WEBVTT
00:00:00.000 --> 00:00:03.160
This is Giancoli Answers
with Mr. Dychko.
00:00:03.840 --> 00:00:06.700
A light-year is the distance
light travels in one year
00:00:06.700 --> 00:00:09.680
and we calculate that distance by
multiplying the speed of light
00:00:09.680 --> 00:00:13.060
multiplied by the time that it spends
traveling which is 1 year.
00:00:13.320 --> 00:00:17.960
And so we have 2.998 times 10 to the 8
meters per second is the speed of light
00:00:17.960 --> 00:00:20.100
but since we have seconds in the bottom,
00:00:20.100 --> 00:00:22.720
we need a bunch of conversion factors
to deal with the fact
00:00:22.720 --> 00:00:24.280
that we are multiplying by 1 year;
00:00:24.280 --> 00:00:27.020
we'll have to express 1 year in seconds.
00:00:28.160 --> 00:00:30.760
So we have,
00:00:31.360 --> 00:00:33.620
well, 1 year over here cancels with
00:00:33.620 --> 00:00:36.280
365.25 days per year
00:00:36.280 --> 00:00:38.720
and then we have 24 hours per day
00:00:38.800 --> 00:00:42.600
and then we have 3600 seconds per hour
00:00:42.600 --> 00:00:45.280
hours cancel and the seconds
will then cancel
00:00:45.280 --> 00:00:48.760
and there we have it, we are gonna be
left only with the units of meters.
00:00:48.760 --> 00:00:51.760
So that's 9.46 times 10 to the 15 meters
00:00:51.800 --> 00:00:55.840
is the light-year distance
expressed in meters.
00:00:56.500 --> 00:01:00.120
Now for figuring out the number of
astronomical units
00:01:00.160 --> 00:01:02.960
in a light-year, we'll take this
00:01:03.500 --> 00:01:09.480
quantity that we haven't rounded yet because
you always use unrounded numbers
00:01:09.620 --> 00:01:13.040
in subsequent calculations to avoid
intermediate rounding error.
00:01:13.240 --> 00:01:17.700
So we have 9.46097 times 10 to the 15 meters
00:01:17.800 --> 00:01:20.880
and then we'll express that in kilometers
00:01:20.880 --> 00:01:24.400
so multiply by 1 kilometer for
every per 1000 meters—
00:01:24.400 --> 00:01:26.940
essentially we are dividing by a 1000—
00:01:26.940 --> 00:01:30.720
meters cancel because we are given
astronomical units
00:01:30.720 --> 00:01:34.100
in terms of kilometers so we have
1 astronomical unit for every
00:01:34.100 --> 00:01:36.340
1.50 times 10 to the 8 kilometers
00:01:36.340 --> 00:01:38.660
and now we'll be left with
astronomical units;
00:01:38.780 --> 00:01:42.380
6.31 times 10 to the 4 astronomical units
00:01:42.380 --> 00:01:45.960
are in 1 light-year.