Astronomy 2e
Astronomy
The birth of
Astronomy
Chapter Summary
2.4 The Birth of Modern Astronomy
Nicolaus Copernicus introduced the heliocentric cosmology to Renaissance Europe in
his book De Revolutionibus. Although he retained the Aristotelian idea of uniform
circular motion, Copernicus suggested that Earth is a planet and that the planets all
circle about the Sun, dethroning Earth from its position at the center of the universe.
Galileo was the father of both modern experimental physics and telescopic astronomy.
He studied the acceleration of moving objects and, in 1610, began telescopic
observations, discovering the nature of the Milky Way, the large-scale features of the
Moon, the phases of Venus, and four moons of Jupiter, Although he was accused of
heresy for his support of heliocentric cosmology, Galileo is credited with observations
and brilliant writings that convinced most of his scientific contemporaries of the reality
of the Copernican theory.
2.2 Ancient Astronomy
Ancient Greeks such as Aristotle recognized that Earth and the Moon are spheres, and
understood the phases of the Moon, but because of their inability to detect stellar
parallax, they rejected the idea that Earth moves. Eratosthenes measured the size of
Earth with surprising precision. Hipparchus carried out many astronomical
observations, making a star catalog, defining the system of stellar magnitudes, and
discovering precession from the apparent shift in the position of the north celestial
pole. Ptolemy of Alexandria summarized classic astronomy in his Almagest; he
explained planetary motions, including retrograde motion, with remarkably good
accuracy using a model centered on Earth. This geocentric model, based on
combinations of uniform circular motion using epicycles, was accepted as authority for
more than a thousand years.
2.3 Astrology and Astronomy
The ancient religion of astrology, with its main contribution to civilization a heightened
interest in the heavens, began in Babylonia. It reached its peak in the Greco-Roman
world, especially as recorded in the Tetrabiblos of Ptolemy. Natal astrology is based on
the assumption that the positions of the planets at the time of our birth, as described
by a horoscope, determine our future. However, modern test clearly show that there is
no evidence for this, even in a broad statistical sense, and there in no verifiable theory
to explain what might cause such an astrological influence.
2.1 The Sky Above
The direct evidence of our senses supports a geocentric perspective, with the celestial
sphere pivoting on the celestial poles and rotating about a stationary Earth. We see
only half of this sphere at one time, limited b the horizon; the point directly overhead is
our zenith. The Sun's annual path on the celestial sphere is the ecliptic - a line that runs
through the center of the zodiac, which is the 18-degree-wide strip of the sky within
which we always find the Moon and planets. The celestial sphere is organized into 88
constellations, or sectors.
3.2 Newton's Great Synthesis
In his Principia, Isaac Newton established the three laws that govern the motion of
objects: (1) objects continue to be at rest or move with a constant velocity unless acted
upon by an outside force; (2) an outside force causes an acceleration (and changes the
momentum) for an object; and (3) for every action there is an equal and opposite
reaction. Momentum is a measure of the motion of an object and depends on both its
mass and its velocity. Angular momentum is a measure of the motion of a spinning or
revolving object and depends on its mass, velocity and distance from the point around
which it revolves. The density of an object is its mass divided by its volume.
F
gravity
=
G
M1 M2
R²
3.1 The Laws of Planetary Motion
Tycho Brahe's accurate observations of planetary positions provided the data used by
Johannes Kepler to derive his three fundamental laws of planetary motion. Kepler's
laws describe the behavior of planets in their orbits as follows: (1) planetary orbits are
ellipses with the Sun at one focus; (2) in equal intervals, a planet's orbit sweeps out
equal areas; and (3) the relationship between the orbital period (P) and the semimajor
axis (a) of an orbit is given by P² = a³ (when a is units of AU and P is in units of Earth
years).
3.6 Gravity with More Than Two Bodies
Calculating the gravitational interaction of more than two objects is complicated and
requires large computers. If one object (like the Sun in our solar system) dominates
gravitationally, it is possible to calculate the effects of a second object in terms of small
perturbations. This approach was used by John Couch Adams and Urbain Le Verrier to
predict the position of Neptune from its perturbations of the orbit of Uranus and thus
discover a new planet mathematically.
3.5 Motions of Satellites and Spacecraft
The orbit of an artificial satellite depends on the circumstances of its launch. The
circular satellite velocity needed to orbit Earth's surface is 8 kilometers per second, and
the escape speed from our planet is 11 kilometers per second. There are many possible
interplanetary trajectories, including those that use gravity-assisted flybys of one object
to redirect the spacecraft toward its next.
3.4 Orbits in the Solar System
The closes point in a satellite orbit around Earth is its perigee, and the farthest point is
its apogee (corresponding to perihelion and aphelion for an orbit around the Sun). The
planets follow orbits around the Sun that are nearly circular and in the same plane.
Most asteroids are found between Mars and Jupiter in the asteroid belt, whereas
comets generally follow orbits of high eccentricity.
3.3 Newton's Universal Law of Gravitation
Gravity, the attractive force between all masses, is what keeps the planets in orbit.
Newton's universal law of gravitation relates the gravitational force to mass and
distance:
The force of gravity is what gives us our sense of weight. Unlike mass, which is
constant, weight can vary depending on the force of gravity (or acceleration) you feel.
When Kepler's law are reexamined in the light of Newton's gravitational law, it become
clear that the masses of both objects are important for the third law, which becomes
a³ = (M1 + M2) x P². Mutual gravitational effects permit us to calculate the masses of
astronomical objects, from comets to galaxies.
Orbits
and Gravity
Earth, Moon
& Sky
4.1 Earth & Sky
The terrestrial system of latitude and longitude makes use of the great circles called
meridians. Longitude is arbitrarily set to 0° at the Royal Observatory at Greenwich,
England. An analogous celestial coordinate system is called right ascension (RA) and
declination, with 0° of declination starting at the vernal equinox. These coordinate
systems help us locate any object on the celestial sphere. The Foucault pendulum is a
way to demonstrate that Earth is turning.
4.2 The Seasons
The familiar cycle of the seasons results from the 23.5° tilt of Earth’s axis of rotation. At
the summer solstice, the Sun is higher in the sky and its rays strike Earth more directly.
The Sun is in the sky for more than half of the day and can heat Earth longer. At the
winter solstice, the Sun is low in the sky and its rays come in at more of an angle; in
addition, it is up for fewer than 12 hours, so those rays have less time to heat. At the
vernal and autumnal equinoxes, the Sun is on the celestial equator and we get about
12 hours of day and night. The seasons are different at different latitudes.
4.3 Keeping Time
The basic unit of astronomical time is the day—either the solar day (reckoned by the
Sun) or the sidereal day (reckoned by the stars). Apparent solar time is based on the
position of the Sun in the sky, and mean solar time is based on the average value of a
solar day during the year. By international agreement, we define 24 time zones around
the world, each with its own standard time. The convention of the International Date
Line is necessary to reconcile times on different parts of Earth.
4.4 The Calendar
The fundamental problem of the calendar is to reconcile the incommensurable lengths
of the day, month, and year. Most modern calendars, beginning with the Roman (Julian)
calendar of the first century BCE, neglect the problem of the month and concentrate on
achieving the correct number of days in a year by using such conventions as the leap
year. Today, most of the world has adopted the Gregorian calendar established in 1582
while finding ways to coexist with the older lunar calendars’ system of months.
4.5 Phases and Motions of the Moon
The Moon’s monthly cycle of phases results from the changing angle of its illumination
by the Sun. The full moon is visible in the sky only during the night; other phases are
visible during the day as well. Because its period of revolution is the same as its period
of rotation, the Moon always keeps the same face toward Earth.
4.6 Ocean Tides and the Moon
The twice-daily ocean tides are primarily the result of the Moon’s differential force on
the material of Earth’s crust and ocean. These tidal forces cause ocean water to flow
into two tidal bulges on opposite sides of Earth; each day, Earth rotates through these
bulges. Actual ocean tides are complicated by the additional effects of the Sun and by
the shape of the coasts and ocean basins.
4.7 Eclipses of the Sun and Moon
The Sun and Moon have nearly the same angular size (about 1/2°). A solar eclipse
occurs when the Moon moves between the Sun and Earth, casting its shadow on a part
of Earth’s surface. If the eclipse is total, the light from the bright disk of the Sun is
completely blocked, and the solar atmosphere (the corona) comes into view. Solar
eclipses take place rarely in any one location, but they are among the most spectacular
sights in nature. A lunar eclipse takes place when the Moon moves into Earth’s shadow;
it is visible (weather permitting) from the entire night hemisphere of Earth.
5.2 The Electromagnetic Spectrum
The electromagnetic spectrum consists of gamma rays, X-rays, ultraviolet radiation,
visible light, infrared, and radio radiation. Many of these wavelengths cannot penetrate
the layers of Earth’s atmosphere and must be observed from space, whereas
others—such as visible light, FM radio and TV—can penetrate to Earth’s surface. The
emission of electromagnetic radiation is intimately connected to the temperature of the
source. The higher the temperature of an idealized emitter of electromagnetic radiation,
the shorter is the wavelength at which the maximum amount of radiation is emitted.
The mathematical equation describing this relationship is known as Wien’s law:
λmax=(3×10⁶)/T. The total power emitted per square meter increases with increasing
temperature. The relationship between emitted energy flux and temperature is known
as the Stefan-Boltzmann law: F=σT⁴
5.1 The Behavior of Light
James Clerk Maxwell showed that whenever charged particles change their motion, as
they do in every atom and molecule, they give off waves of energy. Light is one form of
this electromagnetic radiation. The wavelength of light determines the color of visible
radiation. Wavelength (λ) is related to frequency (f) and the speed of light (c) by the
equation c = λf. Electromagnetic radiation sometimes behaves like waves, but at other
times, it behaves as if it were a particle—a little packet of energy, called a photon. The
apparent brightness of a source of electromagnetic energy decreases with increasing
distance from that source in proportion to the square of the distance—a relationship
known as the inverse square law.
5.6 The Doppler Effect
If an atom is moving toward us when an electron changes orbits and produces a
spectral line, we see that line shifted slightly toward the blue of its normal wavelength
in a spectrum. If the atom is moving away, we see the line shifted toward the red. This
shift is known as the Doppler effect and can be used to measure the radial velocities of
distant objects.
5.5 Formation of Spectral Lines
When electrons move from a higher energy level to a lower one, photons are emitted,
and an emission line can be seen in the spectrum. Absorption lines are seen when
electrons absorb photons and move to higher energy levels. Since each atom has its
own characteristic set of energy levels, each is associated with a unique pattern of
spectral lines. This allows astronomers to determine what elements are present in the
stars and in the clouds of gas and dust among the stars. An atom in its lowest energy
level is in the ground state. If an electron is in an orbit other than the least energetic
one possible, the atom is said to be excited. If an atom has lost one or more electrons, it
is called an ion and is said to be ionized. The spectra of different ions look different and
can tell astronomers about the temperatures of the sources they are observing.
5.4 The Structure of the Atom
Atoms consist of a nucleus containing one or more positively charged protons. All
atoms except hydrogen can also contain one or more neutrons in the nucleus.
Negatively charged electrons orbit the nucleus. The number of protons defines an
element (hydrogen has one proton, helium has two, and so on) of the atom. Nuclei with
the same number of protons but different numbers of neutrons are different isotopes of
the same element. In the Bohr model of the atom, electrons on permitted orbits (or
energy levels) don’t give off any electromagnetic radiation. But when electrons go from
lower levels to higher ones, they must absorb a photon of just the right energy, and
when they go from higher levels to lower ones, they give off a photon of just the right
energy. The energy of a photon is connected to the frequency of the electromagnetic
wave it represents by Planck’s formula, E = hf.
5.3 Spectroscopy in Astronomy
A spectrometer is a device that forms a spectrum, often utilizing the phenomenon of
dispersion. The light from an astronomical source can consist of a continuous spectrum,
an emission (bright line) spectrum, or an absorption (dark line) spectrum. Because each
element leaves its spectral signature in the pattern of lines we observe, spectral
analyses reveal the composition of the Sun and stars.
Radiation
& Spectra
https://www.heavens-above.com/skychart2.aspx
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ml
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spectrum/latest/blackbody-spectrum_en.html
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atom_en.html
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