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Unformatted text preview: FREQUENTLY ASKED QUESTIONS February 20, 2012 Content Questions How do you find the center of mass? The position of the center of mass of a system of N masses is given by ∑ N i =1 m i ~ r i M , where ~ r i are the positions of the masses with respect to some origin. It’s kind of the “average position” of the masses. For two masses A and B , taking the origin as the position of A and the x axis along the line between the masses, the CM is at position x CM = m A x A + m B x B m A + m B = m B x B m A + m B . Now in our notation from class a A = x CM == m B x B m A + m B , and a B = x B- a A , which works out to a B = m A x B ma A + m B , and we get a B /a A = m A /m B . For the Doppler shift, what is the “plane of the sky”? If you imagine the celestial sphere as infinitely far away, a piece of its surface is flat. That’s the plane you are looking at when you look at an object. The angle of inclination i is the angle between that plane and the plane of the orbit: if the orbit is face-on, its plane is perpendicular to the line of sight...
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