The Scientific Method, or How Big is the Sun?

! What is empiricism? What is objectivity?! What are the main principles of the scientific method?

What is Occam’s Razor?! Why do the principles of the scientific method make it

more objective than other world views?! What were Eratosthenes’ and Aristarchus’ experiments?! How are cause and correlation different?! Do you know the basics from LAB 1: angles, powers of

10, prefixes, units. Do you know temperatures in Kelvin? What is a light year? Does it measure time or distance?

! Note the [xtra] beside lectures 1-7 on the syllabus schedule. These may be helpful to learn hard concepts

Learning Objectives

Ancient Greeks! Introduced philosophical (non-supernatural)

explanations for natural phenomena ! Developed and applied a system of empirical

observation and deduction! Aristotle (c. 384 – 322 BCE)

!Knowledge comes from existence; facts are the only reality (empiricism)

!Perhaps the birth of the scientific method

Aristotle

Eratosthenes (276–194 BCE)! A librarian from

Alexandria! Learned that on

June 20 in Syene, the noon Sun would reach to the bottom of a well

! In Alexandria, an obelisk cast a shadow at local noon on the same day

Measuring the Size of the Earth

! Measured the circumference of the Earth to be 250,000 stadia (~25,000 miles)

! Modern value? 24,859.73 miles (polar)

Alexandria

Syene

~ 5,000 stadia

Aristarchus (310 – 230 BCE)

! First to argue for heliocentrism(Sun is at the center of ourSolar System)!Correct but ignored for about

1800 years

! Observed that when the Moon was half-full the angle between the Moon and the Sun was 3o

!Probably intended 3o as a lower limit (it’s a very hard measurement)

The Distance to the Sun

! Aristarchus suggested a > 87o from observations (we now better measure the value to be 89.85o)

! For a > 87o it follows that A/B > 19! Thus, the Sun is at least 19 times farther away than the

Moon (we now measure that it’s more like 400 times)

a (angle)AB

Aristarchus (310 – 230 BCE)! During a solar eclipse, the Sun

and the Moon look the same size. Aristarchus concluded that the Sun was 19 times bigger than the Moon

! During a lunar eclipse, the Earth’s shadow is 3 times the Moon’s size. Aristarchus deduced that the Sun’s diameter was thus ~6.7 times the Earth’s diameter

The Scientific Method

Modify Theorize Predict

Make a Test

Obs

erve

Hallmarks of Scientific Reasoning

! Experimental!Scientific theories are based on observations

(this is Aristotle’s empiricism)! Falsifiable

!Scientific theories make predictions that can be disproved by empirical observations by more than one person (this is objectivity)

! Simple!Search for the simplest theory that explains

the observations (this is called Occam’s razor)

!Do you agree with any of these statements?! I read my horoscope (astrology)! It’s strange how sometimes when I think

about somebody they text or call me! I was destined to be at the University of

Wyoming! psychics sometimes have a feeling that lets

them know things that other people don’t

Astronomy is not Astrology because

Cause is not Correlation

Cause is not Correlation

Astronomy as a Science! Astronomy is different than

most other sciences! Unlike physics, chemistry,

biology, and other sciences, astronomers often can’t create our own experiments

! Nature usually runs the experiments, we just get to observe the results…from very far away

! And many of the “experiments” take millions of years

“Astronomical” Numbers! In astronomy, numbers can get very

large! Distance to the Sun: 93,000,000 miles! Number of stars in our Galaxy:

200,000,000,000! Mass of the Sun:

2,000,000,000,000,000,000,000,000,000,000 kg! Numbers can be very small, too:

! Size of an atom: 0.000000000000001 m

Examples of Prefixes

Number Name Number Prefix Abbreviation

Billion 1,000,000,000 giga GMillion 1,000,000 mega MThousand 1,000 kilo kOne 1One-thousandth 0.001 milli mOne-millionth 0.000001 micro µ One-billionth 0.000000001 nano n

Number Name Number Scientific Notation

Billion 1,000,000,000 109 Million 1,000,000 106 Thousand 1,000 103 One 1 100 One-thousandth 0.001 10-3 One-millionth 0.000001 10-6 One-billionth 0.000000001 10-9

Examples of Scientific Notation

New Units for Astronomy! Often, even prefixes and notation feel

“cumbersome”! Average Distance from Earth to the Sun =

1.5x108 km (or 93 million miles)! So, astronomers define a new unit

! Average distance from Earth to the Sun = 1 Astronomical Unit (AU)

! Useful for measuring distances in the Solar System

Distances Outside the Solar System

! Light years (ly)!The distance

light travels in one year (9.5 trillion km)

!Light years measure distance not time!

! Nearest Star: Proxima Centauri (4.2 ly from Earth)

Leaves Jul, 2017

Arrives Oct, 2021

Returns Jan, 2026

4.24 ly

Other Units in Astronomy! Astronomers create units for other

measurements too! Usually, they use the Earth or the Sun as a

reference point!Masses of planets: Earth-masses (M⊕)

!Masses of stars: solar-masses (M⊙)

!Sizes of stars: solar-radii (R⊙)

!Brightnesses of stars: solar-luminosities (L⊙)

Measuring the Sky: Angles! Astronomers

measure the sky using angles

! To measure both the distances between objects in the skyand the sizes ofobjects in the sky

! A circle, 360o

! The Sun and the Moon are each roughly half a degree (0.5o) across in the sky

Arcseconds! An arcsecond is an angle, but

much smaller than a degree! 1 degree = 60 arcminutes! 1 arcminute = 60 arcseconds! So,

1 arcsecond = 1/3600th of a degree! Just how small is that?

! The size of a dime at 2.3 miles away

2.3 miles

Astronomical Temperatures! Astronomers measure

temperature in Kelvin (K)!Same degree of

temperature size as for Celsius (1°C = 1K)

!At 0K, -273.15°C, -459.67°F, stuff in the Universe (matter) reaches “absolute zero,” and can get no colder

Next Time

A Sky Full of Stars - I.