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  1. K

    Closest approach from initial velocity and impact parameter

    ##\dot r## seems it would equal zero at the point of closest approach, since that will also be a turning point for the particle, so the radial distance is not changing at that instant. I assume this is true for all basic two-body orbits? So, using ##E = \frac{m \dot r^2}{2} + \frac{L^2}{2mr^2}...
  2. K

    Closest approach from initial velocity and impact parameter

    dr/dt is correct, sorry - that was what I intended v to mean but I didn't clarify that, so thank you. Does this mean that my method of taking the KE to be maximum at the instant of closest approach is incorrect, since ##\frac{1}{2} m \dot r^2## only accounts for the radial KE of the particle?
  3. K

    Closest approach from initial velocity and impact parameter

    Here were my assumptions: Energy and angular momentum are both conserved because the only force acting here is a central force. The initial angular momentum of this particle is ##L = mv_0b## and we can treat E as a constant in the homework equation given above. I solved for the KE (1/2 mv^2) in...
  4. K

    Color Index and Intrinsic Magnitude of a Star

    I first determined ##E_{U - B}## by using the second equation listed above: $$U - B = (U - B)_0 + E_{U - B}$$ $$8.15 - 8.50 = -0.45 + E_{U - B}$$ Then since the ratio to the B-V color excess is known, I solved for that and obtained ##E_{B - V} = 0.14##. Using the ratio of total to selective...
  5. K

    B Intensity of Spherical Shell of Stars

    For my original assumption where I defined n to be the number of stars, the dr was unnecessary, I agree. Looking back in the book, n referred to the density of stars instead (which was not explicitly stated, and that was what caused my confusion) which added a 1/dr factor that later had to be...
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    B Intensity of Spherical Shell of Stars

    I think I can make a correction here, actually. My book did not define ##n## at all, but looking through later chapters it seems as though ##n## is more commonly used as a number density, rather than just the number of stars. In this case, setting n = # of stars / 4πr^2 dr would give me the same...
  7. K

    B Intensity of Spherical Shell of Stars

    Given that L is the luminosity of a single star and there are n stars evenly distributed throughout this thin spherical shell of radius r with thickness dr, what is the total intensity from this shell of stars? My calculations were as follows: Intensity is the power per unit area per steradian...
  8. K

    Setup for Spherical Astronomy Problem

    I can't believe I missed that, thank you so much. That cleared up everything.
  9. K

    Setup for Spherical Astronomy Problem

    My apologies for not detailing my attempts at a solution; I'm not sure how to to digitally illustrate or describe the various setups I attempted before looking at the solution to this problem. I am also ONLY asking about the setup, though I included the full question for context. The solution to...
  10. K

    Mass Transfer in a Binary Star System

    Thank you so much! I cubed it instead so that I could replace D with the expression for D in terms of w and it worked out. I'll keep this in mind in the future!
  11. K

    Mass Transfer in a Binary Star System

    Homework Statement: A binary star system consists of M1 and M2 separated by a distance D. M1 and M2 are revolving with an angular velocity w in circular orbits about their common center of mass. Mass is continuously being transferred from one star to the other. This transfer of mass causes...
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