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Limit of Black Hole

  1. Apr 27, 2010 #1
    1. The problem statement, all variables and given/known data
    Calculate the black hole mass limit such that the change in the gravitational acceleration at a distance 50Rs over a small interval of 2m doesn't exceed 10m/s2. Use Newton's Theory of Gravity in the calculation.

    2. Relevant equations

    Schwarszchild Radius:

    Rs = 2GM / c2

    Newton's Theory of Gravity:

    F = GMm / r2



    3. The attempt at a solution

    Totally lost. I'm an American study abroad student in New Zealand and am completely lost with these assignments. Don't know where to go for help.
     
  2. jcsd
  3. Apr 28, 2010 #2
    Firstly, write down the expression for how the acceleration due to gravity changes with distance (from Newton's equations), then times this by 2 [metres] and force it to equal ten (the limit that the field can change) ie

    [tex]\Delta r \left. \frac{\rm{d} g}{\rm{d} r} \right\vert_{r=50 R_\rm{s} }} =10 \rm{\, ms}^{-2}[/tex]

    where [tex]\Delta r = 2 \rm{\, m}[/tex]

    Does this help??
     
  4. Apr 28, 2010 #3
    Thanks. I did the calculations, but I keep getting a negative number. I set my r = 50Rs and for my dg/dr I get -2GMr-3. So when I solve for M is keep getting a negative number.
     
  5. Apr 28, 2010 #4
    A change in the gravitational acceleration can be positive or negative and we are not told whether to move 2 m away or towards the black hole, so solve for the absolute change (i.e. don't worry about the negative sign the solution still answers the problem).
     
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