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 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 test 1) Before the Test: Study hard Get plenty of rest the night before 2) 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, me.

Test #1 Useful Equations P 2  a 3 Kepler’s laws, including: Newton’s laws, including: a = F net / m F = G m 1 m 2 R 2 Gravitation: Speed of electromagnetic waves: c =  Energy = h  max energy  1T1T Wien’s Law: Stefan’s Law: L = A T 4 where the area A = 4  r 2 for a sphere

Angular Measure 90 o 20 o 360 o, or 360 degrees, in a circle. 1 o = 60' or arcminutes 1' = 60" or arcseconds 1" = 1000 mas or milli-arcseconds = 10 3 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 23.5 o DayNight Day Night Sun high in northern sky Sun low in northern sky

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

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 Orion Day Night Day Night Scorpius Orion Night Day NightDay 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 16 th 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

Copernican model was a triumph of the Scientific Method Scientific Method: a)Make high quality observations of some natural phenomenon b)Come up with a theory that explains the observations c)Use the theory to predict future behavior d)Make further observations to test the theory e)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 Theory Prediction

Galileo ( ) 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 ( ) 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 faster when closer to the Sun. slower faster

Newton ( ) 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 = F net m or F net = ma acceleration is a change in velocity or a change in direction of velocity.

Timelines of the Big Names Copernicus Galileo Brahe Kepler Newton

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 =  1T1T (units: Hertz or cycles/sec)

 c = 1 nm = m, 1 Angstrom = m The Electromagnetic Spectrum

1. Refraction Waves bend when they pass through material of different densities. swimming pool air water prism air glass Things that waves do

Example: Blackbody - the microwave background Emits mostly in the radio, with a peak around 200 GHz

cold dusthotter 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