-2.35 (Salpeter [1955](http://dx.doi.org/10.1007/978-3-642-35963-7_16#CR901)). In other words, the number of stars in each mass range decreases rapidly with increasing m... | {
"Header 1": "Essential Astrophysics",
"Header 2": "15.4.2 When Stars Began to Shine",
"token_count": 2012,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
This radio image, taken with the Very Large Array at a wavelength of 6 cm with a field of view of 0.038 9 0.022 degrees, shows two narrow, straight radio-emitting jets of particles that protrude in opposite directions from a giant elliptical galaxy at the center. The redshift of the optically visible elliptical is z = ... | {
"Header 1": "Essential Astrophysics",
"Header 2": "15.4.2 When Stars Began to Shine",
"token_count": 2023,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
Once quasars were known, astronomers located others by obtaining optical spectra of bright, blue-colored, star-like objects that are located well outside the plane of the Milky Way, where stars are not supposed to be, and measuring the large redshifts characteristic of remote quasars. Thousands of quasars have now been... | {
"Header 1": "Essential Astrophysics",
"Header 2": "15.4.2 When Stars Began to Shine",
"token_count": 1068,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
As independently proposed by the astrophysicists Edwin E. Salpeter (1924– ), at Cornell University, and Yakov B. Zeldovich (1914–1987) in Moscow, the tremendous luminosity of every radio galaxy and quasar most likely is supplied by a super-massive black hole, which emits luminous radiation as its powerful gravity pulls... | {
"Header 1": "Essential Astrophysics",
"Header 2": "15.5.2 Super-Massive Black Holes",
"token_count": 2040,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
The brightest sources found in the universe, at least so far, are the gamma-ray bursts whose duration is measured in seconds or less and which never reappear in exactly the same part of the sky. They emit energy at a gamma-ray wavelength shorter than 10-<sup>11</sup> m, so each photon of a gamma ray is about 100,000 ti... | {
"Header 1": "Essential Astrophysics",
"Header 2": "15.5.3 Gamma-Ray Bursts",
"token_count": 1636,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
The redshift, z, of a galaxy increases with its distance, D, according to the Hubble law cz = H0D, where c is the speed of light and H<sup>0</sup> is the Hubble constant. Since distances can only be independently measured for nearby galaxies, the law is expressed as a redshift – magnitude relation applicable at larger ... | {
"Header 1": "Essential Astrophysics",
"Header 2": "15.6.1 Discovery of Dark Energy",
"token_count": 1405,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
The trouble is, nobody understands this mysterious something, this dark energy that permeates space and eventually overwhelms the gravitational self-attraction of the entire material universe. But an old idea, termed the cosmological constant, has been revived to give dark energy another name and couch it in mathematic... | {
"Header 1": "Essential Astrophysics",
"Header 2": "15.6.2 Using the Cosmological Constant to Describe Dark Energy",
"token_count": 1900,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
The power of the cosmological constant is measured from its density parameter $\Omega_A$ given by
$$\Omega_{\Lambda} = \Omega_{\Lambda}(t_0) = \frac{\Lambda c^2}{3H_0^2},\tag{15.33}$$
while the matter density parameter is given in its usual way
$$\Omega_m = \Omega_m(t_0) = \frac{\rho_m(t_0)}{\rho_c}.$$
(15.34... | {
"Header 1": "Essential Astrophysics",
"Header 2": "15.6.2 Using the Cosmological Constant to Describe Dark Energy",
"token_count": 1265,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
Ever since the discovery of the expansion of the universe, we have known that the universe is slowly and inexorably approaching an end. There has never been any known force that can prevent the observable universe from steadily moving into darkness. As Georges Lemaître (1894–1966) so eloquently stated ''The evolution o... | {
"Header 1": "Essential Astrophysics",
"Header 2": "15.6.3 When Stars Cease to Shine",
"token_count": 474,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
| Unit | Symbol | Value |
|--------------------------------|--------------|-------------------------------------------------------------|
| Distance and length | | ... | {
"Header 1": "Essential Astrophysics",
"Header 2": "Appendix II Units",
"token_count": 844,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
Angular resolution, hr, of a telescope of diameter, DT, at a wavelength, k:
$$\theta_r = \frac{\lambda}{D_T} \text{ radians} \tag{A-1}$$
where 1 radian = 2.06265 9 10<sup>5</sup> seconds of arc = 2.06265 9 10<sup>5</sup> <sup>00</sup>.
Angular source extent, hsize, of a celestial source of radius, R, located at a... | {
"Header 1": "Essential Astrophysics",
"Header 2": "Appendix III Fundamental Equations",
"token_count": 1972,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
*Astronomy Methods* is an introduction to the basic practical tools, methods and phenomena that underlie quantitative astronomy. Taking a technical approach, the author covers a rich diversity of topics across all branches of astronomy, from radio to gamma-ray wavelengths. Topics include the quantitative aspects of the... | {
"Header 1": "ASTRONOMY METHODS",
"token_count": 315,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
Views of the entire sky at six wavelengths in galactic coordinates. The equator of the Milky Way system is the central horizontal axis and the galactic center direction is at the center. Except for the x-ray sky, the colors represent intensity with the greatest intensities lying along the equator. In all cases, the rad... | {
"Header 1": "**Cover illustrations**",
"token_count": 734,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
This volume is the first part of notes that evolved during my teaching of a small class for junior and senior physics students at MIT. The course focused on a physical, analytical approach to astronomy and astrophysics. The material in this volume presents methods, tools and phenomena of astronomy thatthe science under... | {
"Header 1": "Preface",
"token_count": 1143,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
Celestial measurements reaching back 3000 years or more were carried out in many cultures worldwide. **Early astronomers** in Greece deduced important conclusions about the nature of the **earth** and the **solar system**. Modern astronomy began in the **renaissance** with the observations of **Tycho Brahe** and **Gali... | {
"Header 1": "Astronomy through the centuries",
"Header 3": "**What we learn in this chapter**",
"token_count": 250,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
The rhythmic motions of the stars, the planets, and the sun in the sky have fascinated humankind from the earliest of times. The motions were given religious significance
Figure 1.1. Stonehenge, an early astronomical observatory used for tracking the sun and moon in their seasonal excur... | {
"Header 1": "Astronomy through the centuries",
"Header 2": "**1.2 Early development of astronomy**",
"Header 3": "*First astronomers*",
"token_count": 1055,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
The Renaissance period in Europe brought about great advances in many intellectual fields including astronomy. The Polish monk Nicholaus Copernicus (1473–1543) proposed the solar-centered model of the planetary system. The Dane Tycho Brahe (1546–1601, Fig. 4) used elegant mechanical devices to measure planetary positio... | {
"Header 1": "*Renaissance*",
"token_count": 1400,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
The study of the sky continued with the development of larger and larger telescopes. Generally these were refractive instruments wherein the light passes through the lenses, as in a pair of binoculars. The glass refracts the different colors of light slightly differently (*chromatic aberration*) so that perfect focusin... | {
"Header 1": "*Telescopes, photography, electronics, and computers*",
"token_count": 647,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
Electromagnetic radiation at radio frequencies was discovered by Heinrich Hertz in 1888. This eventually led to the discovery of radio emission from the sky by Carl Jansky in 1931. This opened up the field of *radio astronomy*, an entirely new domain of astronomy that has turned out to be as rich as conventional optica... | {
"Header 1": "Non-optical astronomy",
"token_count": 1002,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
Dark absorption lines were discovered in the solar spectrum in 1802, and Joseph Fraunhofer (1787–1826) recorded the locations of about 600 of them. Comparison to spectra emitted by gases and solids in earth laboratories showed that the gaseous outer layer of the sun contains elements well known on earth. The quantum th... | {
"Header 1": "Non-optical astronomy",
"Header 3": "*Stars and nebulae*",
"token_count": 1231,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
The fuzzy, irregular band of diffuse light that extends across the night sky is known as the Milky Way. Astronomers determined that this light consists of a dense collection of many isolated stars. The Milky Way was thus found to be a large "universe" of stars of which the sun is a member. It is called the *Galaxy* (wi... | {
"Header 1": "Non-optical astronomy",
"Header 3": "*Galaxies and the universe*",
"token_count": 2048,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
Another consequence of the general theory of relativity is that oscillating masses should radiate gravitational waves. (Recall that oscillating electric charges radiate electromagnetic waves.) A *binary radio pulsar* can consist of two neutron stars in orbit about their common center of mass. If they radiate away enoug... | {
"Header 1": "*New horizons*",
"token_count": 939,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
Astronomers learn about the cosmos through the study of signals arriving at the earth in the form of **electromagnetic radiation** or as **neutrinos**, **cosmic rays**, **meteorites**, and, hopefully in the near future, **gravitational waves**. Electromagnetic radiation travels at speed *c* and can behave either as a *... | {
"Header 1": "**What we learn in this chapter**",
"token_count": 251,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
The astronomical "light" that arrives at the earth from a distant source is known as electromagnetic radiation. This radiation can be described in terms of waves or in terms of *photons*. Electromagnetic waves are propagating electric and magnetic fields whereas photons are discrete bundles of energy. These two descrip... | {
"Header 1": "**2.2 Photon and non-photon astronomy**",
"Header 2": "*Photons (electromagnetic waves)*",
"token_count": 622,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
Information about the cosmos can also be gleaned from the detection and measurement of particulate matter. *Cosmic rays* are bits of matter (protons and heavier atomic nuclei) that travel with high energies, arriving at the earth from distant celestial regions (e.g., the sun, a supernova, an active galactic nucleus). S... | {
"Header 1": "*Cosmic rays and meteorites*",
"token_count": 441,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
As noted in Chapter 1, the universe can be probed through observations of neutrinos and gravitational waves. These are relatively new branches of astronomy, and substantial effort is now being expended on their development. Neutrino observations of the sun have been in progress for a number of years and new more sensit... | {
"Header 1": "*Neutrino and gravitational-wave astronomy*",
"token_count": 310,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
The frequency $\nu$ of an electromagnetic wave is described in units of cycles per second, or hertz (Hz). In a vacuum, the frequency is related to its wavelength $\lambda$ as
$$\lambda v = c \tag{2.1}$$
where c is the speed of light in a vacuum,
$$c = 2.9979 \times 10^8 \text{ m/s} \approx 3.00 \times 10^8 \t... | {
"Header 1": "*Neutrino and gravitational-wave astronomy*",
"Header 3": "Wavelength and frequency",
"token_count": 642,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
The energy *E* (units of joules, J, in the SI system) of a photon is1:
$$E = h\nu \tag{2.5}$$
$$h = 6.626069 \times 10^{-34} \,\text{J s}$$
(Planck constant) (2.6)
<sup>1</sup> We often choose to give SI units (in parentheses) when they are not required, as in (5), to remind the reader of the dimensions. The dime... | {
"Header 1": "*Photon energy*",
"token_count": 1679,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
Photons are often emitted from a body that can be characterized by a temperature T. The SI unit of thermodynamic temperature is the *kelvin* which refers to the scale known as *absolute temperature*. In this system, the freezing temperature of water is at T = 273.15 K (0 °C). Temperature can be defined for a gas in the... | {
"Header 1": "**Temperature**",
"token_count": 704,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
Astronomy can be performed only if the photons can reach our instruments. If they are absorbed or scattered en route from their source, they may never arrive. Whether they do or not depends upon the frequency of the radiation and the contents of the space they traverse. In a pure vacuum, the photons will travel unimped... | {
"Header 1": "Atmospheric absorption",
"token_count": 1311,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
A transparent atmosphere is not sufficient for effective astronomy. The interstellar medium (matter between the stars) must also be sufficiently transparent along the line of sight so the photons can reach the earth (See Chapter 10). In some cases it is not. For example, *interstellar grains* or "dust" absorb optical l... | {
"Header 1": "Atmospheric absorption",
"Header 3": "Interstellar absorption",
"token_count": 238,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
*Problem 2.31.* (a) Verify that the several values given in Fig. 1 for each band boundary are in accord with the expressions given in the text for unit conversions. Check the values on the upper and lower axes as well as those expressed numerically below the figure. (b) Make a table which indicates the values of freque... | {
"Header 1": "2.3 Electromagnetic frequency bands",
"token_count": 290,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
Stars are located on the sky with **two angular coordinates**. Distances to them may be ignored by visualizing all of them as being on a **celestial sphere** at "infinite" distance. The angular coordinates define the star's location on the sphere. Any number of **coordinate systems** can be defined on this sphere. Astr... | {
"Header 1": "Coordinate systems and charts",
"Header 2": "**What we learn in this chapter**",
"token_count": 300,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
The position of a star or galaxy should properly be specified in three dimensions, i.e., the two angular coordinates of the object from the perspective of the observer and a distance from the observer. Knowledge of distance to a given star is not as readily obtained as its angular position which can be measured directl... | {
"Header 1": "Coordinate systems and charts",
"Header 2": "**What we learn in this chapter**",
"Header 3": "Mathematical sphere at \"infinity\"",
"token_count": 884,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
The two angular coordinates indicating position on the celestial sphere are two of the three coordinates of a spherical coordinate system, the radial (distance) component
being ignored. An equator must be defined; it can be any *great circle* about the sphere. (A great circle is any circle whose plane passes through ... | {
"Header 1": "Celestial coordinate systems",
"token_count": 299,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
The horizon coordinate system locates a star relative to the observer's horizon which becomes the equator of this coordinate system. Formally, the horizon is the great circle defined by the intersection of the plane tangent to the earth's surface at the observer's location with the celestial sphere. The two angles are ... | {
"Header 1": "*Horizon coordinates*",
"token_count": 266,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
In equatorial celestial coordinates, the *celestial equator* is the projection of the earth's equator onto the celestial sphere (Fig. 1); it lies in the plane defined by the earth's equator. The celestial latitude, indicated by the Greek character delta δ, is
Figure 3.2. The horizon coo... | {
"Header 1": "*Equatorial coordinates*",
"token_count": 1282,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
Why do astronomers use the continually changing equatorial coordinates? In early telescopes, the mechanical rulings that indicate the two angular scales, right ascension and declination, are fixed to the mount which is fixed to the earth; thus the mechanical pointers (attached to the movable telescope) show the pointin... | {
"Header 1": "*Equatorial coordinates*",
"Header 2": "Why equatorial coordinates?",
"token_count": 429,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
Another coordinate system in common use is the *galactic coordinate system*. In this system, the equator on the celestial sphere is defined to be a great circle that runs along the Milky Way.
A schematic of the Galaxy is shown in Fig. 3. It is a disk-shaped cluster of some 10<sup>11</sup> stars. The visible stars ten... | {
"Header 1": "*Equatorial coordinates*",
"Header 2": "Why equatorial coordinates?",
"Header 3": "*Galactic coordinates*",
"token_count": 1452,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
An important complement to a celestial coordinate system is a catalog of reference stars with precisely measured positions. These are equivalent to surveyors' permanently placed markers (bounds) in your neighborhood which are used for later detailed surveys of particular lots, etc. Without them every survey would have ... | {
"Header 1": "*Ecliptic coordinate system*",
"Header 3": "Reference frames",
"token_count": 640,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
The several coordinate systems are simply redefinitions of the coordinates on the same celestial sphere. In all cases the stars are defined on a two-dimensional surface with two angles, a latitude and a longitude. One can convert the coordinates of a given star from one coordinate system to another with standard spheri... | {
"Header 1": "*Ecliptic coordinate system*",
"Header 3": "**Transformations**",
"token_count": 627,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
The concept of *solid angle* $\Omega$ is fundamental to all of astronomy. It is simply an "angular area" on the sky, or equivalently, on the celestial sphere. This area can be expressed as "square degrees" or "square radians"; the latter unit is called the *steradian*.
The solid angle is expressed in terms of two a... | {
"Header 1": "**3.3** Solid angle on the celestial sphere",
"token_count": 1438,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
Palomar, SRC, and ESO sky surveys
The true comprehensive charts of the faint stars in the sky at optical wavelengths are actually deep (i.e., sensitive) photographs of the sky. The first and most famous of these is the Palomar Observatory Sky Survey (POSS-I) carried out in the early 1950s. It consists of 936 pairs of... | {
"Header 1": "**3.3** Solid angle on the celestial sphere",
"Header 3": "Photographs and charts",
"token_count": 1230,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
Astronomers traditionally went to telescopes with less precise, ∼1 , celestial positions for a couple of reasons. It was quite an onerous task to obtain a very precise 1 position of a previously unmeasured star. Also, many telescopes do not point to a position on the sky more accurately than about 1 . In these cases, a... | {
"Header 1": "*Finding charts*",
"token_count": 379,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
Charts, or maps, of the sky historically complement photographs of the sky. These are printed maps that are produced from the measured positions and brightnesses of the objects of interest with the brighter stellar objects shown as larger dark circles. In times past, it could be a large project to make such plots. Now ... | {
"Header 1": "*Finding charts*",
"Header 3": "*Printed charts*",
"token_count": 290,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
The brightest of objects or those that exhibit characteristics of particular interest are often cataloged in a book, journal, or in computer-readable form. There are numerous catalogs or lists of different kinds of stars (e.g., white dwarfs, emission-line stars, variable stars, etc.) and of interesting extragalactic ob... | {
"Header 1": "*Finding charts*",
"Header 3": "Catalogs of celestial objects",
"token_count": 1157,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
The catalogs must give a name or number to each entry. In many cases this number becomes the name of the object. If the object was evident and conspicuous to early civilizations it probably has a historical name given in classical times. Subsequent catalogs can result in new names for the old objects, e.g., M 31 = NGC ... | {
"Header 1": "*Names of astronomical objects*",
"token_count": 828,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
The earliest radio detections of the brightest discrete sources in a given constellation were named after the constellation with the suffix A, B, etc. in order of descending intensity. Thus Taurus A, and Sagittarius A, Cyg A are, respectively, the radio sources associated with the Crab nebula, the center of the Galaxy,... | {
"Header 1": "*Modern names (\"telephone numbers\")*",
"token_count": 645,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
*Problem 3.21.* (a) What are the approximate equatorial coordinates of the north celestial pole, of the sun on March 21, the star shown in Fig. 1, and the nominal galactic center at $\ell = b = 0$ ? In each case, specify the epoch of your answer. What are the J2000 coordinates of the Crab nebula? (b) Locate *Norton's ... | {
"Header 1": "*Modern names (\"telephone numbers\")*",
"Header 3": "3.2 Coordinates on a celestial sphere",
"token_count": 799,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
*Problem 3.31.* (a) Derive an expression for the solid angle of one polar cap on the celestial sphere, of angular radius $\theta$ . (On the earth, the polar cap could be encompassed by the arctic circle.) What is the *fraction* of the entire sky that is contained in this polar cap of radius $\theta$ ? What is this fr... | {
"Header 1": "*Modern names (\"telephone numbers\")*",
"Header 3": "3.3 Solid angle on the celestial sphere",
"token_count": 415,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
*Problem 3.41*. Compare the problems you would encounter in trying to keep track of the positions of all the trucks in the United States as time progresses with the problems facing astronomers in keeping track of all stars as time progresses.
*Problem 3.42.* Use *Norton's 2000.0 Star Atlas* as a finding chart for the... | {
"Header 1": "*Modern names (\"telephone numbers\")*",
"Header 3": "3.4 Surveys, charts and catalogs",
"token_count": 318,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
**Gravity** is the underlying reason for the **spin of the earth**, the motions of stars within galaxies, and the evolution of stars and the universe. The **apparent motions** of stars in the equatorial coordinate system arise from **precession** and **nutation** of the coordinate system, from **parallax** and **stella... | {
"Header 1": "Gravity, celestial motions, and time",
"Header 3": "**What we learn in this chapter**",
"token_count": 765,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
The motions of the celestial bodies may be understood in terms of two laws articulated by Newton. His *second law* states that a vector force $\mathbf{F}_1$ applied to a mass $m_1$ brings about a vector acceleration $\mathbf{a}$ of $m_1$ according to
$$F_1 = m_1 a$$
(Newton's second law) (4.1)
if the observ... | {
"Header 1": "Gravity, celestial motions, and time",
"Header 3": "4.2 Gravity - Newton to Einstein",
"token_count": 1154,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
An observer on the earth's surface at low latitudes notes that the sun rises in the east and sets in the west. During the night, the same observer would note that the stars and planets also rise in the east, move across the sky, and set in the west. These motions are simply an effect of the earth's daily rotation about... | {
"Header 1": "*Horizon coordinate system*",
"token_count": 1046,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
The earth's orbital motion yields an apparent motion of the sun relative to the celestial sphere (Fig. 3.1). At some date, e.g., March 21, an observer on the earth would find the sun to be in front of a given constellation, if the sun weren't so bright as to obscure our view of the constituent stars.
At some later da... | {
"Header 1": "*Sun and the ecliptic*",
"token_count": 366,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
More relevant to astronomers than the signs of the zodiac are the months when certain regions of the sky are accessible for study. Ground-based optical astronomers can not make observations when the sun is above the horizon because the sun is very bright at optical wavelengths, and the atmosphere scatters the light sev... | {
"Header 1": "*Sun and the ecliptic*",
"Header 3": "*Sun and dark-sky observations*",
"token_count": 527,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/Hale Bradt_2004.pdf"
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.