1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    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!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted