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Review for Test 2 You can bring 1 index card with formulae (only formulae) Bring a scientific calculator About 1/4 quantitative, 3/4 qualitative Show as much work as possible (partial credit) General Comments: Tips on getting the most out of your formula card: Understand what each symbol stands for. Don’t get confused between similar symbols (e.g., g and G). Understand what the formula means physically. You may want to write the formulae in words when you study. Also, understand what plain English words relate to what quantity: e.g. “how fast is the particle moving” --> v =', “how big is the orbit” ---> r = ' Tips on doing numerical problems: It often helps to draw a diagram and visualize the problem. Understand what is given in the problem, and what is asked Figure out which formula applies (or which combination of formulae). Check your calculation, and check your units if relevant. Formulae Covered Before •  Small Angle Equation: Angular size of an object of diameter d at a distance D is given by α = 2.06 x 105 d / D arcsec D d (valid for small angles--numerator is much smaller than denominator) Mechanics and Gravity •  Newton’s laws of motion F=ma (second law) •  Newton’s law of gravitation F = G m1 m2 / r2 Circular speed Vcirc = √(Gm1/r) Escape speed Vescape= √(2Gm1/r) Kepler’s third law: (P/yr) 2 = (a/AU) 3 / [(M1+M2 )/Msun] Electromagnetic Radiation Optics and Telescopes •  •  •  •  •  •  Reflection, refraction Curved mirrors, lenses--focus Basic telescope design: Reflecting telescope: primary, secondary mirrors Refracting telescope: objective, eyepiece lenses Why are large modern telescopes reflecting' The Rationale for Big Telescopes •  Sensitivity--light bucket •  Deff = Dtel x √Ntel e.g., what is the effective (equivalent) diameter of a telescope that has 4 mirrors of 2 m each' •  Resolution--sharpness •  Diffraction Limit: smallest angle that could be resolved by a telescope •  αres=0.25'' x λ (µm)/D(m), •  Larger Dtel gives smaller (finer) resolution in absence of atmospheric blurring Example: Can a telescope of a certain diameter resolve a feature on a distant object or resolve two binary stars apart' EXAMPLE: Can a telescope of a certain diameter resolve a feature on a distant object or resolve two binary stars apart' EXAMPLE: Can a telescope of a certain diameter resolve a feature on a distant object or resolve two binary stars apart' •  Diffraction Limit: smallest angle that could be resolved by a telescope (without atmospheric blurring) •  αres=0.25'' x λ (µm)/D(m), •  Resolution needed to see a structure= •  α=206265 D/d (D=diameter of structure, d=distance from earth) •  Compare the two angles Miscellaneous Techniques •  Adaptive optics •  space telescopes: UV, X-ray, γ-ray, parts of IR Solar System •  General structure--most planets in 1 plane, nearly circular orbits •  Some exceptions--Venus (also pluto) •  Terrestrial planets vs. gas giants-differences and reasons Formation of Solar System •  Nebular theory--steps involved from cloud collapse to formation of solar system •  How it can explain basic facts about solar system--e.g. nearly co-planar orbits of most planets, formation of terrestrial and Jovian planets--why did Jovian planets get so big' Why do they have rings and many moons' Extra-solar planets •  •  •  •  •  How have they been detected' How do they differ from our solar system' How do we explain the differences' Applications of Doppler Effect, Kepler’s law Examples: If a planet is discovered from a wavelength shift of 0.01 % in the star’s spectrum, how fast is the star being “tugged”' •  If a planet is inferred to be 10 AU away from its star from direct imaging and has a period of 5 years, how massive is the star' Terrestrial Planets •  Plate tectonics, continental drift -what evidence do we have' -what drives it' Why are the other terrestrial planets not active geologically' •  Atmospheres--how did Earth’s atmosphere get its current composition' •  Why is the sky blue' Terrestrial Planets cont’d. •  Planet temperatures application of black-body laws Examples: at what wavelength does the radiation from a 300 K planet peak' How much more radiation does a 400K planet emit than a 200K planet' Terrestrial Planets cont’d. •  Greenhouse effect •  Venus vs. Earth vs. Mars-What caused them to evolve to different temperatures'  Moon: tides, influence on Earth Gas Giants •  Compositions, sizes--why different from terrestrial planets and each other •  Interiors