WEBVTT

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This is Giancoli Answers
with Mr. Dychko.

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A light-year is the distance
light travels in one year

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and we calculate that distance by
multiplying the speed of light

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multiplied by the time that it spends
traveling which is 1 year.

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And so we have 2.998 times 10 to the 8
meters per second is the speed of light

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but since we have seconds in the bottom,

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we need a bunch of conversion factors
to deal with the fact

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that we are multiplying by 1 year;

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we'll have to express 1 year in seconds.

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So we have,

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well, 1 year over here cancels with

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365.25 days per year

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and then we have 24 hours per day

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and then we have 3600 seconds per hour

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hours cancel and the seconds
will then cancel

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and there we have it, we are gonna be
left only with the units of meters.

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So that's 9.46 times 10 to the 15 meters

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is the light-year distance
expressed in meters.

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Now for figuring out the number of
astronomical units

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in a light-year, we'll take this

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quantity that we haven't rounded yet because
you always use unrounded numbers

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in subsequent calculations to avoid
intermediate rounding error.

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So we have 9.46097 times 10 to the 15 meters

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and then we'll express that in kilometers

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so multiply by 1 kilometer for
every per 1000 meters—

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essentially we are dividing by a 1000—

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meters cancel because we are given
astronomical units

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in terms of kilometers so we have
1 astronomical unit for every

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1.50 times 10 to the 8 kilometers

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and now we'll be left with
astronomical units;

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6.31 times 10 to the 4 astronomical units

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are in 1 light-year.