The universe is a big place, perhaps the biggest.
Kurt Vonnegut.
That's a nice thinking comment for this module on One to a Trillion.
The question that we want to answer in this module is how big, how far, and
how old are we compared to other stuff in the universe,
whether it be a solar system or the Milky Way Galaxy or the universe at large.
So typically, when you try and answer these kind of questions,
you always scale it down to the human dimension.
We'll be doing this both in terms of space, size and distances.
We'll scale things down to things that are familiar on an every day life level and
also in terms of time, when we'll scale things to a calendar year and
take a look at where we fit inside that calendar year.
So, one example of this is to take the Sun and
make it about the size of a grapefruit.
So, one this scale, this is about a 1 to 10 billion scale.
The earth is about a size of a little ballpoint, so for example,
a pen that you write with, that little ball point there at the end.
And Jupiter would be about the size of a marble.
But even on this scale, I think it's important to get across the point
that the distances between the planets are large.
So on this scale, Earth, the size of a ballpoint pen,
is orbiting about 15 meters away from the grapefruit sized Sun.
Another take on this scale is shown by the image below, where the Sun is about
the size of a large ping pong ball or something like that, and it's showing the,
attempts to show the distance scale and size scale on a single image there.
It's not quite right because at this scale,
the inner terrestrial planets of Mercury, Venus, Earth, and
Mars would each be less than one pixel and so we can't quite go subpixel.
But nevertheless, it does a pretty good job of describing
the size of the solar system inside of this plot.
So on this scale, where the Sun is a grapefruit and the Earth is a ballpoint,
you could walk to Pluto within a few minutes assuming you were the same size.
That you weren't scaled down 1 to 10 billion either.
But on the same scale as well, so, it could take you a few minutes to get
out to Pluto, but the nearest stars are still thousands of kilometers away.
So on this scale, where the Sun is a grapefruit, and Earth is a ballpoint, and
Jupiter is a marble, it would take you a few minutes to walk out to Pluto.
Assuming you were the same size that you are now,
that you weren't also scaled down on a size scale of 1 to 10 billion.
So on this scale, the nearest stars are still thousands of kilometers away.
Which will give you a sense of just how much empty space is
there between our solar system and the nearest stars.
Speaking of the nearest stars, this is shown in the diagram below,
it shows the solar system, the Sun in the middle, and
the nearest star to us is about four light-years away.
That's the Alpha Centauri system,
which in this diagram is shown as a double star system, a two star system.
It's actually a triple star system.
And we'll see that shortly.
So the nearest star to us is four light-years away.
And one light-year is the distance that light travels within one year.
So it's big.
One light-year is around 10 trillion kilometers, and so
it's four of those to get out to the nearest star to us, Alpha Centauri.
And then the nearest star beyond that is called Barnard's Star,
that sits out at about six light-years or so.
So in this diagram, all the distances are shown on a flat plane.
On this image here, it's shown in a more three dimensional rendition where you have
the plane of the solar system, but it also gives an indication of the distances
up and down that you would have to go.
So for example, find Alpha Centauri on this diagram.
And you see, you have to go out and you have to go down a little bit, for
total distance of four light-years or so.
And you should also find Barnard's Star on this diagram.
And this diagram is showing the nearest 25 stars, nearest to us.
So now let's move out in scale a little bit.
So on a scale where the entire Milky Way Galaxy, which is about a hundred
thousand light-years across, is about the size of an American football field.
So on this scale, then the distance from the Sun to Alpha Centauri,
the nearest star, is on the order of millimeters.
So it's that difference between millimeters to get to the nearest stars
to the size of an entire American football field,
gives you a sense of what the size scale of the Milky Way is.
So the Milky Way, how many stars are in the Milky Way?
There's roughly, we haven't exactly counted them,
but you take a picture of representative regions and
then you multiply how many regions it would take to fill in Milky Way,
and there's about a hundred billion stars in the Milky Way Galaxy.
The Sun is a very average garden variety, yellow star.
The image here shows our location in the Milky Way.
We're comfortably out in the suburbs of the Milky Way as we orbit around.
Oh, and by the way, the Solar System is inclined roughly about 90 degrees relative
to the plane of the Milky Way.
So, we kinda go around the Milky Way Sideways,
as we get our sideways view as we go through.
Moving out in scale a little bit more, we have the Milky Way and you can ask, well,
how many galaxies are there?
And so answers to that question come from things like the Hubble Space Telescope,
where you do a pencil beam, you point the telescope at one location and
you look as deep as you can.
And then you count all the galaxies in that little tiny pencil beam and
then you multiply by the number of pencil beams that it would take
to fill up the entire sky.
And the answer that you get is that there are about a hundred billion
galaxies in the observable universe.
There's also a hundred billion stars in a galaxy like the Milky Way and so
a hundred billion times a hundred billion tells you,
there's about 10 to the 22 stars in the observable universe.
And this is comparable to the number of dry sand grains on all of Earth's beaches.
So the number of little sand grains throughout the world
is about equal to the number of stars that you see in the observable universe.
So, now, let's move into the time domain a little bit.
And what we want to do is, the universe is about 13 billion years old or so.
And what we wanna do is compress that into one calendar year.
So, we're gonna make this, human scale, by taking this unimaginably large number of
13.7 billion years and compressing it down into one calendar year.
And on this scale, you can see this image is showing how we go from January 1st,
at 12 PM, where the Big Bang happens out through the evolution of the universe.
So on this scale of the universe compressed into
one calendar year, the Milky Way is born in May.
So it goes from January to May with not much happening in our neck of the woods.
The Milky Way was born circa in May.
The Sun and the solar system becomes born
circa around September and as we move through that time slot,
the image here is showing some key events that go on.
But I want you to note that within the last minute,
Of the calendar year is when human history starts to be begin.
So, for example, the very earliest human
writing is occurring about 15 seconds before midnight.
The Chinese dynasties are nine seconds or so before midnight.
Modern religious figures occur five seconds before midnight.
Columbus when he discovered America, occurs one second before midnight.
And so that's over the scale of an entire year.
So, you get this, hopefully, this impression from this image,
and thinking about a little bit, of the vast time scales that occur
between the universe happening and when we show up on the scene and do our thing.
So the final point we want to do today is to
give an example of what a calculation will look like in the labs in this course.
And we've mentioned the term light-year.
Roughly said, it's about 10 trillion kilometers or so.
And so how do we figure that out?
And so all of the quantitative questions in this course can be done
with arithmetic or very simple algebra.
Solve for x on one side or the other.
So the question how far is a light-year, that question asks how far,
which is telling us we are looking for a distance.
You are likely, I hope, familiar with
the idea that a distance is equal to a speed times a time, or
a speed is equal to a distance divided by a time, those are all the same thing.
And so here, the speed is the speed of light, and the time is one year.
So the speed of light is around 300 kilometers per second.
And because this speed is given in a per second and we want it to a per year,
we have to figure out how many seconds are in a year.
And so to do this, that's shown in the next line on this calculation.
So we have one light-year is equal to the speed of light times one year.
So we have the speed at 300 kilometers per second.
Then we have multiplied by this kind of big quantity where we're converting one
year times 365 days per year times 24 hours per day times 60 minutes per hour
times 60 seconds per minute and that will give us the number of seconds in a year,
and if you wanna quick little mnemonic, as to how many seconds are in a year.
There are pi times 10 to the 7th seconds per year, so
about 3 times 10 to the 7th seconds per year.
But anyway, you take all those just arithmetic,
and you multiply those numbers together, and
you'll get something like about about 9.4 times 10 to the 12 kilometers.
So this is sort of a right answer in that it has the right expected dimensions
of a distance.
You should always check that, and make sure your answer, if you're looking for
a distance, the answer doesn't come out in units of time or speed.
Now, this answer is not exact because, among other things,
there's not exactly 365 days in a year.
And so for most purposes, for
all the calculations that we will do in this course or just in conversation, it's
perfectly fine to say that there are about 10 trillion kilometers in a light-year.
Plus, 10 is a lot easier to remember than something like 9.46216 blah, blah, blah.
Nobody can remember that, but everybody can remember a ten.
So that's a little bit of an example of the scales in space and
scales in time and a little bit of an example of a calculation that
we would be doing in this course.
Thanks. Bye bye.