Dark Matter

Dark Matter: Visualization

In 1932, Jan Oort predicted dark matter to account for differences between mass calculated from astronomical objects’ gravitational effects and mass calculated from “luminous” matter contained in these objects (gas, stars, dust). In 1933, Fritz Zwicky observed that galaxies are moving too fast. In the Coma cluster, the gas is moving very fast, held at high temperatures. There must be a lot of gravity unseen to account for the pressure.

From 1965-1985, Vera Rubin discovered: 1. Rotation Curves – stars at the center and the edges travel at the same speeds, the closer the stars, the faster stars should travel, but evidence refuted this; 2. Gravitational Lensing – light is bent from the source as it travels to the observer.

Dark matter is believed to be a new class of subatomic particles. It cannot be seen or detected directly. Since it does not emit or absorb light and other electromagnetic waves, dark matter can only be predicted from its effects on visible matter. Astronomers believe dark matter account for 84% of matter and 23% of mass-energy in the Universe. Like “halos within halos,” dark matter surrounds galaxies, explaining such phenomena observed.

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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

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)