f we then put this speed and the Hubble constant into Hubble’s law equation, we can solve for the distance.

When Hubble laid his own distance estimates next to measurements of the recession velocities (the speed with which the galaxies were moving away), he found something stunning: there was a relationship between distance and velocity for galaxies. The more distant the galaxy, the faster it was receding from us.

No one at the time quite knew what to make of this discovery.

Humason was collaborating with Hubble by photographing the spectra of faint galaxies

Basically, if we can obtain a spectrum of a galaxy, we can immediately tell how far away it is.

spectra of galaxies contained a wealth of information about the composition of the galaxy and the velocities of these great star systems.

Hubble’s Law

Models for an Expanding Universe

the spectral lines of most galaxies showed an astounding redshift.

a redshift is seen when the source of the waves is moving away from us

d is the distance

just as Lemaître had suggested.

the universe is expanding.

rework the surface of our planet constantly

common sandstones, shales, and limestones

This is the way many, but not all, of the mountain ranges on Earth were formed.

It is a cooling system for the planet.

A block of quartzite on Earth is composed of materials that have gone through all four of these states.

The power to move the plates is provided by slow convection of the mantle

To find primitive rock, we must look to smaller objects such as comets, asteroids, and small planetary moons

white

Jupiter’s moon Io

Volcanoes

astronomy exams

Metamorphic rocks

observations

The square of a planet’s orbital period is directly proportional to the cube of the semimajor axis of its orbit.

Tubingen

sum of the distance from two special points inside the ellipse to any point on the ellipse is always the same

exploding star

beyond the orbit of Pluto.

occupied most of Kepler’s time for more than 20 years

Three years after the publication of Copernicus’ De Revolutionibus, Tycho Brahe was born

parabola, and hyperbola

Note that the eccentricities of the planets’ orbits in our solar system are substantially less than shown here.

We wrap the ends of a loop of string

Kepler’s third law

The universe could be a bit more complex than the Greek philosophers had wanted it to be.

If the foci (or tacks) are moved to the same location, then the distance between the foci would be zero. This means that the eccentricity is zero and the ellipse is just a circle; thus, a circle can be called an ellipse of zero eccentricity. In a circle, the semimajor axis would be the radius.

Kepler found that Mars has an elliptical orbit, with the Sun at one focus (the other focus is empty). The eccentricity of the orbit of Mars is only about 0.1; its orbit, drawn to scale, would be practically indistinguishable from a circle, but the difference turned out to be critical for understanding planetary motions.

clumsy and lacking the beauty and symmetry of its successor.

still taught at Harvard University

phases of Venus

This animation (http://tiny.cc/88cyqy) shows the phases of Venus. You can also see its distance from Earth as it orbits the Sun. The Astronomy Picture of the Day has an animation of Venus  https://apod.nasa.gov/apod/ap060110.html (http://tiny.cc/vadyqy) and a  set of images of Venus as viewed from Earth.  https://apod.nasa.gov/apod/ap170317.html (http://tiny.cc/ebdyqy)

heavenly bodies must be made up of combinations of uniform circular motions.

His great contribution to science was a critical reappraisal of the existing theories of planetary motion and the development of a new Sun-centered, or heliocentric, model of the solar system.

predictions

simple experiment dropping two balls of different weights

We have all experienced seeing an adjacent train, bus, or ship appear to move, only to discover that it is we who are moving.

the Galaxy is roughly spherical

Understanding the nature of this dark matter is one of the great challenges of astronomy today;

should

indicating a great deal of mass beyond the Sun’s orbit.

Stay tuned

least 2 × 1012MSun, which is about twenty times greater than the amount of luminous matter.

basic approach

only about 20 galactic years have passed.

heir orbital velocities are even greater than the Sun’s

rotation curve

If the gravity were supplied by stars or by something else that gives off radiation, we should have spotted this additional outer material long ago.

Rotation Curve of the Galaxy

Little did we suspect how wrong our assumption was.

If the Galaxy had only the mass calculated by Kepler, then the high-speed outer objects should long ago have escaped the grip of the Milky Way.

We call the period of the Sun’s revolution the galactic year.

forced to the reluctant conclusion that this matter is invisible

the mass closer to us can bend the light from farther away. With just the right alignment, the image of the more distant object also becomes significantly brighter.

these should produce dark features in the ultraviolet spectra of objects lying beyond the Galaxy,

concentrated at a point in the center of the sphere

100 billion times the mass of the Sun

Geologists estimate that about half of Earth’s current internal heat budget comes from the decay of radioactive isotopes in its interior.

Uranium-238 Lead-206 4.47 Potassium-40 Argon-40 1.31

This graph

snow

Scientists measure the age of rocks using the properties of natural radioactivity.

This composite image of the Moon’s surface

emission of particles such as electrons

if we have a very large number of radioactive atoms of one type (say, uranium), there is a specific time period, called its half-life, during which the chances are fifty-fifty that decay will occur for any of the nuclei.

techniques that had been developed to date rocks on Earth were applied to rock samples from the Moon

5 kilometers per second

whip through the inner parts of their orbits

48 kilometers per second

Two points in any orbit in our solar system have been given special names.

perigee and apogee

The average orbital data for the planets

Both asteroids and comets are believed to be small chunks of material left over from the formation process of the solar system.

Halley

According to Kepler’s second law, therefore, they spend most of their time far from the Sun, moving very slowly

no life was detected on Mars.

together with a great deal of water ice.

Testing this possibility, however unlikely, was one of the primary objectives of the Viking landers in 1976.

fossil life on Mars

Mars seems to be the most promising place to look for life

We know that the one requirement shared by all life on Earth is liquid water.

Underground water would be the most exciting possibility,

At a pressure of less than 0.006 bar, the boiling point is as low or lower than the freezing point, and water changes directly from solid to vapor without an intermediate liquid state (as does “dry ice,” carbon dioxide, on Earth).

0.007 bar, less than 1% that of Earth.

the runoff channels are probably older than the lunar maria, presumably about 4 billion years old.

Several types of clouds can form in the martian atmosphere.

the sterilizing effect of this ultraviolet light.

the planet had a very different climate long ago.

planet-wide dust storms

Apparently this very large basin had once been underwater.

Some local source of heating must have released this water

The channel is about 2.5 kilometers across.

Apparently the martian climate experiences periodic changes at intervals similar to those between ice ages on Earth.

Climate Change on Mars

the wavelength emitted by the source

The variable v is counted as positive if the velocity is one of recession, and negative if it is one of approach. Solving this equation for the velocity, we find

wavelength gets longer, we call the change in colors a redshift.

656.6 nm

describe changes in the wavelengths of radio waves or X-rays

Check Your Learning

Solving this equation for the velocity

radial velocity motion toward or away from the observer; the component of relative velocity that lies in the line of sight

For particular absorption or emission lines

As wavelength decreases, they shift toward the blue end of the spectrum

The wavelengths of the absorption lines can be measured accurately, however, and their Doppler shift is relatively simple to detect.

difference in wavelength

That’s really an impressive amount of information for stars that are light-years away.

Color Shifts

supermassive black holes by astronomers, to indicate that the mass they contain is far greater than that of the typical black hole created by the death of a single star.

supernova remnants

0.13 light-year

It appears that the monster black hole at the center of our Galaxy is not finished “eating.” At the present time, we observe clouds of gas and dust falling into the galactic center at the rate of about 1 MSun per thousand years.

These stars have now been observed for almost two decades,

temperature of 10 million K.

Very Large Array (VLA) of radio telescopes in Socorro, New Mexico.

the evidence for a supermassive black hole at the center of the Galaxy is convincing indeed.

less than the diameter of Mercury’s orbit.

most important discoveries was the verification of water ice

resulting Doppler shift

mass

radar-bright water ice

silicates

its orbit has the high eccentricity of 0.206, Mercury’s actual distance from the Sun varies from 46 million kilometers at perihelion to 70 million kilometers at aphelion

radius

at least part of the core must be liquid

but wrong about where the Sun lies within the disk.

“dreamed”

most of the stars they could see lay in a flattened structure encircling the sky

previously hidden bulge of old stars that surrounds the center of our Galaxy

our Glaxy is not unique in its characteristics. There are many other flat, spiral-shaped islands of stars, gas, and dust in the universe.

band standing in formation during halftime at a football game

Once the light pollution subsides to negligible levels, the Milky Way can be readily spotted arching over the sky on clear, moonless nights.

You could do a much better job from a helicopter flying over the city than you could if you were standing in Times Square.

concentrated into a central bar and a series of spiral arms

two weeks surrounding the new moon, when the faint stars and Milky Way don’t have to compete with the Moon’s brilliance

Mount Wilson Observatory,

shaped rather like a peanut

William Herschel was a German musician who emigrated to England and took up astronomy in his spare time.

Heavier-element abundance

important clues to how the Milky Way Galaxy formed

This invisible mass has been give the name dark matter

In 1785

Probing the Atom

The Bohr Atom

The Atomic Nucleus

The number of neutrons is not necessarily the same for all atoms of a given element.

The type of element is determined by the number of protons in the nucleus of the atom

They are also shown much closer than they would actually be

isotopes1 of oxygen

nearly circular orbit our Moon occupies today.

potential solutions to most of the major problems raised by the chemistry of the Moon

major isotopes1 of oxygen,

Moon is both tantalizingly similar to Earth and frustratingly different.

increasing evidence

a “bullet” about the size of Mars

Figure 2.

Milky Way Galaxy as it would look from above

The concentration of matter in the arms exerts sufficient gravitational force to keep the arms together over long periods of time

Scientists have used supercomputer calculations to model the formation and evolution of the arms.

might

differential galactic rotation

show that a great deal of interesting chemistry must have taken place when the solar system was forming.

Such a fall occurs when a single larger object breaks up during its violent passage through the atmosphere

with the different materials sorted according to density.

Some Striking Meteorites

This value (which we round off to 4.5 billion years in this book) is taken to represent the age of the solar system

The most remarkable thing about these organic molecules is that they include equal numbers with right-handed and left-handed molecular symmetry.

do not appear to come from the comets

complex organic molecules in them—chemicals based on carbon, which on Earth are the chemical building blocks of life.

The ages of stony meteorites can be determined from the careful measurement of radioactive isotopes and their decay products.

The Formation of the Galaxy

If we know the distance to a galaxy, we can convert how bright the galaxy appears to us in the sky into its true luminosity

If every light bulb in a huge auditorium is a standard 100-watt bulb, then bulbs that look brighter to us must be closer, whereas those that look dimmer must be farther away.

they could measure distances using certain kinds of intrinsically luminous variable stars, such as cepheids

cepheid variables

type Ia supernovae

(credit: NASA, ESA, A. Riess (STScI))

Other Measuring Techniques

make out an individual cepheid variable star in the galaxy M100 and measure its distance to be 56 million light-years.

Observations show that supernovae of this type all reach nearly the same luminosity (about 4.5 × 109LSun) at maximum light.

we know the precise way light is dimmed by distance

The Discovery of Neptune

his friend Edmund Halley

born in Lincolnshire, England, in the year after Galileo’s death

In this simplified model of a hydrogen atom

Stellar Populations

We can now take a brief introductory tour

Learning Objectives