A Grand Tour of the Heavens Measurements Scientific Notation How big is…? Scientific Method
Measuring Things • For us to communicate “how much” something is, we must use units. • What if I were to offer a job to you that pays an annual salary of 60,000 per year? Would you accept the job? • Three fundamental units used in the SI system (SI is the most common system of units used in science) • unit of mass, kilogram (kg) • unit of distance, meter (m) • unit of time, second (s)
Scientific Notation • There is an easier way to express numbers so that we don’t have to count all those digits and commas. 9850 kg = 9.85 x 103 kg = 9.85 x 106 g 299,792, 458 m/s = 2.99792458 x 108 m/s 384,403 km = 3.84403 x 106 km = 3.84403 x 109 m • The mass of the earth is 5.97 x 1024 kg. Do you really want to write that number without using scientific notation?
Mass • a measure of inertia (how much net force is needed to accelerate an object) • independent of location in the universe • a measure of how much “stuff” an object is made of and what kind of “stuff” it’s made of; it depends on the atomic composition of which an object is made
Powers of Ten The following 9 minute video was made in 1968. Yes, that may seem old, but it gives us a great perspective on the limits of our Universe.
Mass and Weight • mass is NOT the same thing as weight! • near a large body such as a planet or moon or star, w = mg where g is the local acceleration due to gravity. • g depends on the mass of the large body
Distance • “how far” one point is from another point. • need to define the two points • distance of the center of the moon from the center of the earth • distance of the center of the moon from the center of the sun • need a standard • a meter, as defined by the length of a meterstick, is too arbitrary • a meter should be based on another unchanging and unarbitrary value.
What about Light? • Albert Einstein made a presupposition that the speed of light is the same in all reference frames (i.e. no matter how fast you are traveling and no matter what direction you’re traveling in, you will measure the same value for the speed of light). • Einstein also proposed that nothing travels faster than the speed of light in a vacuum. • The speed of light is a universal speed limit! • The speed of light is a universal constant!
c • c = 299,792,458 m/s and is DEFINED to be this value. • Therefore, in one second, light travels 299,792,458 meters. • 1 m = the distance light travels in 1/299,792,458 second
Light Year (ly) • 1 light year is the distance light travels in one year. • 1 ly = 9.46 x 1015 m • It takes about 8.3 minutes for light from the Sun to reach Earth. distance to the Sun / speed of light = 500 seconds = 8.3 minutes
The Second • Throughout history, time has been measured in various ways. • Astronomy has long been important in defining time. • A month was originally measured by lunar phases, the day is measured by the earth’s rotation about its axis, and the year is measured by the earth’s motion about the sun. • A day is broken into hours, hours into minutes, and minutes into seconds. • But what are some problems with using this method to define a second?
The Second • The time duration for Earth to rotate once about its axis (a day) is not necessarily constant. Earth’s rate of rotation is slowing down. • A day cannot be measured as precisely as we would like. • We now define a second in terms of the frequency of the light emitted by excited electrons in cesium atoms. The electrons emit light at a frequency of 9,192,631,770 Hz. Thus, one second is the time required for this light to make 9,192,631,770 oscillations. The official clock of the United States is the cesium fountain clock, NIST-F1, at NIST. • The uncertainty of NIST-F1 is so low that it will neither gain nor lose a second in 20 million years! • http://leapsecond.com/great2005/tour/
The Nature of Science • Science is the systematic enterprise of gathering knowledge about the world and organizing and condensing that knowledge into testable theories. • You will notice four important things in this definition • observing (i.e. experimenting) • developing a model for understanding and predicting • testing the model • doing this in a systematic way
Five Eras of Astronomy • Ancient (Dawn of History to fall of Roman Empire ~ 5th Century) • Medieval (5th to 15th Century) • Renaissance (Copernican Revolution to middle of 17th Century) • Modern (Newton’s Gravitation to end of 19th Century) • 20th Century and Beyond (Einstein’s relativity until now)
Ancient Astronomy • Primitive Astronomy • Sun, Moon, and changing seasons observed and studied. • Belief that the Earth was flat. • Solid Earth with a watery underworld.
Ancient Astronomy • Babylonians and Chaldeans • First to study skies and associate legends and myths. • The quest for divine knowledge developed astrology.
Ancient Astronomy • The Chinese • First to take records of observations • Understanding was lacking
Ancient Astronomy Stonehenge (2000 B.C.)
Ancient Astronomy • Eratosthenes of Cyrene (now Shahhat, Libya) measures the circumference of the Earth with extraordinary accuracy by determining astronomically the difference in latitude between the cities of Syene (now Aswan) and Alexandria, Egypt.
Ancient Astronomy • Greeks • Thought Earth was flat with a rotating crystalline sphere above. • Anaximander was first philosopher to suggest a round Earth to explain effects of the horizon. • Plato and Aristotle furthered the idea of a spherical Earth using lunar eclipse observations.
Ancient Astronomy • Ariatarchus proposed that the Earth was not the center of the Universe, but was not accepted because it made the Earth inferior. • Hipparchus catalogued over 100 stars noting position and motion. • Ptolemy was an Earth-centered (geocentric) man. • Epicycles described variation in motions. Explains retrograde. • System became part of the church doctrine.
Medieval Astronomy • Status Quo • Observations, data collections, better estimations of size.
Renaissance • 1473, Copernicus was born. • Tried to prove Ptolemy’s system that seemed to have a few inaccuracies. • Determined that it was truly a heliocentric solar system. • Knew ideas would not be accepted by church so waited until the year he died (1543) to publish.
Renaissance • Tycho Brahe • Danish astronomer, born in 1546 • Enormous amounts of data and observations made. • Lost nose in a duel with a fellow student. • Believed in geocentric theory. • After he died, his assistant looked through all his work, Johannes Kepler.
Renaissance • Kepler • All data fit the heliocentric theory • Three laws of planetary motion revolutionizing astronomy
Second law: a line that connects a planet to the sun sweeps out equal areas in equal times.
Third law: the square of the period of any planet is proportional to the cube of the semi-major axis of its orbit.
Renaissance • Galileo Galilei, born 1564 • Conflict with church • Used telescopes to look at Moon, Venus, Sun, and Jupiter • Forced to recant his view by the church.
Modern Astronomy • Sir Isaac Newton • Laws of Gravitation, Physics, Mathematic • Principia Mathematica