Physics II workshop_Part_34

Physics II workshop_Part_34 - Carefully write down the fit...

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Carefully write down the fit equation and consider the following questions. 1. Is a linear function a good fit to the data? 2. Compare the fit equation to the equation for a straight line: y = mx + c . What can you conclude about the relationship between T and a ? 3. Assume that the planets are actually undergoing uniform circular motion (not a bad approximation in most cases) in which the radius of the planet’s orbit is equal to the semi-major axis a . Decide what provides the centripetal force and then apply Newton’s 2 nd law to derive a general equation relating the orbital period T to the semi-major axis, a . This should involve the mass of the Sun, M ~ and Newton’s gravitational constant, G . 4. Compare your equation to your linear fit to the log T – log a graph. What is the significance of the numerical coefficients of the fit (i.e. m and c )? 5. Use the coefficients of your linear fit to determine the mass of the Sun. Compare your result to the actual mass (you can find this in Appendix C of the textbook). Write out your answers neatly and attach a print-out of your graph.

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Physics II workshop_Part_34 - Carefully write down the fit...

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