Lecture 2 Our Place in the Universe (Cont'd)

Astronomy 110 –1 Lecture 2

Our Place in the Universe (Cont’d)

103 = 10 x 10 x 10 = 1000 102 = 10 x 10 = 100 101 = 10 100 = 1 10-1 = 1/10 = 0.1 10-2 = 1/10 x 1/10 = 0.01 10-3 = 1/10 x 1/10 x 1/10 = 0.001

Then: 300 = 3 x 100 = 3 x 102 2,500 = 2.5 x 1000 = 2.5 x 103

101 x 101 = 100 = 102 101 x 102 = 10 x 100 = 1000 = 103 102 x 102 = 100 x 100 = 10000 = 104  When multiplying two powers of ten, add the exponents

1000 ÷ 100 = 103 ÷ 102 = 10 = 101 10 ÷ 10 = 101 ÷ 101 = 1 = 100 10 ÷ 100 = 101 ÷ 102 = 1/10 = 10-1  When dividing, subtract exponent of divisor from exponent of numerator

(104)3 = 104 x 104 x 104 = 1012  Rule of thumb: when raising to a power, multiply exponents

What about √(104)? √(104) = 102  taking roots is the same as raising to a fractional power, in this case 1/2 power: √(104) = (104)1/2 = 102

√ is the same as raising to 1/2 power 3√ is the same as raising to 1/3 power 4√ is the same as raising to 1/4 power

To multiply powers of ten, add exponents: 10n x 10m = 10(n+m) To divide powers of ten, subtract exponents: 10n ÷ 10m = 10(n-m) To raise powers of ten to other powers, multiply exponents: (10n)m = 10(nxm) where m can be fractional for roots.

Radius of Earth = 6,400 km = 6.4x103 km.

Galaxy diameter = 1,000,000,000,000,000,000,000 m = 1021 m.

Size of H atom = 0.000,000,000,05 m =5x10-11 m.

Rule of thumb: • number of places decimal is moved to the left is the positive power of ten; • number of places decimal is moved to the right is the negative power of ten.

14/01/09 7 Copyright © 2009 Pearson Education, Inc. Basic units used in Astronomy • astronomical unit (AU): average distance between Earth and Sun = 150 million km or 1.5 108 km (about 108 mi or 100 million miles) [Technically = semi-major axis of Earth’s orbit around Sun]

• light year: distance that light travels in 1 year = 9.46 1012 km (about 6 1012 miles, or 6 trillion miles)

This distance is fixed because light in a vacuum always travels at the same speed = 300,000 km/s or 3 105 km/s (1.86 105 mi/s)

Calculation: distance = velocity x time 1 light year = speed of light x 1 year

= 3 105 km/s x 1 yr x 365 day/yr x 24 hr/1 day x 60 min/1 hr x 60 sec/1 min = 9.46 1012 km

[do exercise by rounding off numbers]

You cannot add or subtract numbers unless they have the same units.

You can multiply units: area is feet x feet = (feet)2, or, volume is meter x meter x meter = (meter)3.

You can divide units: speed = miles ÷ time = miles per hour

2. Converting from m/s to km/hr 1 m = 10-3 km 1 hr = 60 min x 60 s = 3600 s = 3.6 103 s Or 1 s = 1 ÷ 3.6 103 hr ≅ 2.8 10-4 hr So: 1 m/s = 1 m x 10-3 km/m ÷ ( 1s x 2.8 10-4 hr/s) = 3.6 km/hr

How long is 1 light second? 1 light second = distance traveled by light in 1 second distance = speed x time speed of light = 3 105 km/s

1 light second = 3 105 km/s x 1s = 3 105 km

In units of miles: 1 mi = 1.6 km 1 light second = 3 105 km x 1 mi/1.6 km ≅ 2 105 mi

14/01/09 13 Copyright © 2009 Pearson Education, Inc. How did we come to be? Telescopic observations of distant galaxies show that the entire universe is expanding From observed rate, we estimate that it occurred about 14 billion years ago Here is how we think things happened … 14/01/09 14 Copyright © 2009 Pearson Education, Inc. 1. The Big Bang

14/01/09 16 Copyright © 2009 Pearson Education, Inc. 3. Stars manufacture the elements of Earth and Life Stars are born in clouds of gas and Massive stars dust; planets may explode when form in surrounding they die, disks scattering the elements they have produced into space

Stars shine with energy released by nuclear fusion, which ultimately

14/01/09 18 Copyright © 2009 Pearson Education, Inc. How can we know what the universe was like in the past? • Light travels at a finite speed (300,000 km/s). Destination Light travel time Moon 1 second Sun 8 minutes Sirius 8 years Andromeda Galaxy 2.5 million years

• Try to find the distance to these objects in km using scientific notation

Remember: distance = speed x time speed of light = 3 105 km/s

14/01/09 20 Copyright © 2009 Pearson Education, Inc. Example: This photo shows the Andromeda Galaxy as it looked about 1/2 million years ago. Question: When will we be able to see what it looks like now?

A. Because no galaxies exist at such a great distance. B. Galaxies may exist at that distance, but their light would be too faint for our telescopes to see. C. Because looking 15 billion light-years away means looking to a time before the universe existed.

• What is our place in the universe? — Earth is part of the solar system, which is in the Milky Way Galaxy, which is a member of the Local Group of galaxies in the Local Supercluster. • How did we come to be? — The matter in our bodies came from the Big Bang, which produced hydrogen and helium. — All other elements were constructed from H and He in stars and then recycled into new star systems, including our solar system.

• How can we know what the universe was like in the past? — When we look to great distances, we are seeing events that happened long ago because light travels at a finite speed. • Can we see the entire universe? — No. The observable portion of the universe is about 14 billion light-years in radius because the universe is about 14 billion years old.

Our goals for learning:

• How big is Earth compared to our solar system? • How far away are the stars? • How big is the Milky Way Galaxy? • How big is the universe? • How do our lifetimes compare to the age of the universe?

14/01/09 27 Copyright © 2009 Pearson Education, Inc. How big is Earth compared to our solar system? Let’s reduce the size of the solar system by a factor of 10 billion; the Sun is now the size of a large grapefruit (14 cm diameter).

How big is Earth on this scale?

A. an atom B. a tip of a ball point pen C. a marble D. a golf ball

How big is Earth on this scale?

A. an atom B. a tip of a ball point pen C. a marble D. a golf ball

14/01/09 29 Copyright © 2009 Pearson Education, Inc. The scale of the solar system • On a 1-to-10 billion scale: — Sun is the size of a large grapefruit (14 centimeters). — Earth is the size of a tip of a ball point pen, 15 meters away.

On our 1-to-10 billion scale, it’s just a few minutes’ walk to Pluto.

How far would you have to walk to reach Alpha Centauri? A. 1 mile B. 10 miles C. 100 miles D. the distance across the United States (2500 miles)

On our 1-to-10 billion scale, it’s just a few minutes’ walk to Pluto.

How far would you have to walk to reach Alpha Centauri? A. 1 mile B. 10 miles C. 100 miles D. the distance across the United States (2500 miles)

The Milky Way has about 100 billion stars. On the same 10 billion-to- 1 scale…

Suppose you tried to count the more than 100 billion stars in our galaxy, at a rate of one per second…

How long would it take you? A. a few weeks B. a few months C. a few years D. a few thousand years

Suppose you tried to count the more than 100 billion stars in our galaxy, at a rate of one per second…

How long would it take you? A. a few weeks B. a few months C. a few years D. a few thousand years

It has as many stars as grains of (dry) sand on all Earth’s beaches.

14/01/09Zooming Out or Zooming In 26 Orders of Magnitude 38 Copyright © 2009 Pearson Education, Inc. How do our lifetimes compare to the age of the universe? The Cosmic Calendar: A scale on which we compress the history of the universe into 1 year Jan 1: Big Bang February: Milky way forms

September: Earth forms Fig. 1.10  On this scale: Human civilization is just a few seconds old, and a human lifetime lasts only a

14/01/09fraction of a second. 39 Copyright © 2009 Pearson Education, Inc. What have we learned? • How big is the Earth compared to our solar system? —On a scale of 1-to-10 billion, the Sun is about the size of a grapefruit. The Earth is the size of a tip of a ball point pen about 15 m away. The distances between planets are huge compared to their sizes. • How far away are the stars? —On the same scale, the stars are thousands of kilometers away. • How big is the Milky Way Galaxy? —It would take more than 3000 years to count the stars in the Milky Way Galaxy at a rate of one per second. The Milky Way Galaxy is about 100,000 light-years across.

14/01/09 40 Copyright © 2009 Pearson Education, Inc. What have we learned? • How big is the universe? —100 billion galaxies in the observable universe —14 billion light-years in radius —As many stars as grains of sand on Earth’s beaches • How do our lifetimes compare to the age of the universe? —On a cosmic calendar that compresses the history of the universe into 1 year, human civilization is just a few seconds old, and a human lifetime is a fraction of a second.

Our goals for learning: • How is Earth moving in our solar system? • How is our solar system moving in the Milky Way Galaxy? • How do galaxies move within the universe? • Are we ever sitting still?

• rotation – spinning of an object around its axis • orbit (revolution) – orbital motion of one object around another • expansion of the universe – increase in average distance between galaxies as time progresses

14/01/09 43 Copyright © 2009 Pearson Education, Inc. How is Earth moving in our solar system? • Contrary to our perception, we are not “sitting still.” • We are moving with the Earth in several ways, and at surprisingly fast speeds.

Earth rotates around its axis once every day.

14/01/09 44 Copyright © 2009 Pearson Education, Inc. Earth orbits the Sun (revolves) once every year… • at an average distance of 1 AU ≈ 150 million km. • with Earth’s axis tilted by 23.5º (pointing to Polaris). • and rotates in the same direction it orbits, counter- clockwise as viewed from above the North Pole.

14/01/09 45 Copyright © 2009 Pearson Education, Inc. Our Sun moves randomly relative to the other stars in the local solar neighborhood… • at typical relative speeds of more than 70,000 km/hr. • but stars are so far away that we cannot easily notice their motion. … and it orbits the galaxy every 230 million years.

Most of Milky Way’s light comes from the disk and the bulge …

…. but most of the mass is in its halo

Galaxies are carried along with the expansion of the universe.

But how did Hubble figure out that the universe is expanding?

• all galaxies outside our Local Group are moving away from us. • the more distant the galaxy, the faster it is racing away. Conclusion: We live in an expanding universe.

Earth rotates on axis: > 1,000 km/hr Earth orbits Sun: > 100,000 km/hr Solar system moves among stars: ~ 70,000 km/hr Milky Way rotates: ~ 800,000 km/hr,.carrying the Sun around its center once every 230 million years

Milky Way moves relative to others Universe in the Local Group (300,000 km/hr expands towards Andromeda)

• How is Earth moving in our solar system? —It rotates on its axis once a day and orbits the Sun at a distance of 1 AU = 150 million km. • How is our solar system moving in the Milky Way Galaxy? —Stars in the Local Neighborhood move randomly relative to one another and orbit the center of the Milky Way in about 230 million years.

• How do galaxies move within the universe? —All galaxies beyond the Local Group are moving away from us with expansion of the universe: the more distant they are, the faster they’re moving. • Are we ever sitting still? —No!