Temperature of the Universe

What is the universe’s temperature? How has it changed and evolved? What causes the temperature to change? How is the temperature estimated? Is it continuously cooling or constant? –Pcelsus

Black Body Curve of the Cosmic Microwave Background

13.75 billion years ago, the Universe was much smaller and hotter. In the 1960s, Robert Dicke predicted a remnant “glow” from the Big Bang. In 1965 at the Bell Labs, radio astronomers Amo Penzias and Robert Wilson discovered that glow, named the cosmic microwave background radiation. The CBR was seen in all directions in empty space, with a black body curve (temperature ~3K in every direction). About 1 second after the Big Bang, the Universe was very hot, at ~1 billion K. At 3 minutes, protons and neutrons combine to form the nuclei of atoms. As space cooled, material condensed and atomic particles, then elements, molecules, stars, and galaxies formed. The hydrogen/ helium ratio (3:1) found today is about the same as what’s expected after the Big Bang. Atoms were “ionized” with electrons roaming free without being bound. At 300,000 years after the Big Bang, the Universe becomes transparent with a temperature of 3,000K. Light red-shifted by a factor of 1000, and the expansion of the Universe ensued.

Today, the Universe is 2.73K, or 2.73°C above absolute zero, but at the beginning of space and time, the Big Bang, the Universe reached over one billion degrees. From a single pinpoint, the Universe emerged as a scorching hot primordial soup of subatomic particles moving at high velocities. As the Universe expanded, the temperature cooled as more space was created and density decreased. The Universe is continuously cooling as it expands.

Measuring the temperature isn’t as simple as sticking a thermometer in space and waiting until it stabilizes at a certain temperature. Instead, scientists measure indirectly using the cosmic microwave background, or leftover radiation emitted by hot plasma 38,000 years after the Big Bang. As the Universe expanded, the electromagnetic waves of the CMR elongated and decreased in energy, leading to cooler temperatures. Using Planck’s law, scientists measured the black body radiation of the Universe. Planck’s law states that every object radiates electromagnetic energy according to temperature. Black body curves are lopsided, with the curve peaking at different wavelengths depending on the object. In fact, space has a nearly perfect black body curve, since physical objects tend to absorb and reflect light in certain wavelengths.

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Albert Einstein’s Legacy

ALBERT EINSTEIN (1879-1955)

Albert Einstein

Legacy

  • Reformulated the concept of time and space (E = mc² => special relativity)
    • Time is not an absolute quantity but appears to flow at a different rate depending on relative motion
  • Opened the road to quantum mechanics
    • Light “hits” like a particle
    • Light waves have “quantized” and “discrete” energies, depending on their wavelengths
  • Presented a revised theory of relativity
    • General relativity: space is curved
    • Foundation of modern cosmology

Einstein’s World

  • Reality of atoms and molecules in hot debate
  • Light poorly understood: “What was the medium light traveled in?”
  • Phenomena of radiation
  • Absorption lines in the Sun were observed, but could not be explained

Einstein helped clear these mysteries and began the era of modern physics.

Einstein’s Early Life and Career

Born in Ulm, German Empire in 1879, Albert Einstein excelled in physics and mathematics but failed in other subjects. Einstein dropped out of high school in 1895 and restarted school in Aarau, Switzerland, where he studied Maxwell’s works (~1870), which stated that electricity and magnetism obeyed the same set of physical laws — hence, electromagnetism. Einstein discovered that the velocity of light remained constant no matter the media. Although Einstein was brilliant, he irritated professors as he was too independent. In 1902, Einstein became a patent office clerk at the Swiss Patent Office in Bern. By 1905, Einstein had written six scientific papers, three of which explored the existence of molecules and the “kinetic theory.” For his other three papers, one published in March explained his light-quantum hypothesis (light hits like a particle), a fundamental step of quantum mechanics. For this, Einstein received a Nobel Prize in 1921. Another paper published in June was Einstein’s first paper on Special Relativity that explored light contraction and time dilation approaching the speed of light. In September of 1905, Einstein published his second paper on special relativity, in which he included the famous equation E = mc².

* General relativity includes gravity, while special relativity does not.

General Relativity and Special Relativity

Special Relativity

  1. The laws of physics are the same in all uniformly moving reference frames, or in all directions
  2. In any uniformly moving reference frame, the velocity of light (c) is the same whether emitted by a body at rest or a body in motion

Time Dilation and Length Contraction

Time Dilation: Time itself doesn’t tick at the same rate approaching the speed of light; instead, the time synchronization veers off; so approaching the speed of light, time appears to tick much slower.

Length Contraction: The lengths of moving objects are contracted when viewed by a stationary viewer

Mass and Energy

  • The mass of a moving body increases compared to its “rest mass” because it takes a bigger force to accelerate
  1. Acceleration: speed gained in a given time
  2. An object accelerating up is smaller because of time dilation; acceleration is harder the more massive the object is
  • Energy is responsible for powering stars, nuclear decay, and nuclear energy

Einstein’s Impact

  • At first, the scientific community met Einstein’s special relativity theory with silence, but Max Planck, who won the Nobel Prize for explaining black body radiation, realized the importance of Einstein’s work and publicized it; from 1906, scientists took notice and visited Einstein to talk about science
  • Einstein’s scientific circles grew stating 1908; became associate professor in 1911 and a professor of the Swiss Federal Institute of Technology in 1912
  • Einstein’s findings demanded a new way of thinking as Newton’s Law of Gravity was only valid from speeds much smaller than light
  • Einstein named the “birth of special relativity” “The Step”
  • 1907: The Equivalence Principle – gravity corresponds to acceleration
  • 1911: Bending of light in a gravitational field, a consequence of the Equivalence Principle, could be checked with astronomical observations
  • 1912-1915: Extend relativity to objects moving in an arbitrary way with respect to one another
  • 1915: General Relativity “Gravity curves space”: there’s no need for the “force” of gravity; all motion is along “straight lines” in curved space-time and matter tells space how to move
    • Evidence: starlight bends around the Sun; Mercury’s orbit will precede at a different rate than Newton predicted
  • 1919: Arthur Eddington leaders solar eclipse expedition and confirms special relativity
  • 1929: Edwin Hubble observes expansion of the Universe
    • Friedmann said that Einstein’s equations supported an expanding Universe, but Einstein proposed the “cosmological constant” to keep the Universe static

Light and Telescopes

LIGHT: THE BASICS

Longer Wavelengths vs. Shorter Wavelengths

Wavelength: the distance from the crest of one wave to the crest of the successive wave

Frequency: longer wavelengths corresponds to lower frequency and lower energy, shorter wavelengths correspond to high frequency and higher energy

Radiation: transmission of energy through space

Transmission: light rays or electromagnetic waves bending through a different medium

  • All waves have a source (e.g. electromagnetic waves originate from vibrating charged particles)
  • All waves, except electromagnetic waves, transmit through a medium

Wavelengths in Visible Light

Electromagnetic Spectrum: electromagnetic waves ranging from low frequency,  low energy, and long wavelength to high frequency, high energy, and short wavelength that originate from vibrating charges from the Sun; all electromagnetic waves travel at the same speed, or the speed of light (c = 300,000 km/sec or 186,000 miles/sec)

PROPERTIES OF LIGHT

Reflection: light rays or electromagnetic waves bouncing off reflective surfaces (e.g. mirror)

Refraction: light rays or electromagnetic waves bending through a different medium (e.g. air to water)

PROBLEMS WITH LIGHT AND MIRRORS

Spherical Aberration

Spherical Aberration: when light rays incident on the edges of the spherical mirror are focused at a different point from light rays incident closer to the center of the mirror –> blurry images; corrected by using parabolic mirrors

Chromatic Aberration

Chromatic Aberration: as light rays travel through a lens, different wavelength rays are bent by different amounts, resulting in different focal points

OPTICAL TELESCOPES

Three Types: 1. Reflective (mirrors), 2. Refractive (lens); 3. Combined or Catadioptic (both mirrors and lens): combines advantages of refractive and reflective telescopes, while avoiding disadvantages

  • Objective: main lens or mirror
  • Eyepiece: lens that magnifies images
  • Focal Length: distance between the center of the lens and the its focus
  • Aperture: diameter of objective

Functions of Telescopes: to collect light, to resolve details, to magnify, to measure, to record

Problems of Optical Telescopes: “seeing” (Earth’s atmosphere refracts light), air transparency, light pollution

Hubble Space Telescope

Unusual Telescopes

  • Radio: Arecibo, VLA, COBE
  • Microwave, or RadarPIONEER, COBE
  • InfraredSIRTF, IRAS, SPITZER
  • UltravioletCOPERNICUS, IUE
  • X-rayHEAO, EXOSAT, CHANDRA
  • Gamma RayGRO, EINSTEIN, COMPTON
  • OrbitalHUBBLE
  • Multiple MirrorsKECK
  • Interferometry: VLA, VLT

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

Modern Astronomy: 1500-1800

Modern Astronomy (1500 – 1800 A.D.)

Nicolaus Copernicus

Nicolaus Copernicus (1473-1543)

The Polish astronomer Nicolaus Copernicus advocated the heliocentric view, calculated distances to planets and period of planets, and explained the retrograde motion. Before his death in 1543, Copernicus revolutionized astronomy by publishing his work,  De revolutionibus orbium coelestium (On the Revolutions of the Celestial Spheres).

Heliocentric Theory

Tycho Brahe

Tycho Brahe (1546-1601)

The Danish astronomer Tycho Brahe made accurate measurements of planetary positions by using a “quadrant.”

Astronomers Using a Quadrant

Johannes Kepler

Johannes Kepler (1571-1630)

As Tycho Brahe’s student, Johannes Kepler received his teacher’s measurements when Brahe died in 1601. In 1610, Kepler then derived the three laws of planetary motion using Brahe’s measurements and empirical rules. Instead of the circular orbits that Copernicus advocated, Kepler discovered that the planets and stars traveled in elliptical orbits.

Kepler’s 1st Law

Kepler’s 1st Law (1609) The planets move around the Sun in ellipses, having the Sun at one of its foci.

Ellipse: 1) each orbit has a shape and a size; 2) the eccentricity (e = 1- B/A) describes how elongated the ellipse is; 3) the size is described by the semi-major axis (2A); 4) when B=A, the orbit is circular and e=0 (eccentricity ranges from 0 to 1, with 1 as the most eccentric)

Kepler’s 2nd Law

Kepler’s 2nd Law (1609)/ Law of Equal Areas: Each planet revolves in such a way that the line joining it to the Sun sweeps over equal areas in equal time intervals

Kepler’s 3rd Law (1618)/ Harmonic Law: The square of the period of revolution is proportional to the cube of the average distance of the planet to the Sun (P²=A³, where P = the period in years and A = the semi-major axis of an orbit in AU)

Consequence: Distant planets take longer to orbit the Sun and travel at slower speeds

Galileo Galilei

Galileo Galilei  (1564-1642)

Italian astronomer Galileo Galilei, the “father of modern science,” was the first to use the telescope to observe the Moon, Jupiter and its moons (Io, Europa, Ganymede, and Callisto), Saturn, and phases of Venus. His observations supported the heliocentric view. After making the telescope in 1609, Galileo observed mountains on the Moon and discovered the Galilean moons of Jupiter. While Ptolemy thought Venus will always appear as a “crescent” and never as a full circle, Galileo discovered that Venus appears in phases. However, Galileo, deemed a heretic by the Roman Catholic Church Inquisition in 1615, was placed under house arrest for the rest of his life.

Isaac Newton

Isaac Newton (1642-1727)

LIFE & ACHIEVEMENTS: English physicist Isaac Newton, often known as the greatest and most influential scientist who ever lived, revolutionized astronomy and physics with his three laws of motion and law of universal gravitation. Born in 1642 (Galileo’s death) and into a world of mysticism, Newton was the last philosopher/ scientist. Newton derived Kepler’s three laws of planetary motion, invented calculus, and answered fundamental questions about the nature of light, motion, and time. Still, with all his achievements, Newton invented a new kind of telescope, studied theology, alchemy, and chemistry.

THE WORLD AROUND NEWTON: At the time, “gravity” meant solemn and was a mood, not a force. People believed that the world was not “solvable.” Light and heavy things separated themselves “naturally.” Time was hard to separate and the concept of motion was not well-defined. Philosophers/ scientists constrained motion to: pushing, pulling, carrying, twirling, combining, separating, waxing, and waning. Aristotle had defined things “in motion” as: an apple ripening, a dog running, a child growing up, and a spinning top.

EARLY LIFE: At Cambridge University, Aristotle was the sole authority on logic, ethics, rhetoric, cosmology, and mechanics. Because his tutor was a linguist, Newton mostly studied on his own. Born poor, Newton conserved paper costs by writing in a tiny font.

ROAD TO DISCOVERY: While Galileo had discovered uniform acceleration (all bodies fall at the same rate), Newton asked: How and why does something’s velocity change? In 1664, the plague in England caused Cambridge to close down, but Newton continued to discover fundamental ideas in astronomy and physics. By first reading works such as Euclid’s “Elements” and that of Descartes, Newton explored the concept of infinity, curvature, and the rate of the bending of lines, trajectories. “To resolve problems of motions,” Newton then invented calculus. To explore the nature of light, Newton used a prism to “isolate” blue light and passed the blue light through a second prism; the light stayed blue. Newton discovered that prisms only separate color and white light was “made up of” different colors. Furthermore, light comes from the Sun in eight minutes, the Moon tugs at the Earth to create waves, and the same Universal Laws exist throughout the Universe.

IMPACT: Newton defined these concepts: “mass,” “action,” “reaction,” “momentum,” “inertia,” “to feel the force of gravity.” He quantified the world with calculus and made people Newtonians (think that the world is solvable). Starting from the Newtonian Age, scientists linked mathematics and science to prove facts and claims.

Law of Universal Gravitation: Every particle in the Universe attracts every other particle with a force proportional to the product of their mass and inversely proportional to the square of the distance between them.

Gravity = the force between two objects that depends on the objects’ masses and on the distance between them

  • Gravity is a mutual force acting on both bodies
  • The force on each body is t he same size, but in opposite directions

Newton’s 1st Law/ Law of Inertia: Every material object continues in its state of rest, or of motion in a straight line, unless it is compelled to change that state by external forces. In other words, a stationary object will stay at rest, while a moving object will stay in constant motion unless an unbalanced force acts on it. “Constant” motion = at a constant speed and a constant direction.

Inertia = the resistance of any physical object to its state of motion or at rest

Balanced Forces = Forces cancel one another and no change in motion results (e.g. sitting in a chair)

Unbalanced Forces = One force is greater than another, causing a change in motion (e.g. jumping off a diving board)

Speed and Velocity = Velocity combines the speed of an object and the direction of motion and is equal to the change in distance over change in time (V = d/t) (e.g. speed = driving 60 miles/ hr; velocity = driving 60 miles/hr east)

Newton’s 2nd Law: The acceleration of an object is directly proportional to the net force acting on it

Acceleration = a change in velocity; objects of different masses on earth fall at the same rate

Newton’s 3rd Law

Newton’s 3rd Law: For every action there is an equal and opposite reaction.

Forces and Orbits: For objects in uniform circular motion, the force of gravity is perpendicular to the motion, the object orbits at constant speed, gravity changes the direction only of the motion, and there is still an acceleration.

Elliptical Orbits: For planets in elongated orbits, gravity changes both the direction and the speed of the planet, the planet slows down as it moves away from the Sun, and the planet speeds up as it approaches the Sun

Gravity Depends on MassF gravity = G x (m1m2)/r², where m1 and m2 are the masses of the two objects, r is the distance between the two masses, G is Newton’s gravitational constant (6.7 x 10-¹¹ m³kg s²)

Newton’s Derivation of Kepler’s Laws Using His Law of Gravitya1 = F gravity/ m1 = G x m2/r²; accelerations are smaller for objects far from the Sun (when r is large)

Newton’s Derivation of Kepler’s 3rd LawP² = [( 4∏ )/ G (m1 + M2)] (R³)