AST3019 Homework #1 Assigned: Jan 17, 2012 Due: Jan 31, 2012 1. You and your friend carry identical meter sticks and clocks. Your friend goes on a fast moving train holding the meter stick parallel to the direction of motion. In the time it takes your clock to tick off 1 second, you see your friend’s clock tick off 0.75 seconds. How long does your friend’s stick appear to you? How long does your stick appear to your friend, assuming they are parallel to each other? 2. Work through the mathematical steps in section 7.4.1 to arrive at equation 7.5 in the book, but for the source and receiver moving apart (i.e. the term will be 1-v/c rather than 1+v/c in the result). Next, convert this equation from frequency to wavelength to derive an expression for redshift (z), where z is defined as the shift in wavelength, Δλ , divided by the rest wavelength λ o . Show that this equation reduces to the classical result (z = v/c) when v << c. 3. Derive the Schwarzschild radius by taking the escape velocity from any object with
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