ISP 205, Section 3, Spring 2003, Prof. Stein

INTRODUCTION

OUTLINE

Large Numbers

Introduction: A Tour of the Universe

Scientific Models or Theories

Summary

Large Numbers, Scientific Notation

Reading: Voyages, p 4 & Appendix 4

Scientists use scientific notation to help with the arithmetic of large and small numbers

The same number can take different forms

To multiply, multiply the numbers in front and add the exponents of the power of 10:

To divide, divide the numbers in front and subtract the exponents of the power of 10:

To add or subtract, you have to first make the exponents the same:

Introduction: Tour of the Universe

Reading: Voyages, Prologue, pp 1-13

What is the Universe?

• The universe is everything that exists

What is in the Universe?

• The Earth

  

  Nearly spherical planet of rock and iron

  Diameter: 1.3x10⁴ km

  Distance from Sun: 1.5x10⁸ km = 1 AU (Astronomical Unit)

  Model: MI (200 mi) = baseball (7 cm)

  CA = 2000 mi = 70 cm (3/4 m) away

  DC = 400 mi = 14 cm away

  Earth (Diameter_earth=12,800 km) = baseball (D=7 cm)

  Moon (2R_moon=3,400 km) (D_E-M = 384,000 km) = marble 2 m = 7 ft away

  Sun (2R_sun=1,400,000 = 1.4x10⁶ km) (D_ES = 150,000,000 = 1.5x10⁸ km)
        = 7.7 m ball, 0.8 km away (Harrison Rd)

• The Solar System

  Nine planets + asteroids + comets that orbit the Sun

  Mercury

  

  2/5 the size of the Earth
  0.4 AU from Sun

  Venus

  

  About same size as Earth
  3/4 distance of Earth from the Sun

  Mars

  

  Half the size of the Earth
  1.5 times farther from Sun than Earth

  Jupiter

  

  11 times the size of the Earth
  5 AU from Sun

  Saturn

  

  9 times the size of the Earth
  10 AU from Sun

  Uranus

  

  4 times the size of the Earth
  19 AU from Sun

  Neptune

  

  4 times the size of the Earth
  30 AU from Sun

  Pluto

  

  Model: Sun (2R_sun=1,400,000 = 1.4x10⁶ km) = baseball (2R=7 cm)

  Earth (R_Earth = 6,400 km = 1%R_sun) (D_E-S = AU (astronomical unit) = 215 R_sun)

  is penpoint 7 m away

  Neptune (30 AU) is 200 m away

  Pluto (40 AU) is 280 m away (on average)

  Model: Sun = basketball
  

  Earth = appleseed 30 m from basketball
  

  Jupiter = grape 150 m from basketball
  

  Pluto = sand grain about 1 km from basketball

• Sun
  The Sun in white light

  The Sun in hydrogen light

  www.nso.edu/sunspot/latest_solar_images.html

  The Sun is a fairly typical STAR, a ball of gas, held together by gravity that generates its own energy.
  The Sun is a 4x10²⁶ watt light bulb
  The Sun is 10² times larger than the Earth
  The Earth is 1.5x10⁸ km away from the Sun
  Light takes 8 min to travel from the surface of the Sun to Earth. Light moves at 3x10⁵ km/s.

• Stars

  Stars appear faint because they are very far away.
  The nearest star, Proxima Centauri, is 4.3 LY away. That is, it takes light 4.3 years to reach us from this star.
  A Light Year (LY) is almost 10¹³ km.
  Most stars are smaller than the Sun
  A few stars are much larger than the Sun

  Betelgeuse
  Some stars are in star clusters
  Globular Cluster M10 contains about 10⁵ stars

  Model: Sun (2R_sun=1,400,000 = 1.4x10⁶ km) = baseball (2R=7 cm)

  Nearest Star (alpha Cen, 41,000,000,000,000 = 4.1x10¹³ km = 4.3 LY)
        is 2000 km = 1200 mi away (DTW-DEN)

  (1 LY = distance light travels in year at speed of 3x10⁵ km/s = 9.5x10¹² km = 10¹³ km)

  Model: Sun is a grape

  The nearest star, Proxima Centauri, is 100 mi away

  Vega (alpha Lyr) (overhead in Sep) (2.5x10¹⁴ km = 26 LY)
        is 7000 mi away (DTW-Shanghai)

  Sirius (alpha CMa, brightest *) (8.3x10¹³ km = 8.8 LY)
        is 4000 km = 2500 mi away (DTW-SFO)

  Betelguese (alpha Ori) (6x10¹⁵ km = 600LY)
        is 300,000 km away (Moon)

• Galaxies

  Most stars are in vast groups of stars called galaxies.
  Our Sun and solar system are in a group of about 10¹² stars called the Milky Way Galaxy.

  The Milky Way
  The Milky Way is shaped like a frisbee with a bulge in the center.
  Its diameter is about 10⁵ LY.
  Its thickness is about 2x10³ LY.
  Galaxies similar to the Milky Way are called spiral galaxies

  seen edge on

  seen face on

  The closest large spiral galaxy to us (2x10⁶ Ly away) is in the constellation Andromeda and is called the Andromeda galaxy or M31. It is similar to the Milky Way.

  Andromeda Galaxy (M31)
  Stars, gas and "dust" are kept together in a galaxy by gravity.

  Model: Sun (2R_sun=1,400,000 = 1.4x10⁶ km) = baseball (2R=7 cm)

  Milky Way Galaxy (Diam_MW = 1,000,000,000,000,000,000 = 1x10¹⁸ km = 1x10⁵ LY)
        diameter is 5x10⁷ km (Venus at closest)

  Andromeda Galaxy (20,000,000,000,000,000,000 = 2x10¹⁹ km = 2x10⁶ LY)
        is 1x10⁹ km away (Uranus)

• Clusters of galaxies

  The Milky Way and Andromeda belong to a cluster of over 40 galaxies called the Local Group. In addition to these two large galaxies it contains many smaller galaxies. The nearest (5x10⁶ LY away) large cluster of galaxies (about 10⁴ stars) is in the constellation Virgo and is called the Vigro cluster.

  Virgo
  An even larger cluster of galaxies is the Coma cluster in the constellation Coma Bernecis. It is 2.5-3.0x10⁸ LY away and at least 10⁷ LY in diameter.
  Coma
  Most of the ordinary matter in clusters of galaxies is in the form of hot gas which we can see by the x-rays it emits. However, the material we can see (stars and hot gas) is not enough to produce sufficient gravity to hold the cluster together at the speeds the galaxies and gas are moving around. Since clusters of galaxies seem to be kept together, we believe there must be some additional matter, which we do not see, called "Dark Matter" that produces enough gravity to hold the cluster together.

• Large Scale Structure

  Clusters of galaxies are themselves organized into superclusters with voids in between, something like soap bubbles with the clusters of galaxies mostly on the surfaces of the bubbles.

  
  Virgo Cluster

  

  
  Superclusters & Voids

  
  On a large enough scale the universe is uniform

  Model: Milky Way Galaxy (2R_MW = 1,000,000,000,000,000,000 = 1x10¹⁸ km = 1x10⁵ LY)
    = baseball (7 cm) (hard to define, no sharp edge)

  Andromeda (local group) (20,000,000,000,000,000,000 = 2x10¹⁹ km = 2x10⁶ LY away)
        is 1.4 m away

  Virgo Cluster (6,000,000,000,000,000,000,000 = 6x10²⁰ km = 6x10⁷ LY) is 42 m away

  Visible Universe (1.5x10¹⁰ LY) is 10 km = 6 mi away (downtown Lansing)

• Cosmic Microwave Background Radiation

  The very young universe was dense, hot and opaque. When it cooled below 3000 K it became transparent. We now observe a relic from that early era -- the light that was emitted when the universe became transparent. It is called the "Cosmic Microwave Background (CMB) Radiation".

  
  It has nearly the same intensity from all directions, with a tiny variation due to the Earth's motion through the universe and even smaller fluctuations that were the seeds of the galaxies etc. we see today.

Links

Scientific Models or Theories

Reading: Voyages, p 3

Goal:

Simplest rule to explain most phenomena

Scientific Models (Theories, Laws):

Isolate relevant experience from distracting or trivial effects

Discern a stable relationship in the flux of events

Express the relationship mathematically.

1. Process of model building: (similar to everyday problem solving)

   1. Have Problem

   Observations to explain or conflict between observations and existing model

   Define what problem is. Ask the right questions.

   2. Generate a New Model/Theory

   Use divergent, flexible thinking; brainstorming.

   More than one possible solution, weigh pros and cons.

   Usually modify old model, occasionally something entirely different.

   based on fundamental ideas, previous theories, aesthetics

   Choose a model

   3. Test Model/Theory - Act on it

   Make Predictions

   Compare predictions of model with new observations.

   How well does model correspond to reality?

   Revise model/theory if necessary (-> step 1).

   

   [video: magic hut (start 3m54s)(20 min)]

2. Criteria for Fruitful, Successful Model
   • Relate many observations. Simple, easy to grasp. Few assumptions.
   • Makes predictions that agree with experience.
   • Solves significant problems.
   • Stimulates new investigations.

3. Limitations
   Models are based on limited experience. They are extrapolated to a range of similar situations and are applied in a broader context than that in which they were developed. Sooner or later, advances in experience reach a limit where assumptions are no longer valid. Theories are seen to be too limited or too inaccurate.
   Examples:
   • sunspots vs. Republicans in Senate (extrapolation)
   • sunspots vs. rainfall (limited observations)
   • height vs. age (biased observations)

4. Proof
   Can disprove a theory by failure to correctly predict phenomena. Cannot prove a theory correct. Scientists know that none of the theories and models we use are perfect:

   The criterion for a good model is its usefulness for the task for which it is used.

   Can increase our confidence in it by successes in predicting phenomena.

   Activity: surviving in the wilderness

Summary

• The building blocks of the universe are STARS.
• Some stars have planets.
• Stars are grouped in GALAXIES (like people in cities). There are about 10¹² stars in a large galaxy.
• Most galaxies are grouped in CLUSTERS OF GALAXIES with 10² - 10⁴ galaxies in a cluster.
• One relic of the early, hot universe is the COSMIC MICROWAVE BACKGROUND (CMB) radiation.
• Planetary systems, stars, galaxies and clusters of galaxies are held together by GRAVITY.
• Most matter is galaxies and clusters of galaxies is not visible, it is DARK MATTER.
• LIGHT travels at 3x10⁵ km/s. It takes time for light to reach us. We see distant objects as they were long ago.
• Science is a METHOD. The GOAL of science is to make a MODEL or THEORY of something we want to understand. Scientists then TEST the model or theory by comparing its predictions with observations or experiments.

This page has been accessed times.

Updated: 2003.01.06 (Monday) 20:41:31 EST
Visions of the Universe