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This is College Physics Answers
with Shaun Dychko.
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There is supposedly a super
massive black hole
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at the center of many galaxies
including ours
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and suppose a black hole has a mass of
10 to the 9 suns,
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what would its radius be?
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We will convert this into kilograms by
multiplying by
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1.99 times 10 to the 30 kilograms per Sun
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and that's 1.99 times 10 to the 39 kilograms.
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And the radius of a black hole is
called the Schwarzschild radius
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and it's 2 times the gravitational constant
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times mass over speed of light squared.
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So that's 2 times
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6.67 times 10 to the minus 11
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Newton meters squared per kilogram squared
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times the mass divided by
speed of light squared
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and that's 2.95 times 10 to the 12 meters.
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And that might seem like a big number
but it's only about 10 times
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more than the distance between
the Sun and the Earth.
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We are asked to figure out what is
this distance in light years?
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So the first thing we should do is figure out
how many meters a light year is.
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So we have the speed of light
multiplied by a year
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that's converted into seconds
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and that's 9.46097 times 10 to
the 15 meters per light year.
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So the number of light years then is
the radius—
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our answer for part (a)—
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times 1 light year for every 9.46097 times
10 to the 15 meters
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which is 3.12 times 10 to
the minus 4 light years.