Where We AreWhere We Are

OrOr

Location, Location, LocationLocation, Location, Location

Part 1: It’s a Big Universe Out Part 1: It’s a Big Universe Out ThereThere

We are at the center of the Universe, We are at the center of the Universe, and there is no center of the and there is no center of the Universe. Universe.

By the end of the course you will By the end of the course you will understand why.understand why.

Time and SpaceTime and Space

Critical to your understanding is the Critical to your understanding is the fact that, the farther away in fact that, the farther away in distance we look, the further back in distance we look, the further back in time we are seeing.time we are seeing.

It’s like having the worst seats at a It’s like having the worst seats at a concert: every note emanating from concert: every note emanating from the stage reaches you seconds after the stage reaches you seconds after it was played.it was played.

However,However,

Before we can talk intelligently about Before we can talk intelligently about time and space and where we are, time and space and where we are, we must have some numerical tools we must have some numerical tools with which to work.with which to work.

Big NumbersBig Numbers

Before we can talk about time and Before we can talk about time and space in quantified terms, we have space in quantified terms, we have to get past big numbers.to get past big numbers.

Scientific Notation is both a method Scientific Notation is both a method of denoting numbers and a way of of denoting numbers and a way of looking at things.looking at things.

To understand Scientific Notation, To understand Scientific Notation, you merely have to be able to count you merely have to be able to count by tens.by tens.

CharacteristicCharacteristic

If someone gave you ten $10 bills If someone gave you ten $10 bills you would have 10X10 dollars or you would have 10X10 dollars or $100.$100.

A convenient way of writing 10X10 is A convenient way of writing 10X10 is 101022. We say ten to the second power.. We say ten to the second power.

If someone gave you ten $100 bills If someone gave you ten $100 bills you would have 10 X 10X10 or 10you would have 10 X 10X10 or 1033 dollars. dollars.

The little raised number above the The little raised number above the 10 is called an 10 is called an exponentexponent. It means . It means how many times you multiply a how many times you multiply a number (10) by itself.number (10) by itself.

You may remember You may remember 22 is squared and is squared and 33 is cubed, but we will have many is cubed, but we will have many more exponents than more exponents than 22 or or 33..

10101515 is much more convenient than is much more convenient than 1,000,000,000,000,000!1,000,000,000,000,000!

If someone gave you ten $20 bills If someone gave you ten $20 bills you’d have 2 X 10X10 dollars, or you’d have 2 X 10X10 dollars, or 2X102X1022..

You’d say “two times ten to the You’d say “two times ten to the second.” You could say “two second.” You could say “two hundred”, but words will fail you if hundred”, but words will fail you if you try to say 4X10you try to say 4X102626..• Realize that some calculators display Realize that some calculators display

4E26; it means the same as 4X104E26; it means the same as 4X102626..

Surprise!Surprise!

You’ve just learned to express You’ve just learned to express numbers in Scientific Notation!numbers in Scientific Notation!• When we talk about quantities in When we talk about quantities in orders orders

of magnitudeof magnitude we are talking about we are talking about powers of ten.powers of ten.

You can use scientific notation to You can use scientific notation to express small numbers too.express small numbers too.

1 penny ($0.01) is 101 penny ($0.01) is 10-2-2 dollars dollars• Can you see why???Can you see why???

LogarithmsLogarithms

Log, for short. Log, for short. Sometimes used to squeeze a wide Sometimes used to squeeze a wide

range of numbers onto a graphrange of numbers onto a graph Log 10 = 1, Log 100 = 2, Log 1000 = Log 10 = 1, Log 100 = 2, Log 1000 =

3 (get the pattern?)3 (get the pattern?)• Log 50? Between 1 and 2 (~1.7)Log 50? Between 1 and 2 (~1.7)• Log 900? Between 2 and 3, but closer to Log 900? Between 2 and 3, but closer to

3 (~2.95)3 (~2.95)

Samples:Samples:

US population: 3X10US population: 3X1088

World population: 6X10World population: 6X1099

2012-2013 US federal budget: 2012-2013 US federal budget: $4X10$4X101212

Global Domestic Product (2011): Global Domestic Product (2011): $8X10$8X101313

• Remember, the 3, 6, 4, and 8 are less Remember, the 3, 6, 4, and 8 are less important than the 8, 9, 12, and 13important than the 8, 9, 12, and 13

ScientificScientific Samples: Samples:

Weight of the Earth: 6X10Weight of the Earth: 6X102424 kg kg Distance to the Moon: 4X10Distance to the Moon: 4X1088 m m Time the Universe has been around: Time the Universe has been around:

4X104X101717 seconds seconds Power output of the Sun: 4X10Power output of the Sun: 4X102626 W W Weight of one atom of hydrogen: Weight of one atom of hydrogen:

2X102X10-27-27 kg kg Do NOT memorize these numbers!Do NOT memorize these numbers!

OK…OK…

Let’s get a feel for number words:Let’s get a feel for number words:• 101099 (a billion) seconds ago was 1976 (a billion) seconds ago was 1976• 101099 minutes ago was 100 AD minutes ago was 100 AD• 101099 hours ago was 112,000 BC hours ago was 112,000 BC• 101099 days ago was 3 million BC days ago was 3 million BC• 101099 years ago, the Earth had already years ago, the Earth had already

been around for 3 ½ billion years, and been around for 3 ½ billion years, and the Universe had existed for almost 13 the Universe had existed for almost 13 billion years.billion years.

1X101X1099 dollars ago was less than 3 dollars ago was less than 3 hours ago in Congress.hours ago in Congress.• $127,000 every second!$127,000 every second!• http://www.famousbirthdays.com/• Billion.xls

Cosmic CalendarCosmic Calendar

Geologists have a term for very long spans Geologists have a term for very long spans of time: they call it of time: they call it Deep TimeDeep Time..

Whenever you read about an outrageous Whenever you read about an outrageous process or event in this course and wonder process or event in this course and wonder how can this be, remember: the how can this be, remember: the cosmological time scale is far, far longer* cosmological time scale is far, far longer* than human references. It is truly than human references. It is truly Deep Deep TimeTime..

*With one or two very important *With one or two very important exceptions! exceptions!

Before We Quantify Space:Before We Quantify Space:

((againagain) Critical to ) Critical to your understanding your understanding is the fact that, the is the fact that, the farther away in farther away in distance we look, distance we look, the further back in the further back in time we are time we are seeing.seeing.

Think fireworks: Think fireworks: the boom follows the boom follows the flash in timethe flash in time

Centimeters and ParsecsCentimeters and Parsecs

When measuring anything, it is convenient When measuring anything, it is convenient to use units that correspond to the to use units that correspond to the measured value without always resorting measured value without always resorting to huge or tiny numbers.to huge or tiny numbers.

Centimeters are fine when measuring your Centimeters are fine when measuring your height, but lame when describing the height, but lame when describing the distance to Las Vegasdistance to Las Vegas• BTW, that would be 44,256,960 cm!BTW, that would be 44,256,960 cm!

Mostly HumongousMostly Humongous

With the exception of the atomic With the exception of the atomic particles we will be discussing, particles we will be discussing, everything about space is notoriously everything about space is notoriously

BIGBIG.. Therefore, kilometers will do only for Therefore, kilometers will do only for

nearby objects like the Moon: we nearby objects like the Moon: we need bigger distant units.need bigger distant units.

Hey You!Hey You!

When measuring distances in the Solar When measuring distances in the Solar System, the AU, or Astronomical Unit, is System, the AU, or Astronomical Unit, is the preferred measuring stick.the preferred measuring stick.

1AU = 1.5X101AU = 1.5X101111 meters, the distance from meters, the distance from the Earth to the Sun.the Earth to the Sun.

The distance to Pluto, the once and future The distance to Pluto, the once and future planet, is about 40 AU.planet, is about 40 AU.• The next slide neatly wraps up AU, Scientific The next slide neatly wraps up AU, Scientific

Notation, and LogsNotation, and Logs

Flash! IBEX space telescope fails to find bow shock!

Still too smallStill too small

But this is the Stars and Galaxies But this is the Stars and Galaxies course!course!

1AU will quickly become too small to 1AU will quickly become too small to use, worse than centimeters to Las use, worse than centimeters to Las Vegas.Vegas.

cc

It’s time you are acquainted with the It’s time you are acquainted with the cosmic speed limit, “c”.cosmic speed limit, “c”.

““c” is the speed of light in a vacuum, c” is the speed of light in a vacuum, like space, the famous c in E = mclike space, the famous c in E = mc22..

Light travels at 300,000 km/second, Light travels at 300,000 km/second, which is about 670 million mph.which is about 670 million mph.

Nothing goes faster than “c” in a Nothing goes faster than “c” in a vacuum.vacuum.

Distance = speed X timeDistance = speed X time

If we use “c” for speed and 1 year for If we use “c” for speed and 1 year for time, we get the Light Year (LY).time, we get the Light Year (LY).

1 LY is about 101 LY is about 101616 meters, or 6 trillion meters, or 6 trillion miles.miles.

The second nearest star is 4.3 LY The second nearest star is 4.3 LY away.away.• (What star is nearer?)(What star is nearer?)

A Time Machine*A Time Machine*

When you look at a star 4.3 LY away, you When you look at a star 4.3 LY away, you are looking at it as it was 4.3 years ago.are looking at it as it was 4.3 years ago.

When you look at the Moon, you are When you look at the Moon, you are seeing it as it was 1.5 seconds ago.seeing it as it was 1.5 seconds ago.• Its distance could be called 1.5 Its distance could be called 1.5 light-secondslight-seconds

When you look at the most distant reaches When you look at the most distant reaches of the Universe, you are seeing it as it was of the Universe, you are seeing it as it was ~10~101010 years ago! years ago!

*again!

Another Way to MeasureAnother Way to Measure

If you brought it to class, take out a If you brought it to class, take out a thumb and hold it out in front at thumb and hold it out in front at arm’s length.arm’s length.

Blink one eye and then the other. Blink one eye and then the other. See how your thumb appears to See how your thumb appears to move while something further away move while something further away seems stationary?seems stationary?

Parallax*Parallax*

This is called This is called parallaxparallax, and it offers , and it offers another way to measure distance.another way to measure distance.

Without going into the math, if you Without going into the math, if you know how long your arm is and you know how long your arm is and you can measure the distance between can measure the distance between your eyes, you can tell far distances your eyes, you can tell far distances by how much your thumb moves.by how much your thumb moves.

*A CAPER exercise

CirclesCircles

You probably know that there are You probably know that there are 360360oo in a circle. in a circle.

Astronomers break degrees down Astronomers break degrees down into into minutesminutes and and secondsseconds of of arcarc, , merely by dividing 1merely by dividing 1oo by 60 (for by 60 (for minutes of arc) and then 60 again minutes of arc) and then 60 again (for seconds of arc).(for seconds of arc).• This gives convenient small angles.This gives convenient small angles.

2+22+2

By putting together the idea of By putting together the idea of parallax, AU, and parallax, AU, and arc seconds, arc seconds, Astronomers have come up with an Astronomers have come up with an alternative to the LY.alternative to the LY.

1 1 ParsecParsec is the distance where the is the distance where the parallax angle subtends 1” (second) parallax angle subtends 1” (second) of arc.of arc.

It’s about 3.26 LYIt’s about 3.26 LY

Finally, PrefixesFinally, Prefixes Rather than say a billion years or a million Rather than say a billion years or a million

parsecs, we use the prefixes mega- and parsecs, we use the prefixes mega- and giga-.giga-.

A billion years will be a Gigayear, or Gyr.A billion years will be a Gigayear, or Gyr. A million parsecs will be a Megaparsec, or A million parsecs will be a Megaparsec, or

Mpc.Mpc.• The Solar System is 5 Gyr old.The Solar System is 5 Gyr old.• The distance to M31, the Andromeda Galaxy is The distance to M31, the Andromeda Galaxy is

0.6 Mpc.0.6 Mpc.

Interim summary. Understand:Interim summary. Understand:

Scientific NotationScientific Notation LogsLogs Deep TimeDeep Time Astronomical UnitAstronomical Unit ParallaxParallax ArcsecondArcsecond PrefixesPrefixes

Part 2: The AncientsPart 2: The Ancients

These realms of big numbers, deep These realms of big numbers, deep time, and vast space were unknown time, and vast space were unknown to ancient peoples.to ancient peoples.

Therefore, their interpretation of the Therefore, their interpretation of the heavens, though thoughtful and heavens, though thoughtful and picturesque, is fatally flawed.picturesque, is fatally flawed.

Nonetheless, it is they with whom we Nonetheless, it is they with whom we will start our discovery.will start our discovery.

Center of the UniverseCenter of the Universe

The ancient model of the Cosmos, all The ancient model of the Cosmos, all the way up until the 17the way up until the 17thth Century, Century, was a was a GeocentricGeocentric model. model.

There were other models, but There were other models, but Geocentricity was the norm.Geocentricity was the norm.• Perhaps you’ve known someone like this Perhaps you’ve known someone like this

? ?

SensibleSensible

Earth at the center of the Universe Earth at the center of the Universe makes sense:makes sense:• Everything in the sky seems to move Everything in the sky seems to move

overhead;overhead;• You don’t You don’t feelfeel any motion; any motion;• The gods would naturally place their The gods would naturally place their

subject realm at the center.subject realm at the center.

Before we get all impressed with Before we get all impressed with our modern selves…our modern selves…

What happens every morning in the What happens every morning in the East?East?

Actually, the Earth turns on its axis Actually, the Earth turns on its axis so that each part of it in turn faces so that each part of it in turn faces the Sun.the Sun.• How could you How could you proveprove that to someone that to someone

who thought otherwise?who thought otherwise?

To be fair…To be fair…

We know the distances involved We know the distances involved whereas ancient people didn’t;whereas ancient people didn’t;

We have instruments to measure all We have instruments to measure all sorts of physical and astronomical sorts of physical and astronomical quantities whereas they didn’t;quantities whereas they didn’t;

They weren’t stupid, and we aren’t They weren’t stupid, and we aren’t necessarily smarter: we just have necessarily smarter: we just have better information.better information.

Geocentrism:Geocentrism:

..Had the Earth at the center of the ..Had the Earth at the center of the Universe,Universe,

..Had the Moon, Sun, and five planets ..Had the Moon, Sun, and five planets circling the Earth on crystalline circling the Earth on crystalline spheres,spheres,

..Had the stars fixed to a great ..Had the stars fixed to a great canopy that also circled the world.canopy that also circled the world.

The different spheres for the Sun, Moon, planets, and stars clearly explained why some objects took longer that others to cross the sky.

Other Phenomena: Moon PhasesOther Phenomena: Moon Phases

Other Phenomena: EclipsesOther Phenomena: Eclipses

A B

Mapping the SkyMapping the Sky One thing ancient astrologers did One thing ancient astrologers did

was map out the sky into regions was map out the sky into regions known as known as ConstellationsConstellations (“stars (“stars together”).together”).

The Zodiac is but one set of The Zodiac is but one set of constellations.constellations.

Constellations are purportedly Constellations are purportedly pictures in the sky, pictures in the sky, IFIF you have a you have a vivid imagination.vivid imagination.• StellariumStellarium is a free planetarium program is a free planetarium program

Important Points and LinesImportant Points and Lines

Celestial EquatorCelestial Equator Celestial PolesCelestial Poles Vernal EquinoxVernal Equinox Autumnal EquinoxAutumnal Equinox MeridianMeridian EclipticEcliptic Copy these down for the next slideCopy these down for the next slide

Old and NewOld and New

We still use the ancient constellation We still use the ancient constellation names to locate regions in the sky, names to locate regions in the sky, but you noticed that no two but you noticed that no two constellations take up the same constellations take up the same space.space.• What does this say about the equally-What does this say about the equally-

spaced horoscopic zodiac?spaced horoscopic zodiac? Modern Astronomers use a grid Modern Astronomers use a grid

system not all that different from system not all that different from Earthbound latitude and longitude.Earthbound latitude and longitude.

RA and DeclinationRA and Declination Like Longitude and Like Longitude and

Latitude on EarthLatitude on Earth The Earth turns once The Earth turns once

every 24 hours, so the every 24 hours, so the sky is divided into 24 sky is divided into 24 hours of hours of Right Right AscensionAscension..

Declination runs from 0Declination runs from 0oo at the celestial equator at the celestial equator to +90to +90oo at the North at the North Celestial Pole (Polaris) Celestial Pole (Polaris) and -90and -90oo to the South to the South Celestial Pole.Celestial Pole.

TMI for A102, but essential in A105L

So Where Are We?So Where Are We? Via hubris and convenience, we are at Via hubris and convenience, we are at

the center of the Universe.the center of the Universe.• In time we will disabuse you of that notion.In time we will disabuse you of that notion.

Broadly speaking we’ve examined:Broadly speaking we’ve examined:• Big numbers/Scientific Notation/Logs;Big numbers/Scientific Notation/Logs;• Deep time, vast space;Deep time, vast space;• Locating and measuring distances to Locating and measuring distances to

Astronomical objects.Astronomical objects. Where do we go from here?Where do we go from here?

Back in Time, Out There!Back in Time, Out There!