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MARK HARTMAN: This
morning, we're

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00:00:20,820 --> 00:00:22,950
going to learn a new skill.

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00:00:22,950 --> 00:00:27,340
OK, so we're going
to say a new skill,

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and that's going to be
comparing quantities.

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00:00:37,950 --> 00:00:39,730
Comparing quantities
is really important.

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00:00:39,730 --> 00:00:41,820
We've already done it a
couple of different times.

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00:00:41,820 --> 00:00:45,360
We compared the angular size
of our expert project objects

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00:00:45,360 --> 00:00:47,610
with the angular
size of the sun.

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00:00:47,610 --> 00:00:51,390
We compared the flux that we
got from the sun to the flux

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00:00:51,390 --> 00:00:55,020
that we would expect to get
from our expert project objects.

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00:00:55,020 --> 00:00:59,600
We've also been talking
a lot about distances,

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00:00:59,600 --> 00:01:02,950
to the nearest star, distances
to the center of the galaxy.

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00:01:02,950 --> 00:01:06,810
So when we dealing with a bunch
of these really large numbers

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00:01:06,810 --> 00:01:09,750
that we use for
scientific notation,

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00:01:09,750 --> 00:01:11,700
we also want to be
able to compare them,

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00:01:11,700 --> 00:01:14,440
and this is the way that
we're going to do it.

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00:01:14,440 --> 00:01:16,890
So I first have a
question to ask you,

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00:01:16,890 --> 00:01:21,500
which is if I took
this solar system--

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00:01:21,500 --> 00:01:24,330
we're going to talk about
size scales right here.

27
00:01:24,330 --> 00:01:30,660
We're going to talk
about comparing sizes

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00:01:30,660 --> 00:01:32,814
as an example of how
to compare quantities.

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00:01:32,814 --> 00:01:34,980
We're going to learn about
how to compare quantities

30
00:01:34,980 --> 00:01:36,622
using ratios.

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00:01:36,622 --> 00:01:37,830
So I have a question for you.

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00:01:37,830 --> 00:01:39,850
If I took the whole
solar system--

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00:01:39,850 --> 00:01:41,970
which is the sun at
the very, very center--

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00:01:41,970 --> 00:01:46,050
and then I shrunk it down--

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00:01:46,050 --> 00:01:48,530
the sun with all the planets,
all the way out to Pluto,

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00:01:48,530 --> 00:01:50,460
right, Pluto's orbit.

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00:01:50,460 --> 00:01:53,100
If I shrunk the whole
solar system down until it

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00:01:53,100 --> 00:01:54,480
was the size of a quarter--

39
00:01:54,480 --> 00:01:56,271
and, actually, does
anybody have a quarter?

40
00:01:56,271 --> 00:01:58,890
I don't think I have
a quarter on me.

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00:01:58,890 --> 00:02:01,764
I promise you'll get
your quarter back.

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00:02:01,764 --> 00:02:02,430
Whoever's first.

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00:02:02,430 --> 00:02:03,990
SHAKIB AHMED: [INAUDIBLE]

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00:02:03,990 --> 00:02:05,890
MARK HARTMAN: Aw,
Shakib's first.

45
00:02:05,890 --> 00:02:07,140
Thanks, man.

46
00:02:07,140 --> 00:02:09,539
All right, so this
is the quarter.

47
00:02:09,539 --> 00:02:12,180
The sun would be a tiny,
tiny, tiny, little dot

48
00:02:12,180 --> 00:02:14,130
that you couldn't even
see at the middle,

49
00:02:14,130 --> 00:02:17,452
and the outside is the orbit
of Pluto, right, that's

50
00:02:17,452 --> 00:02:18,660
the edge of the solar system.

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00:02:22,040 --> 00:02:27,000
If I shrunk the solar system--

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00:02:27,000 --> 00:02:31,230
and I'm just going to
abbreviate that SS--

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00:02:31,230 --> 00:02:45,250
to the size of a quarter,
where would the next star be?

54
00:02:45,250 --> 00:02:50,722
Where would the next star or
the next nearest solar system?

55
00:02:50,722 --> 00:02:52,180
I want you to talk
with your group,

56
00:02:52,180 --> 00:02:55,300
and I want you to
make a prediction.

57
00:02:55,300 --> 00:02:57,250
If I held the solar
system right here,

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00:02:57,250 --> 00:02:58,990
where would the next star be?

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00:02:58,990 --> 00:03:02,660
Where would the next
solar system be?

60
00:03:02,660 --> 00:03:04,600
OK, like how far
away would it be?

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00:03:11,950 --> 00:03:14,630
AUDIENCE: How many solar
systems can a galaxy have?

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00:03:14,630 --> 00:03:16,255
MARK HARTMAN: We're
going to get there.

63
00:03:20,950 --> 00:03:23,770
So just a quick estimate, talk
about it for just a minute,

64
00:03:23,770 --> 00:03:24,970
and come up with one answer.

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00:03:24,970 --> 00:03:27,490
And I'm going to have you
guys share them, rapid fire.

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00:03:35,510 --> 00:03:37,730
I think what we will do,
we'll just pour them out

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00:03:37,730 --> 00:03:38,837
into different buckets.

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Everybody will have a
little bucket of M&Ms,

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00:03:40,670 --> 00:03:42,895
and they get to choose
the right color.

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SIMBA KOL: Because he said
30 a color, so I'm like,

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00:03:45,020 --> 00:03:46,620
that's 150 M&Ms.

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00:03:46,620 --> 00:03:49,250
MARK HARTMAN: No, no, we just
have to say, each one of these

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represents a certain energy.

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00:03:51,210 --> 00:03:53,520
And then in a little
cup, we have a bunch.

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And they'll just have those with
them and say, OK, this is one.

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SHAKIB AHMED: Last
time I had to do 30.

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MARK HARTMAN: Yes.

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00:04:01,290 --> 00:04:05,030
AUDIENCE: Forgot your $0.50.

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00:04:05,030 --> 00:04:07,700
MARK HARTMAN: So if you put
a $0.50 piece next to it.

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So estimate it in terms
of centimeters or inches

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00:04:10,235 --> 00:04:12,110
or something, like if
you put it right there,

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it would maybe be like an inch
away, a couple of inches away,

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something like that.

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AUDIENCE: Two inches.

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MARK HARTMAN: It's close.

86
00:04:17,670 --> 00:04:18,050
Whatever.

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00:04:18,050 --> 00:04:19,190
SHAKIB AHMED: No, it's not.

88
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MARK HARTMAN: OK,
here's the solar system.

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00:04:21,019 --> 00:04:22,474
Ooh.

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00:04:22,474 --> 00:04:31,685
[SIDE CONVERSATION]

91
00:04:31,685 --> 00:04:35,320
AUDIENCE: I'd say like
three and four inches.

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00:04:35,320 --> 00:04:37,710
MARK HARTMAN: OK, let's
go around the room.

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00:04:37,710 --> 00:04:40,800
Have you guys had
a chance to decide?

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00:04:40,800 --> 00:04:41,550
Make a decision.

95
00:04:41,550 --> 00:04:42,510
Who would like to go first?

96
00:04:42,510 --> 00:04:44,468
Who would like to volunteer
their answer first?

97
00:04:48,030 --> 00:04:51,202
How about that group?

98
00:04:51,202 --> 00:04:51,910
AUDIENCE: A foot.

99
00:04:51,910 --> 00:04:53,250
MARK HARTMAN: A foot.

100
00:04:53,250 --> 00:04:55,990
How far is the next
star in this model?

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00:04:55,990 --> 00:04:58,030
One foot.

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00:04:58,030 --> 00:05:01,560
So here's the solar system.

103
00:05:01,560 --> 00:05:04,290
The next star would
be like there.

104
00:05:04,290 --> 00:05:06,516
All right, what
about this group?

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00:05:06,516 --> 00:05:07,884
AUDIENCE: $0.50.

106
00:05:07,884 --> 00:05:09,492
I mean, like two quarters.

107
00:05:09,492 --> 00:05:11,384
MARK HARTMAN: Like
two quarters width.

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00:05:11,384 --> 00:05:13,050
AUDIENCE: That would
be like two inches.

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00:05:13,050 --> 00:05:14,300
MARK HARTMAN: Like two inches.

110
00:05:14,300 --> 00:05:17,910
So one foot, two inches--

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00:05:17,910 --> 00:05:19,440
OK, how about this group?

112
00:05:19,440 --> 00:05:20,520
AUDIENCE: One foot.

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00:05:20,520 --> 00:05:21,478
MARK HARTMAN: One foot.

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00:05:21,478 --> 00:05:24,030
OK, we'll just put a
check next to this one.

115
00:05:24,030 --> 00:05:25,590
What about this group?

116
00:05:25,590 --> 00:05:28,302
Don't let other people
influence your decision.

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AUDIENCE: To the dome.

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00:05:30,030 --> 00:05:32,710
MARK HARTMAN: To
the MIT dome, right?

119
00:05:32,710 --> 00:05:35,256
You mean the one that was on
top, that we took a picture of?

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00:05:35,256 --> 00:05:35,880
AUDIENCE: Yeah.

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00:05:35,880 --> 00:05:37,620
MARK HARTMAN: OK, the one
in the next building over.

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00:05:37,620 --> 00:05:38,790
AUDIENCE: One mile.

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00:05:38,790 --> 00:05:43,080
MARK HARTMAN: OK, so let's say
to the next building, which

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00:05:43,080 --> 00:05:48,997
is maybe, yeah, like maybe a
quarter mile, maybe 1,000 feet,

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00:05:48,997 --> 00:05:49,830
something like that.

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00:05:49,830 --> 00:05:50,291
AUDIENCE: It's far.

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00:05:50,291 --> 00:05:50,874
AUDIENCE: Wow.

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00:05:53,520 --> 00:05:56,010
MARK HARTMAN: OK,
so you're all wrong.

129
00:05:59,400 --> 00:06:04,468
The next star would actually
be on the other side of campus.

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00:06:04,468 --> 00:06:06,140
AUDIENCE: We were close.

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00:06:06,140 --> 00:06:10,540
MARK HARTMAN: So it's about
six football fields away.

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00:06:10,540 --> 00:06:16,600
So that's 600 yards,
which is about 2000 feet.

133
00:06:16,600 --> 00:06:20,060
Well, no, that's wrong, yeah.

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Six football fields, each
football field is 100 yards.

135
00:06:23,020 --> 00:06:28,350
So 600 times 3, 1800 feet.

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00:06:28,350 --> 00:06:31,000
OK, so maybe we
are close, right.

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00:06:31,000 --> 00:06:33,867
Maybe not to that dome,
the little one outside,

138
00:06:33,867 --> 00:06:35,950
but has anybody been to
the infinite corridor yet?

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00:06:35,950 --> 00:06:36,491
AUDIENCE: No.

140
00:06:36,491 --> 00:06:37,860
AUDIENCE: Where is it?

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00:06:37,860 --> 00:06:39,050
MARK HARTMAN: A couple of
people have taken picture

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00:06:39,050 --> 00:06:40,450
of the infinite corridor.

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00:06:40,450 --> 00:06:42,670
That's the one with
the big MIT dome on it,

144
00:06:42,670 --> 00:06:47,230
which is about four or five
or six buildings that way.

145
00:06:47,230 --> 00:06:52,030
So space is mostly empty space.

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00:06:52,030 --> 00:06:56,530
Between our solar system and
the very next star is that far.

147
00:06:56,530 --> 00:07:00,160
Have we gone to the next
nearest star besides the sun?

148
00:07:00,160 --> 00:07:05,410
No, the furthest any human piece
of technology has ever been

149
00:07:05,410 --> 00:07:07,480
are the Voyager
spacecrafts, which

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00:07:07,480 --> 00:07:09,820
are just right beyond
the edge of this quarter.

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00:07:09,820 --> 00:07:10,560
AUDIENCE: Really.

152
00:07:10,560 --> 00:07:12,226
MARK HARTMAN: Yeah,
so right now they're

153
00:07:12,226 --> 00:07:13,810
just right beyond
the edge of Pluto.

154
00:07:13,810 --> 00:07:14,811
AUDIENCE: How far it is?

155
00:07:14,811 --> 00:07:16,185
MARK HARTMAN:
We're going to talk

156
00:07:16,185 --> 00:07:17,840
about that in just a minute.

157
00:07:17,840 --> 00:07:22,240
So our next nearest star is
actually about, let's say,

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00:07:22,240 --> 00:07:25,455
six football fields.

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00:07:25,455 --> 00:07:27,880
AUDIENCE: That's far.

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00:07:27,880 --> 00:07:31,840
MARK HARTMAN: That's going to
be about 2000 feet, or about

161
00:07:31,840 --> 00:07:34,720
a half a mile away.

162
00:07:34,720 --> 00:07:38,372
All right, well, Juan, what
was the question that you asked

163
00:07:38,372 --> 00:07:39,580
just a couple of minutes ago?

164
00:07:42,290 --> 00:07:43,490
How many--

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00:07:43,490 --> 00:07:47,810
AUDIENCE: Oh, how many solar
systems can a galaxy have?

166
00:07:47,810 --> 00:07:49,310
MARK HARTMAN: How
many solar systems

167
00:07:49,310 --> 00:07:53,490
or how many stars with
planets orbiting around

168
00:07:53,490 --> 00:07:55,672
are fit in a galaxy
or make up a galaxy?

169
00:07:55,672 --> 00:07:57,380
Because we know there's
the solar system,

170
00:07:57,380 --> 00:07:59,990
and then we also
live in a galaxy.

171
00:07:59,990 --> 00:08:02,580
And there's a picture
of one right over there.

172
00:08:02,580 --> 00:08:07,400
That is a cartoon of what we
think our galaxy looks like.

173
00:08:07,400 --> 00:08:09,470
That's the Milky Way
galaxy, a cartoon.

174
00:08:09,470 --> 00:08:12,410
We can't actually-- you know,
if we've only gone this far,

175
00:08:12,410 --> 00:08:16,100
we can't go outside
and see the galaxy.

176
00:08:16,100 --> 00:08:22,190
So my next question
is, on this scale,

177
00:08:22,190 --> 00:08:25,790
if our solar system was a
quarter, how big is the galaxy?

178
00:08:30,560 --> 00:08:32,539
Is it going to be bigger
or smaller than the--

179
00:08:32,539 --> 00:08:34,559
AUDIENCE: It's going
to be like 100 blocks.

180
00:08:34,559 --> 00:08:36,559
MARK HARTMAN: It's going
to be bigger than this.

181
00:08:36,559 --> 00:08:39,350
So, again, I want
you guys to predict,

182
00:08:39,350 --> 00:08:42,440
if now knowing that the next
nearest star is a half a mile

183
00:08:42,440 --> 00:08:46,431
that way, how big
is the whole galaxy?

184
00:08:46,431 --> 00:08:47,930
So think about it
for just a minute.

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00:08:47,930 --> 00:08:48,638
AUDIENCE: Boston.

186
00:08:48,638 --> 00:08:49,610
MARK HARTMAN: Got.

187
00:08:49,610 --> 00:08:52,170
How big is the galaxy if the
solar system is a quarter?

188
00:08:52,170 --> 00:08:52,670
This group.

189
00:08:52,670 --> 00:08:54,128
AUDIENCE: About
the size of Boston.

190
00:08:54,128 --> 00:08:56,120
MARK HARTMAN: About
the size of Boston.

191
00:08:56,120 --> 00:08:58,687
Size of Boston.

192
00:08:58,687 --> 00:09:00,020
AUDIENCE: Including the suburbs.

193
00:09:00,020 --> 00:09:01,070
MARK HARTMAN: Which is maybe--

194
00:09:01,070 --> 00:09:02,060
including the suburbs--

195
00:09:02,060 --> 00:09:05,440
OK, fine, maybe
like 15 or 20 miles.

196
00:09:05,440 --> 00:09:07,034
OK, next group.

197
00:09:07,034 --> 00:09:08,450
AUDIENCE: As big
as Massachusetts.

198
00:09:08,450 --> 00:09:11,372
MARK HARTMAN: As big
as Massachusetts.

199
00:09:11,372 --> 00:09:15,075
[SIDE CONVERSATION]

200
00:09:15,075 --> 00:09:16,322
OK, this group.

201
00:09:16,322 --> 00:09:19,560
AUDIENCE: The size of the
Northeastern United States.

202
00:09:19,560 --> 00:09:21,110
MARK HARTMAN: OK,
so New England.

203
00:09:21,110 --> 00:09:24,740
[SIDE CONVERSATION]

204
00:09:24,740 --> 00:09:27,410
So that's like all the way
up to Maine, all the way down

205
00:09:27,410 --> 00:09:29,390
to Rhode Island and Connecticut.

206
00:09:29,390 --> 00:09:31,442
OK, last group.

207
00:09:31,442 --> 00:09:33,050
AUDIENCE: From here to Mars.

208
00:09:33,050 --> 00:09:35,570
MARK HARTMAN: From here to Mars.

209
00:09:35,570 --> 00:09:39,310
From here, this place on
Earth, all the way to Mars.

210
00:09:39,310 --> 00:09:40,228
OK.

211
00:09:40,228 --> 00:09:42,100
[SIDE CONVERSATION]

212
00:09:42,100 --> 00:09:43,024
AUDIENCE: To Mars.

213
00:09:43,024 --> 00:09:43,940
MARK HARTMAN: To Mars.

214
00:09:43,940 --> 00:09:44,760
All right, Jaylen.

215
00:09:44,760 --> 00:09:46,468
AUDIENCE: Isn't the
galaxy like infinity?

216
00:09:46,468 --> 00:09:49,040
MARK HARTMAN: No, no, no, no,
talk out loud to all of us.

217
00:09:49,040 --> 00:09:51,290
AUDIENCE: Wait, we don't how
big the galaxy is, right?

218
00:09:51,290 --> 00:09:52,360
MARK HARTMAN: Can
you hear him, is he--

219
00:09:52,360 --> 00:09:52,985
AUDIENCE: What?

220
00:09:52,985 --> 00:09:53,600
No.

221
00:09:53,600 --> 00:09:55,264
MARK HARTMAN: No, talk to them.

222
00:09:55,264 --> 00:09:56,930
I'm just the person
writing things down.

223
00:09:56,930 --> 00:09:58,700
You guys are the ones who
are figuring things out.

224
00:09:58,700 --> 00:10:00,650
AUDIENCE: We don't know how
big the galaxy is right?

225
00:10:00,650 --> 00:10:02,150
MARK HARTMAN: We're talking
about how big the galaxy is,

226
00:10:02,150 --> 00:10:02,604
yep.

227
00:10:02,604 --> 00:10:04,420
AUDIENCE: Yeah, but we
don't know big it is, right?

228
00:10:04,420 --> 00:10:06,336
AUDIENCE: We're just
predicting how big it is.

229
00:10:06,336 --> 00:10:08,030
MARK HARTMAN: Do we?

230
00:10:08,030 --> 00:10:12,470
You're confusing the
galaxy with the universe.

231
00:10:12,470 --> 00:10:17,540
The galaxy is all of the stars
that are close to us in space.

232
00:10:17,540 --> 00:10:20,450
We'll talk about other galaxies.

233
00:10:20,450 --> 00:10:22,520
The galaxy itself
is not infinite.

234
00:10:22,520 --> 00:10:25,260
It's not infinitely large, OK?

235
00:10:28,060 --> 00:10:30,250
All right, we're going
to move on, but keep

236
00:10:30,250 --> 00:10:33,940
that question in mind as we go.

237
00:10:33,940 --> 00:10:35,994
What is this?

238
00:10:35,994 --> 00:10:36,494
Hmm.

239
00:10:39,310 --> 00:10:42,051
Think about when you
heard that, OK, and then

240
00:10:42,051 --> 00:10:44,050
we'll get back to that,
especially when we start

241
00:10:44,050 --> 00:10:45,460
talking about
cosmology, which is

242
00:10:45,460 --> 00:10:48,340
the study of the whole
universe all together.

243
00:10:48,340 --> 00:10:51,520
So to Mars is wrong.

244
00:10:51,520 --> 00:10:53,560
That's too far.

245
00:10:53,560 --> 00:10:57,160
If the solar system was
the size of a quarter,

246
00:10:57,160 --> 00:11:04,040
the size of the galaxy would
be the size of North America.

247
00:11:04,040 --> 00:11:06,090
So Shakib, can you
come stand over here?

248
00:11:06,090 --> 00:11:07,030
AUDIENCE: Serious?

249
00:11:07,030 --> 00:11:07,970
Wow.

250
00:11:07,970 --> 00:11:11,530
AUDIENCE: You said
that, half of the US.

251
00:11:11,530 --> 00:11:13,610
MARK HARTMAN: So that's
wrong, wrong, wrong.

252
00:11:13,610 --> 00:11:15,140
You guy said New England.

253
00:11:15,140 --> 00:11:18,940
Now New England
is like that big.

254
00:11:18,940 --> 00:11:20,740
Half of the US is like that.

255
00:11:20,740 --> 00:11:23,800
So can you put that just
over there on the board--

256
00:11:23,800 --> 00:11:25,630
Northeastern part.

257
00:11:25,630 --> 00:11:30,070
So the galaxy would be
the size of North America.

258
00:11:30,070 --> 00:11:31,727
AUDIENCE: That seems crazy.

259
00:11:31,727 --> 00:11:33,310
AUDIENCE: [INAUDIBLE]
are really good.

260
00:11:33,310 --> 00:11:34,413
[INAUDIBLE]

261
00:11:34,413 --> 00:11:36,148
MARK HARTMAN: Ah-ha, so--

262
00:11:36,148 --> 00:11:38,932
AUDIENCE: Or Mexico.

263
00:11:38,932 --> 00:11:40,655
MARK HARTMAN: So
we actually-- let's

264
00:11:40,655 --> 00:11:43,030
just make it a little more
New England-centric-- we would

265
00:11:43,030 --> 00:11:46,090
be somewhere, I
forget, I think we're

266
00:11:46,090 --> 00:11:48,190
above Pennsylvania somewhere.

267
00:11:48,190 --> 00:11:50,670
We're out here on this side.

268
00:11:50,670 --> 00:11:52,870
Well, it's kind of round anyway.

269
00:11:52,870 --> 00:11:58,630
But if you wanted to create
a scale model of our galaxy,

270
00:11:58,630 --> 00:12:05,770
you would take $200
billion quarters.

271
00:12:05,770 --> 00:12:08,590
And you would drive around
all of North America.

272
00:12:08,590 --> 00:12:13,210
And you would put them about
a half a mile apart each.

273
00:12:13,210 --> 00:12:15,760
And you would put them up to--

274
00:12:15,760 --> 00:12:18,160
I forget exactly
how tall it is--

275
00:12:18,160 --> 00:12:24,220
but probably up to about
10 miles in the sky.

276
00:12:24,220 --> 00:12:29,380
The galaxy is about 100
times wider than it is thick.

277
00:12:29,380 --> 00:12:32,830
So if you think about a CD,
a CD is about 100 times wider

278
00:12:32,830 --> 00:12:34,240
than it is thick.

279
00:12:34,240 --> 00:12:37,660
So the galaxy is a very
flat thing, all right.

280
00:12:37,660 --> 00:12:39,730
So it doesn't have a
whole lot of thickness.

281
00:12:39,730 --> 00:12:42,670
But its width is
actually really large.

282
00:12:42,670 --> 00:12:45,610
So you'd have to drive
around in a bus or 17

283
00:12:45,610 --> 00:12:48,460
buses full of these quarters.

284
00:12:48,460 --> 00:12:52,540
Close, actually, it would
probably be more than that.

285
00:12:52,540 --> 00:12:54,430
And you would have
to put these quarters

286
00:12:54,430 --> 00:12:55,540
at about that far apart.

287
00:12:55,540 --> 00:12:57,550
Except, here in the
middle of the US,

288
00:12:57,550 --> 00:12:59,530
you'd put them much
closer together.

289
00:12:59,530 --> 00:13:01,180
Instead of being a
half a mile apart,

290
00:13:01,180 --> 00:13:03,650
maybe they would be
from this quarter

291
00:13:03,650 --> 00:13:04,900
to the other side of the room.

292
00:13:04,900 --> 00:13:07,180
AUDIENCE: Let's do it.

293
00:13:07,180 --> 00:13:09,460
MARK HARTMAN: That would be
a good summer CAI project.

294
00:13:09,460 --> 00:13:10,720
It would take a long time.

295
00:13:10,720 --> 00:13:13,880
AUDIENCE: Let's
call [INAUDIBLE]..

296
00:13:13,880 --> 00:13:16,480
MARK HARTMAN: So that
gives you a sense

297
00:13:16,480 --> 00:13:18,700
of the fact that the
galaxy where we live

298
00:13:18,700 --> 00:13:23,660
is so much bigger
than our solar system.

299
00:13:23,660 --> 00:13:26,350
And we'll come back
to this discussion

300
00:13:26,350 --> 00:13:28,054
when we talk about
other galaxies

301
00:13:28,054 --> 00:13:29,970
and talk about where
they are in the universe.

302
00:13:29,970 --> 00:13:32,710
OK, we'll do this thing again.

303
00:13:32,710 --> 00:13:35,840
But now that we have
this idea in our mind,

304
00:13:35,840 --> 00:13:39,100
let's think about how could we
represent this mathematically?

305
00:13:39,100 --> 00:13:41,250
If I wanted to say--

306
00:13:41,250 --> 00:13:45,000
and, actually, did you
take pictures of these?

307
00:13:45,000 --> 00:13:47,000
OK, could you take a
picture of that real quick?

308
00:13:49,600 --> 00:13:52,210
So I'm going to
put this over here.

309
00:13:52,210 --> 00:13:54,042
So if we're comparing sizes--

310
00:13:54,042 --> 00:13:56,250
I just had asked you, how
far is it to the next star?

311
00:13:56,250 --> 00:13:59,250
How big is the galaxy if
the solar system was shrunk

312
00:13:59,250 --> 00:14:00,900
to the size of a quarter?

313
00:14:00,900 --> 00:14:04,810
So, in general, we're going to
want to answer questions like--

314
00:14:04,810 --> 00:14:07,800
and then put this in
your notes down below--

315
00:14:07,800 --> 00:14:17,770
the galaxy is how
many times bigger--

316
00:14:17,770 --> 00:14:20,570
well, let's say
larger because bigger,

317
00:14:20,570 --> 00:14:23,890
I mean, it could be mass;
it could mean volume--

318
00:14:23,890 --> 00:14:32,274
how many times wider
than the solar system?

319
00:14:32,274 --> 00:14:33,960
All right, another
question could

320
00:14:33,960 --> 00:14:39,660
be, my object is how many times
more luminous than the sun?

321
00:14:39,660 --> 00:14:42,990
Or I have two stars,
how many times larger

322
00:14:42,990 --> 00:14:45,970
is one star than another?

323
00:14:45,970 --> 00:14:47,850
So if we have a sentence
that's like this,

324
00:14:47,850 --> 00:14:50,140
we can rewrite this in
mathematical language.

325
00:14:50,140 --> 00:14:53,070
And we can say, so the
galaxy is how many times

326
00:14:53,070 --> 00:14:55,380
wider than the solar system?

327
00:14:55,380 --> 00:14:57,360
I just write this as math.

328
00:14:57,360 --> 00:15:00,710
I can say the diameter because
that's the width of the galaxy.

329
00:15:00,710 --> 00:15:04,230
We said it was kind of
round shape like a CD.

330
00:15:04,230 --> 00:15:13,950
So we're going to say, the
diameter of the galaxy is--

331
00:15:13,950 --> 00:15:17,530
that means equals, in terms
of talking about math--

332
00:15:17,530 --> 00:15:20,700
how many times-- well,
that's like the thing that

333
00:15:20,700 --> 00:15:24,840
we're looking for, so
we'll call that x--

334
00:15:24,840 --> 00:15:31,440
is how many times, x times,
wider than the solar system?

335
00:15:31,440 --> 00:15:36,240
Well, now we're going to
say times the diameter

336
00:15:36,240 --> 00:15:37,140
of the solar system.

337
00:15:42,740 --> 00:15:45,375
Can everybody see
this over here?

338
00:15:45,375 --> 00:15:48,910
You may have to crane your head
around a corner a little bit.

339
00:15:48,910 --> 00:15:52,740
So what we're really looking
for is, how many times bigger is

340
00:15:52,740 --> 00:15:55,120
the galaxy than
the solar system?

341
00:15:55,120 --> 00:15:58,770
If we wanted to solve
this equation for x,

342
00:15:58,770 --> 00:16:01,510
that number, how many
times bigger is it,

343
00:16:01,510 --> 00:16:03,321
how would we do that?

344
00:16:03,321 --> 00:16:03,820
Nicky.

345
00:16:03,820 --> 00:16:09,078
AUDIENCE: Divide the
diameter of the solar system

346
00:16:09,078 --> 00:16:11,480
into the galaxy.

347
00:16:11,480 --> 00:16:13,580
MARK HARTMAN: OK,
so I want to divide

348
00:16:13,580 --> 00:16:26,260
both sides by the diameter
of the solar system, right?

349
00:16:26,260 --> 00:16:30,010
Now I can simplify because
these two cancel out.

350
00:16:30,010 --> 00:16:33,460
And then I'll just
rewrite underneath.

351
00:16:33,460 --> 00:16:40,480
I can now write the
diameter of the galaxy

352
00:16:40,480 --> 00:16:47,390
over the diameter of the solar
system is equal to this number.

353
00:16:47,390 --> 00:16:49,760
It's equal to some
number that tells me,

354
00:16:49,760 --> 00:16:53,530
how many times wider is it?

355
00:16:53,530 --> 00:16:56,330
So let's check our model, right?

356
00:16:56,330 --> 00:16:58,130
I just kind of
told you that this

357
00:16:58,130 --> 00:16:59,870
is what the model would be.

358
00:16:59,870 --> 00:17:02,660
Let's actually put in the
diameter of the galaxy

359
00:17:02,660 --> 00:17:05,970
and the diameter of the solar
system and see what we get.

360
00:17:05,970 --> 00:17:12,589
So the diameter of the
galaxy is about 9 times 10

361
00:17:12,589 --> 00:17:16,460
to the 20th meters.

362
00:17:16,460 --> 00:17:20,540
Remember yesterday, we had said
that the center of the galaxy

363
00:17:20,540 --> 00:17:24,800
is about 2 times 10 to the
20th meters away from Earth.

364
00:17:24,800 --> 00:17:27,780
So let's look on our chart here.

365
00:17:27,780 --> 00:17:32,570
If we're out here 2 times 10 to
the 20th meters is like that.

366
00:17:32,570 --> 00:17:37,040
So 9 times that is going
to be maybe 4 times wider--

367
00:17:37,040 --> 00:17:41,230
1, 2, 3, 4, that's about right.

368
00:17:41,230 --> 00:17:44,120
OK, so 9 times 10
to the 20th meters

369
00:17:44,120 --> 00:17:48,170
over the diameter of the
solar system in reality

370
00:17:48,170 --> 00:17:55,955
is 4.4 times 10 to the
power of 12 meters.

371
00:17:59,018 --> 00:18:03,810
All right, so we
just simplify this.

372
00:18:03,810 --> 00:18:07,680
I'm going to take this
up and put it over here.

373
00:18:07,680 --> 00:18:12,300
We simplify this by
saying 9 over 4.4.

374
00:18:12,300 --> 00:18:14,130
We just gather the
numbers together.

375
00:18:14,130 --> 00:18:16,840
And then we gather the
powers of 10 together.

376
00:18:16,840 --> 00:18:21,060
10 to the 20th divided
by 10 to the 12th.

377
00:18:21,060 --> 00:18:23,520
And then we gather
the units together,

378
00:18:23,520 --> 00:18:26,521
and we have meters over meters.

379
00:18:26,521 --> 00:18:28,590
And that still
equals x, this number

380
00:18:28,590 --> 00:18:31,470
that we're trying to find out.

381
00:18:31,470 --> 00:18:33,030
Let's simplify that again.

382
00:18:33,030 --> 00:18:35,625
9 over 4.4 is about 2.

383
00:18:38,160 --> 00:18:41,680
Remember how we do
division of powers of 10.

384
00:18:41,680 --> 00:18:46,530
That's 10 to the
power of 20 minus 12.

385
00:18:46,530 --> 00:18:49,690
And then meters over
meters cancels out.

386
00:18:49,690 --> 00:18:51,300
So our number doesn't
have any units

387
00:18:51,300 --> 00:18:58,190
because it's just how many
times bigger is it, equals x.

388
00:18:58,190 --> 00:19:04,235
So we simplify 2 times 10 to
the power-- what's 20 minus 12--

389
00:19:04,235 --> 00:19:04,735
8.

390
00:19:08,046 --> 00:19:10,380
So 2 times 10 to the 8.

391
00:19:10,380 --> 00:19:12,240
Let's write that out.

392
00:19:12,240 --> 00:19:15,555
That's 2 with
eight 0s after it--

393
00:19:15,555 --> 00:19:21,660
1, 2, 3, 4, 5, 6, 7, 8.

394
00:19:21,660 --> 00:19:31,050
So that means the galaxy
is 200 million times bigger

395
00:19:31,050 --> 00:19:33,354
than the solar system.

396
00:19:33,354 --> 00:19:34,770
Now, I could have
done that first,

397
00:19:34,770 --> 00:19:36,936
and you would have been
like, ooh, wow, 200 million,

398
00:19:36,936 --> 00:19:38,070
that's a lot.

399
00:19:38,070 --> 00:19:39,930
But it doesn't make as much--

400
00:19:39,930 --> 00:19:42,810
it doesn't give as much gut
reaction as when you say,

401
00:19:42,810 --> 00:19:45,930
well, here's a quarter
and the size of the galaxy

402
00:19:45,930 --> 00:19:48,240
would be the size of
North America, which is

403
00:19:48,240 --> 00:19:50,640
why we talked about that first.

404
00:19:50,640 --> 00:19:52,190
So let's--