The Celestial Sphere

The Sun and stars show regular patterns of motion that reflect the rotation of the Earth around its North- South axis and the revolution of the Earth around the Sun. The motions show how the Solar System works — that indeed, the heliocentric “sun-centered” is true.

FRAMES OF REFERENCE: An observer can see half the celestial sphere at any given time, or 6 of 12 constellations. On Earth at any given time, different observers see different parts of the sky, and different motions of starts in their sky. This proves that Earth is a sphere that rotates once per day.

Twelve Constellations of the Ecliptic

CONSTELLATIONS: Constellations are groups of stars forming a pattern or an outline, such as Scorpius (Scorpion), Ursa Major (The Bear), Cygnus (The Swan), and Orion (The Hunter). Constellations in the circumpolar zone are close to the North Celestial Pole and stay up all night and year round, while those in the equatorial zone are near the Celestial Equator and changes during the night and year. An asterism is a sub-group of a constellation, such as the Big Dipper in Ursa Major. The twelve constellations of the zodiac (of the ecliptic) appear during certain months of the year: Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, and Pisces.

The Celestial Sphere

THE NIGHT SKY: While stars “twinkle,” planets do not; planets only reflect light from stars. Stars appear to twinkle because light passes through Earth’s atmosphere and different pockets of air at different temperatures.

MAGNITUDE: In the original magnitude system, 1 is the brightest visible and 6 is the faintest visible. The difference of 5 magnitudes (6-1=5) is actually a factor of 100 in magnitudes. A magnitude 6 star is 100 times fainter than a magnitude 1 star. The modern system differs from the original one, with some stars brighter than magnitude 1 stars and others fainter than magnitude 6 stars. Human eyes respond to light logarithmically: m= -2.5log(b), where b = brightness of star by counting the number of photons per second.

ANGULAR MOVEMENTS & MEASURING WITHOUT A TELESCOPE: The width of your finger held at arm’s length equals 1 degree, while the width of your fist equals 10 degrees (e.g. full moon is about the width of half a finger, or 0.5 degrees).

1 revolution = 360°

2∏ radians = 360°

1° = 60 arcminutes = 60′

1′ = 60 arcseconds = 60”

1° = 60′ x 60°/1′

1° = 3,600”

Light and Black Body Radiation

Light is composed of mass-less infinitesimal particles called photons that travel at the speed of light (300,000,000 m/s).

Electromagnetic Spectrum

THE ELECTROMAGNETIC SPECTRUM: depicts the different wavelengths and energies of light

Radio Waves –> Microwaves –> Infrared Light –> Visible Light (ROYGBIV) –> Ultraviolet Radiation –> X-Rays –> Gamma Rays (longest –> shortest wavelengths, lowest –> highest energies)

  • The Electromagnetic Spectrum and Stellar Spectra = continuous spectrum (energy emission over a  broad range of wavelengths – curve)
  • Laser = line spectrum (energy emission at a narrow range of wavelength – peak)

Black-bodies at Different Temperatures

A “black-body” is an object which absorbs all light incident on it and doesn’t reflect or transmit any light. Black bodies are perfect emitters of light. Their classification depends only on temperature, and not other properties such as chemical composition; hence, black-body radiation is also “thermal” radiation. In 1900, Max Planck discovered that a black body emits an energy spectrum of light. Black body radiation includes lava flow (800 K), incandescent light bulbs – tungsten wire heated (2,800 K). Comparing two black bodies of different temperatures, the hotter black-body will: 1) emit more radiation (more luminous); 2) emit more photons; 3) peaks at shorter wavelengths; 4) have a bluer color. Measuring the shape of a star’s spectrum can reveal the star’s temperature.

Wien’s Lawγ peak = 2,900 μm K/ T; using the wavelength of the black-body’s spectrum’s peak to determining the star’s surface temperature

Luminosity: amount of energy radiated by an object per second, in Watts

Brightness: how bright an object appears as seen by an observer; also known as flux received from the star

Stefan- Boltzmann LawL = σT4 x surface area, where L = luminosity, T = temperature, and σ = 5.67 x 10-8 W/ (m²•K4), Stefan-Boltzmann constant; to determine a star’s luminosity

 Apparent Brightness: how bright stars appear to the observer; depends on luminosity and distance

  • considering a set of photons that emerge at the same moment from the star’s surface, the spherical shell of photons is 4∏r², where r = distance from the star
  • L/4∏r² (L = luminosity) = energy per second per surface area of photons
  • apparent brightness or flux: b = L/4∏r²

Absolute Brightness: considering temperature and mass and disregarding distance, how bright the stars actually are

PHOTONS AND THE ATOM

The Atom

The Atom and Its Subatomic Particles

  • Subatomic particles: Electrons (-), Protons (+), and Neutrons (neutral)
  • The mass of a proton is 1830 times the mass of an electron; the mass of a proton is approximately equal to the mass of a neutron
  • While protons and neutrons form the atom’s nucleus, electrons have discrete energy levels in atom
  • The electron can only be on energy levels, not in between
  • Outer orbits have higher energy than inner orbits
  • Most of the space within an atom is empty!

Absorption/ Emission: Photons

Photons: Emission and Absorption

  • Photons are emitted in random fashion (cascade from level to level or all at once – from current level to the ground state, or the lowest energy level, the closest to the nucleus)
  • Absorption of a photon causes the electron to a higher energy level
  • A photon can only be absorbed if its energy is equal to the difference in energy between two energy levels
  • An electron can only stay in a higher energy level for a very short time
  • Ionization: If a photon is large enough, it can kick the electron out of the atom
  • Recombination: When a free electron becomes bound to an atom
  • Electrons give up energy by emitting a photon

Emission Lines from Gas Clouds

Emission Line Spectrum

  • A dilute (non-opaque) gas cloud is not a back-body emitter
  • Atoms in a hot, dilute cloud of ionized gas will emit a characteristic pattern of spectra lines (Emission Line Spectrum)

Absorption Line Spectra

Absorption Spectrum

  • Normal stars have absorption lines
  • Black-body radiation originates from the star’s interior