Okay, welcome back.
So when we deal with astronomy, when we
get started with astronomy, one of the most
difficult things is to deal with the enormous
size scales and time scales involved with astronomy.
It's really easy in astronomy just to have
everything be really, really big, and really, really old.
But that's really, not that helpful when we're trying to be specific
and trying to understand different evolutionary
processes that may operate on very
different, though very long, time scales.
So, for example, the age of the earth is 4.5 billion years, right?
and the dinosaurs were wiped out about 65 million years ago.
How do you hold those two numbers in your hand and make sense of them, right?
the way that scientists do this is through something
called scientific notation, that's how we deal with large numbers.
So the age
of the Earth is 4,500,000,000 years old, but that
gets written as 4.5 times ten to the nine years.
There's the first part of the number, the 4.5, which
tells you where you are in your order of magnitude.
But the important part is the order of magnitude, and that's the ten to the nine.
It's the exponent on the ten.
So we're talking about nine Powers of ten, essentially, for the age of the Earth.
Now all of that may have not made much
sense to you, so let's try and use something
that is familiar to all of us, in order
to understand the scientific notation, and let's use money, right.
Because we all understand the power of money, and we all know how much money
we have in our bank accounts and in our hand and what it feels like.
So what we're going to do is we're going to think about dollars.
We're goonna run through a set of examples thinking
about dollars and thinking about those dollars in terms
of order of magnitude.
So lets start off with lets say you have a dollar.
We all know what a dollar is.
And what can a $1 buy right?
Well basically these days a $1 will buy you a snickers bar.
Okay.
So $1 gets you a snickers bar and you know if you like snickers bars
that's great but your not going to be able to go much further than that.
So how about one order of magnitude more?
Let's jump up one order of magnitude, $10 and what will that buy you?
Well essentially $10 will get you a
you know,kind of bad compilation CD of 70s hits or a really great
one perhaps of Bob Marley depending on you know, which store you go to.
But that's what $10, when you jump one order of
magnitude, we go from a Snickers bar to a CD.
And what about the next order of magnitude?
That would be going up to 10 to the two, 10 raised to
the two power of dollars, $100, and what will it, that get you?
Well, that'll get you dinner at a nice restaurant, you know?
Not the fanciest
restaurant, but a pretty fancy restaurant, $100 should get you there.
So in two orders of magnitude, we've gone from a Snickers bar, which
isn't going to do much for you, to, you know, a nice restaurant.
Okay.
How about three orders of magnitude, $1000?
Well, $1000 will get you a plane ticket, you know, to some place nice.
Perhaps to, you know, a nice vacation, okay.
So $1000, three orders of magnitude takes us from
the Snickers bar to the ride on a jet plane.
One more order of order of magnitude, and that will take us up to a luxury car.
Now of course you're not going to be able to get a
luxury car for $10,000, but maybe for $60 or $70 or $80,000.
Again, this is what we mean by order of magnitude.
you might be able to at least, you know, get, get started on the luxury car.
Okay, so that is four orders of magnitude from the Snickers
bar to driving around in, you know, a nice Sports coupe.
How about five
orders of magnitude.
Well, five orders of magnitude will take you to you know, being able to get
that nice apartment perhaps that you could
use while you're driving around your sports coupe.
So, you know, $1000 got you a plane ticket to a nice place, could be Paris.
$10 to the 4, ten, tens of thousands of dollars gets you a sports coupe to drive
around in Paris and hundreds of thousands of
dollars will maybe get you an apartment in Paris.
Okay?
So just
five orders of magnitude, that's really what you have to think about.
Just five orders of magnitude took us from a Snickers
bar to a, an expensive apartment in a nice city.
Okay, and that is the important thing to see, is just five orders of magnitude
what the difference, the physical difference in our
experience would be, in having that much money.
Now in astronomy, we may easily jump up
15, 20 orders of magnitude in both size and
time scale, in going from one kind of physical process to another.
So getting a handle on orders of magnitude would be a really
essential thing for being able to understand the rest of the class.
Okay.
