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Homework Help: Orbit speed and radius

  1. Sep 24, 2012 #1
    A comet orbits a star. At its closest approach (r=4*10^10 km) it has a speed of v=50 km/s. How fast is the comet at its maximum distance (R=10*10^10 km)?

    Could someone verify my results?

    F=GMm/r^2=mv^2/r

    f=GMm/R^2=mV^2/R

    F/f = R^2/r^2 = Rv^2/rV^2 -> R/r = v^2/V^2

    R=2.5r -> 2.5r/r = v^2/V^2 -> V^2 = 2500/2.5 km^2/s^2 -> V = √1000 km/s
     
  2. jcsd
  3. Sep 24, 2012 #2

    TSny

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    The comet is moving in a very elliptical orbit rather than a circular orbit. You cannot take r and R as radii of circular motion. Try something else. (Hint: Use an appropriate conservation principle.)
     
  4. Sep 24, 2012 #3
    What about angular momentum?

    mvr=mVR

    50*4*10^10=x*10*10^10

    x=20
     
  5. Sep 24, 2012 #4

    TSny

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