Review for Test #1 on February 16

Topics:• Foundations of Astronomy - measurement, exponential notation, etc.• The Copernican Revolution - Newton’s Laws, Gravitation, etc.• Radiation and the Electromagnetic Spectrum - Black bodies

Methods • Conceptual Review and Practice Problems Chapters 0 - 2• Review lectures (on-line) and know answers to clicker questions• Try practice quizzes on-line (in MA)•Bring:• Notes & Text (Test is open book)• Simple calculator (no electronic notes)

Reminder: There are NO make-up tests for this class

Test #1 Review

How to take a multiple choice test1) Before the Test:• Study hard• Get plenty of rest the night before2) During the Test:• Draw simple sketches to help visualize problems• Solve numerical problems in the margin• Come up with your answer first, then look for it in the choices• If you can’t find the answer, try process of elimination• If you don’t know the answer, Go on to the next problem and

come back to this one later• TAKE YOUR TIME, don’t hurry• If you don’t understand something, email me.

Test #1 Useful Equations

P2 a3 Kepler’s laws, including:

Newton’s laws, including: a = Fnet / m

F =G m

1 m

2

R2

Gravitation:

Speed of electromagnetic waves: c = Energy = h

max energy

1T

Wien’s Law:

Stefan’s Law: L = A T4 where the area A = 4r2 for a sphere

Angular Measure

90o

20o

360o, or 360 degrees, in a circle.

1o = 60' or arcminutes1' = 60" or arcseconds1" = 1000 mas or milli-arcseconds = 103 mas

The Celestial Sphere

Features:- Does not rotate with Earth- Poles, Equator- Coordinate System

An ancient concept, as if all objects at same distance.

But to find things on sky, don't need to know their distance, so still useful today.

The Earth's rotation axis is tilted with respect to its orbit around the Sun => seasons.

Summer Winter

Scorpius Orion

Tilt is 23.5o

DayNight Day NightSun high in northern sky

Sun low in northern sky

One solar day later, the Earth has rotated slightly more than 360o .A solar day is longer than a sidereal day by 3.9 minutes(24 hours vs. 23 hours 56 minutes 4.091 seconds).

Cycle of phases slightly longer than time it takes Moon to do a complete orbit around Earth.

Cycle of phases or "synodic month"

Orbit time or "sidereal month"

29.5 days 27.3 days

Eclipses

Lunar Eclipse

When the Earth passes directly between the Sun and the Moon.

Sun Earth Moon

Solar Eclipse

When the Moon passes directly between the Sun and the Earth.

Sun EarthMoon

Types of Solar Eclipses Explained

Precession

The Earth has a bulge. The Moon "pulls down" on the side of the bulge closest to it, causing the Earth to wobble on its axis (how do we know this?)

Earth

Moon

Spin axis

**Vega Polaris

Precession Period 26,000 years!

Winter: July or January?

Winter: January

Scorpius OrionDayNight Day Night

Scorpius OrionNightDayNight Day

Summer: January or July?

Summer: July

Now

13,000 years from now

We choose to keep July a summer month, but then in 13,000 years, summer occurs on other side of orbit!

"Heliocentric" Model

● Rediscovered by Copernicus in 16th century.

● Put Sun at the center of everything.

● Much simpler. Almost got rid of epicycles.

● But orbits circular in his model. In reality, they’re elliptical, so it didn’t fit the data well.

● Not generally accepted at the time.

Copernicus 1473-1543

Copernican model was a triumph of the Scientific Method

Scientific Method:

a) Make high quality observations of some natural phenomenonb) Come up with a theory that explains the observationsc) Use the theory to predict future behaviord) Make further observations to test the theorye) Refine the theory, or if it no longer works, make a new one

- Occam’s Razor: Simpler Theories are better-You can prove a theory WRONG but not RIGHT

Observation

TheoryPrediction

Galileo (1564-1642)

Built his own telescope.

Discovered four moons orbiting Jupiter => Earth is not center of all things!

Discovered sunspots. Deduced Sun rotated on its axis.

Discovered phases of Venus, inconsistent with geocentric model.

Kepler (1571-1630)

Used Tycho Brahe's precise data on apparent planet motions and relative distances.

Deduced three laws of planetary motion.

Kepler's First Law

The orbits of the planets are elliptical (not circular) with the Sun at one focus of the ellipse.

Ellipses

eccentricity =

(flatness of ellipse)

distance between foci major axis length

Kepler's Second Law

A line connecting the Sun and a planet sweeps out equal areas in equal times.

Translation: planets move fasterwhen closer to the Sun.

slower faster

Newton (1642-1727)

Kepler's laws were basically playing with mathematical shapes and equations and seeing what worked.

Newton's work based on experiments of how objects interact.

His three laws of motion and law of gravity described how all objects interact with each other.

Newton's Second Law of Motion

When a force, F, acts on an object with a mass, m, it produces an acceleration, a, equal to the force divided by the mass.

a = Fnet

m

or Fnet = ma

acceleration is a change in velocity or a change in direction of velocity.

Timelines of the Big Names

Copernicus

Galileo

Brahe

Kepler

Newton

1473-1543 1546-16011473-1543

1564-1642

1571-1630

1642-1727

Radiation travels as waves.Waves carry information and energy.

Review: Properties of a wave

wavelength ()

crest

amplitude (A)

velocity (v)trough

is a distance, so its units are m, cm, or mm, etc.

Period (T): time between crest (or trough) passages

Frequency (): rate of passage of crests (or troughs),

Also, v = 1T

(units: Hertz or cycles/sec)

c =

1 nm = 10 -9 m , 1 Angstrom = 10 -10 m

The Electromagnetic Spectrum

1. Refraction

Waves bend when they pass through material of different densities.

swimming pool

air

water

prism

airairglass

Things that waves do

Example: Blackbody - the microwavebackground

Emits mostly in the radio, with a peak around 200 GHz

cold dust hotter star (Sun)

“cool" star

frequency increases, wavelength decreases

Approximate black-body spectra of astronomical objects demonstrate Wien's Law and Stefan's Law

very hot stars