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Event Horizon calculation

  1. Mar 3, 2014 #1
    Here's the question:

    One of the brightest stars in our night sky is a red supergiant with a mass about 10× the
    Sun’s mass and a radius about 1000× the Sun’s radius. At the end of its life it will explode
    as a supernova and then collapse and become a black hole. How large will the black hole’s
    event horizon be compared to the size of the supergiant now.

    The answer choices are given as multiple choice:

    (A) 0× the supergiant’s radius
    (B) 0.00000004× the supergiant’s radius
    (C) 0.000004× the supergiant’s radius
    (D) 0.0004× the supergiant’s radius
    (E) 0.04× the supergiant’s radius

    -----------------------------------------------------------------------------------------------

    My attempt:

    I'm going to use formula for Schwarzschild radius which is: r = 2*G*m / c^2

    The question said mass 10x the Sun's mass, so Sun's mass = 1.98 * 10^30 kg, the mass I'm using will be 10x that, which is: 1.98 * 10^31 kg

    And then I plugged that into the formula and got: 14.7690207 km

    Then, the question says that the radius of the Supergiant is 1000x that of the Sun's radius. I have the Sun's radius as: 695000 km, so 695000 * 1000 km is what I am using.

    Finally, I take 14.7690207 km and divide it by 695,000,000 and get: 0.0000000212503895

    The answer is closest to (B), but what I calculated is literally half of answer (B).

    I figured, maybe the event horizon is like the diameter, so what I have is actually the ratio of the radius, so I should double it and that would give me (B), but I am not sure if that's right or not.

    What am I missing here? Thanks in advance.
     
  2. jcsd
  3. Mar 3, 2014 #2

    phyzguy

    User Avatar
    Science Advisor

    I think you forgot the factor of 2 in the r = 2Gm/c^2. A 10 solar mass black hole should have e Schwarzschild radius of about 30 km.
     
  4. Mar 3, 2014 #3
    Oh yeah, you're right. Thanks!
     
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