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...