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Homework Help: Planetesimal Accretion

  1. Jun 3, 2014 #1
    Kinda stumped. The question gives three equations and I don't know what to do with them, because given the equations there's always more than one unknown. Any assistance/tips would be appreciated!

    If a planetesimal has a cross-sectional area of πR2 (where R is the planetesimal's radius) and is sweeping through a cloud of smaller particles of fixed size with a velocity V, the number of collisions per second will be:

    dn/dt = (πR2N)/m

    where ρN=the space density (kg/m3) of particles in the cloud and m=the mass of each particle.

    If each collision results in the target particles sticking to the planetesimal, the planetesimal will gain mass at a rate of

    dM/dt = πR2N

    where M=the planetesimal mass.

    The time to grow to radius R is

    t = (4R/V)/(ρPN)

    where ρP=the density of the planetesimal itself. (Assume that ρN and V stay constant as particles are swept up.)

    Assuming that a reasonable value for the density of accretable material in inner part of the early solar nebula is ρN = 10-7 kg/m3, estimate the time to accrete a body of 1,000 km radius. Assume a reasonable ρP.
  2. jcsd
  3. Jun 4, 2014 #2

    Simon Bridge

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    Homework Helper

    Don't see your problem.
    You are given an equation t=... and you know all the variables.
  4. Jun 4, 2014 #3


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    Homework Helper

    That was a duplicate post. Solved in the other thread in Introductory Physics.

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