ASTR 430

Sample Midterm Hints

Problem 1: Step 1 is to find an expression for the radial velocity v_r. There are a few ways to do this. One way is to start with the equation for the total velocity v and the azimuthal velocity v_theta. Squaring and subtracting gives vr. You get v_theta from angular momentum (Kepler's second law). Try it! Once you have vr, differentiate with respect to f, or r and set equal to zero. Your answer should be a place along the orbit defined as a value of f or r.

Problem 2: Go read the book!! :)

Problem 3: a) This should be straight-forward because the most general dimensionless constant that you can form is just a constant. The trick here is to assume that the constant is about one, which is often a good approximation.
b) Here you can form a dimensionless constant, so your answer should have a dimensionless function in it.

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