Our solar system's an exciting place. 
one of the most exciting developments in 
the past few decades has been the 
realization that our solar system is not 
unique. 
There are solar systems all over the 
place and we're starting to learn 
something about them. 
And it seems very fitting to end this 
week of solar system science with some 
discussion of what it is that we found 
out there, the topic that goes under the 
name extrasolar planets, or exoplanets 
for short. 
And so, 
the fact that planets should exist around 
other stars and that the sun is not 
unique in having planets is an old idea. 
the fact that we saw protoplanetary disks 
around stars suggests that many stars 
will have planets. 
and people have been looking for planets 
around other stars for a long time. 
The first successful discovery was in 
1988, so only 27 years ago. 
by now at last count, there are 853 
confirmed planets orbiting 672 different 
stars, so we have whole solar systems 
that we have found and the field is 
growing very fast. 
I think we're just starting to learn what 
these extra solar systems have to teach 
us. 
finding planets is a tough business. 
what you're looking for basically is a 
chunk of rock or gas that is not hot and 
is not glowing and is very near to 
something, a star, that is hot and is 
glowing, so it is a difficult problem 
trying to actually see a planet at great 
distance. 
we see the light of the star, but seeing 
the reflected light off a planet is a 
difficult proposition. 
despite this, it has been applied and all 
32 planets and 38 systems have been 
actually imaged. 
In other words were found in actual 
images of a star, the way this is done is 
the same way we will learn next week. 
technology developed to image the outer 
regions of the star, of the Sun, the 
corona when basically superimposes a disc 
that blocks out the star light in the 
one's telescope and then looks for the 
dim lights around it. 
there are future missions that are 
designed to specifically image extra 
solar planets and we might be able to 
increase the rate of discovery. 
Anyone can learn a lot about a planet if 
one can actually image it. 
But most of the 900 planets we've seen 
have not been discovered that way. 
In fact, most of the time, all you can 
see is the light of a star. 
So, how does the light of a star tell you 
that there is a planet orbiting it? 
The following few simulations might help 
understand that. 
One key to understanding how a star can 
tell us that a planet is orbiting it is 
to remember that if a planet is orbiting 
the star, then the star is also orbiting 
the planet. 
In fact, they are both orbiting their 
common center of gravity as this 
animation here will show us. 
We have here a planet and a star. 
I have just, for the purposes of 
discussion, given them a mass ratio of 
one to four. 
And, what we see is that they each orbit 
I've assumed a circular orbit and they 
each orbit in a circle about the relative 
common center of mass, which is here this 
green X. 
And what we see is that, the radii of the 
two circles are of course distances from 
the center of mass. 
In other words if the larger star here is 
four times as massive as the smaller as 
the smaller planet, then the radius of 
the orbit in which the star orbits is a 
fourth the radius of the orbit in which 
the 
planet orbits. 
In other words, if this, orbital radius 
is our and this orbital radius is our 
planet, 
then, since they're orbiting their center 
of mass, these satisfy mass of the planet 
times the radius of the planet's orbit is 
equal to the mass of the star times the 
radius of the star's orbit. 
And of course, the distance between the 
planet and the star, since they're on 
opposite sides, are the distance is 
simply rs plus rp, 
the sum of the two radii. 
And this distance is constant at all 
times, 
of course, most planets don't orbit in 
circular orbits but as usual we will make 
that simplifying assumption, it'll help 
us make calculations more 
straightforward. 
Of course, since typically, a star is far 
more massive than the planets that orbit 
it, the star will move a far small, in a 
far smaller circle than well the planets 
and detecting the motion of a star might 
be difficult because the motion is very 
small. 
To give us a sense for, of how this works 
we'll try to detect, imagine detecting 
from a distance, a solar, the planets of 
a solar system we understand, namely our 
Solar System. 
And indeed, because earth orbits the sun, 
the sun is also orbiting the earth, 
the center of mass of earth and sun lies 
well deep within the sun. 
And it would be very difficult to 
actually note the motion of the sun. 
In fact the only planet whose common 
center of mass with the sun lies outside 
just outside the surface of the sun is 
Jupiter. 
And in this animation, we see that if we 
take into account only the gravitational 
effects of Jupiter, then we observe the 
sun moving, around in a circle around a 
point just outside the surface of the 
sun. 
Saturn's influence is the next most 
remarkable and because we now have two 
periodic motions, the sun's motion is a 
little bit more complicated and no longer 
moves in a circle. So by doing some 
interesting analysis, we could, in fact, 
disentangle perhaps, the two motions due 
to the sun, to Saturn and Jupiter if we 
can observe this motion. 
So, we need to understand how 
far the sun is moving and try to see what 
limits this places on our ability to 
detect planets. 
So now, we, we, we have an idea. 
Maybe we can observe that a planet is 
orbiting a star by watching the star 
wobble. 
We need to understand how much the star 
will wobble. 
We expect it not to be very much, 
but because it is a periodic motion, we 
might be able to actually distinguish it 
and realize that what is going on is that 
it, there's a planet orbiting it. 
And we said, that if we assume circular 
orbits, there's a distance r between the 
star and the planet, then we can write r 
as R is the radius of the circle in which 
the star moves plus the radius of the 
circle in which the planet moves and the 
two radii are determined by the center of 
mass relation. 
And plugging one relation into the other, 
I see that the total distance is Rs + Rp, 
but Rp is Rs * Ms / Mp. 
We write it this way and now, I can solve 
this equation for Rs, 
Rs = to R / 1 + Ms / Mp. 
And then, I can pick a common denominator 
on the bottom to write Mp + Ms and Mp 
comes here. 
Mp + Ms is nothing but the total mass, 
which I'll call M. 
And this is not surprising, their amount 
by which the star moves, is related to 
the distance between the two by the ratio 
between the planet's mass and the total 
mass, the larger the planet the more the 
star will move. 
Not too surprising, lets see what that 
tells us for example about an idea, 
let's try to detect Jupiter. 
How far would the sun move? 
Well, plugging in this result we just 
figured out. 
I find that the radius of the circle in 
which the sun moves due to the 
gravitational effect of Jupiter is the 
ratio of the mass of Jupiter to the mass 
of the sun times the radius of Jupiter's 
orbit, which I've put in here and that's 
indeed right outside the sun. 
This is 740,000 kilometers. 
The sun itself is about 696,000 
kilometers in radius. 
This point lies right outside the sun. 
Detecting the wobble of a star due to the 
effects of a planet that orbits it is 
going to be difficult. 
In fact, of all of the planets that we 
know, one was detected by this method, 
this is called astrometry. 
So, 
finding the motion discerning the motion 
of the star is not going to be our most 
successful strategy. 
What else can we do? 
Let's go back to the simulation and see a 
different approach. 
The secret, it turns out, 
is that while it is very difficult to 
measure the position of a star with the 
precision necessary to detect a planet 
surrounding it, 
we may be able to detect its wobble by 
measuring its velocity. 
How can you measure velocity without 
measuring position? 
That's an interesting question. 
Well, there is a sense in which we can 
measure velocity directly without 
measuring position and this is the 
Doppler effect. 
Remember that the spectrum of a star will 
contain absorption lines for whatever 
gases are in the star's atmosphere, as we 
saw for the spectrum of the sun, 
we can identify a particular absorption 
line and find that it is shifted in 
frequency or in wavelength from its 
natural wavelength. 
We can use the Doppler formula. 
I remind you that lambda is lambda 0 * 1 
- v / c, where c is the speed of light 
and v is the speed with which something 
is moving. 
Since spectral lines are very, very 
narrowly known we can measure rather 
small 
velocities compared to the speed of 
light. 
In fact, down to a few meters per a 
second. 
So one part in 10^8 we can make pretty 
accurate velocity measurements provided 
there is a Doppler effect. 
Remember, the Doppler effect only obtains 
if the object to the source of light is 
moving towards us or away from us. 
So in the position in, that, this 
animation currently depicts, of course, 
we have no such luck, because as this 
planet orbits the star and the star 
orbits the planet, 
there is no motion at all 
no change in the star's distance from us 
so there, that there is absolutely no 
radial velocity component. The star or 
the planet neither approach us nor 
recede. 
On the other hand, if I tilt and I 
imagine that the system happens to be 
oriented in this direction, 
then what I observe is that now the 
planet, and therefore the star, 
periodically approaches earth and recedes 
from earth and maybe we can detect the 
variations in wavelength of some 
absorption line by measuring the velocity 
with which the star is moving. 
And, the way we do this is precisely by 
doing spectroscopy. 
Let's take a look. 
This animation sort of shows you the set 
up. 
We have here a planet orbiting the star, 
therefore the star orbiting the planet, 
albeit in a much smaller circle. 
We cannot see the planet, but we can see 
the star and things here are perfectly 
aligned. 
The motion of the system is in such a 
plain that the entire velocity of this 
vector of the star will be visible to us. 
There is no motion out of the plain of 
this image, which would be invisible to 
us and we observe some absorption lines 
in the spectrum of the star. 
And when the star is receding from us, 
the absorption lines are shifted to the 
red, when the star is approaching us, 
they are shifted to the blue. 
And in, we see this periodic shift in the 
Doppler 
shift in the absorption lines and by 
detecting the periodicity, we can measure 
the period with which the planets orbits 
the star and perhaps learn some more. 
Of course, the Doppler shift here is 
greatly accelerated. 
Let's do a little calculation to see what 
kind of velocities we'd be trying to 
detect. 
So perhaps, the way that we can detect 
the fact that a planet is orbiting a 
star, hence the star orbiting a planet, 
is to hope that the orientation of the 
orbit is such that at least some fraction 
of the star's motion is radial towards us 
or away from us and we can use Doppler 
shifts to detect that velocity. 
Let's figure out how fast the star would 
be moving. 
so we have the system. 
how fast is the star moving? 
Well, the star moves around the circle of 
radius Rs, as we said, 
and it moves with a velocity speed Vs, 
whose velocity is continually changing. 
So, 
as we know, the acceleration, from our 
second week of class, the acceleration 
with which the star accelerates towards 
the center is Vs^2 / Rs and if I multiply 
this by the mass of the star this is the 
force acting on the planet, on the star 
to accelerate it and of course this is 
Newton's gravitational force. In other 
words, this is G * Mp * Ms / by the 
square of the distance between them. 
So let's put that in. 
Here's our equation. 
what do we do with this equation? 
Well, of course. 
we first realize that the Ms completely 
cancels from here, 
this is characteristic of gravity. 
now what I want to do is figure out v. 
I want to know how fast the star moved. 
so from here, I have that vs^2 is given 
by G times the mass of the planet times 
the radius of the circle in which the 
star moves divided by R^2. 
But it would help to remember that we 
computed that the radius of the circle in 
which the star moves is related to R by 
the mass of the planbet divided by the 
total mass. 
And so, using that in here, I find that 
this is G * Mp / R^2 * R * Mp / total M. 
And what I find is that this is given by 
well, I can cancel one of the Rs here and 
I find that vs^2 is g * 
Mp^2 / M * R, 
which is almost nice, except I will find 
it more convenient to write G * M / R, 
this is a quantity with dimensions of 
velocity squares, * ratio of Mp to the 
total M^2. 
All I've done here is multiply and divide 
by the mass the total mass. 
And so, this is my expression for vs and 
when I plug it in, I see that the 
following things are true for M is 
usually typically just the mass of the 
star, the mass of the planet is small. 
Anyway what we see is that massive 
planets will cause more motion. 
This is certainly true, 
but, unlike the case in the when we were 
trying to do astrometry, in the case of 
radial velocity measurements, the closer 
a planet is to its star, 
the smaller R, the more 
radial velocity the star will acquire. 
So this method will be useful in 
discovering planets that are massive and 
orbit close in. 
We can solve this equation now for vs by 
taking the square root and this is the 
expression we get. 
Again, the largest values of velocity 
will arise from heavy planets that orbit 
near their stars. 
We can plug in the numbers for Jupiter. 
If you look at this quantity in the 
square root, it's simply the orbital 
velocity of Jupiter to good 
approximation. 
And so, plugging in the numbers we see, 
that due to Jupiter orbiting it, the sun 
moves at 12.5 meters per second. 
This is a small velocity relative to the 
speed of light, but wavelengths can be 
measured with extreme precision. 
We would have very little trouble if 
orbits were aligned correctly, 
identifying the motion of the sun by ten 
meters per second, and in fact, this is 
one of the most productive ways of 
detecting extrasolar planets. 
a total of almost 500 planets in almost 
400 solar systems have been detected by 
what we call radial velocity 
measurements. 
And remember, 
this is only possible for a systems so 
aligned that part at least of the motion 
is radial. 
If the system happens to lie so that the 
motion of the planet in the star is 
perpendicular to our line of site, there 
just is no radial component, 
there is no Doppler shift. 
We're out of luck trying to find it. 
despite this, this has been one of the 
most productive ways of measuring it. 
But if the system is aligned properly, 
we can do even better. 
Let's check this out. 
One great advantage of the radial 
velocity measurement detection is that if 
we have some way of estimating mass of 
the star, independently, we'll see that 
we have such methods, then, it gives us 
information about the 
mass of the orbiting planet, 
ass well as the distance at which it 
orbits. 
And so, we can extract the beginnings of 
more data about what kind of planet we 
see, and what kind of orbit. 
And there some circumstances, if the 
alignment is just right, we can do even 
better. 
if the alignment is such that the planet 
in fact transits in front of the star, 
then the planet will partially eclipse 
its star. 
And the way we will observe this is that 
the star light appears to dim when the 
planet is transiting and we call this 
measurement measuring the light curve. 
The light curve is the dependence of the 
brightness of the star on time. 
And, what we will see is a periodic 
change as the brightness of the star dips 
periodically, 
when the planet transits it, we can use 
this to compute the period. 
We can use this to study from the details 
of the shape of the light curve. 
You can learn many things about the 
planet and such as its size, its mass. 
If we're lucky, we might even see the 
planet's atmosphere beginning the eclipse 
process, and see the star through the 
planet's atmosphere, and attempt to do 
spectroscopy, and understand the 
chemistry of this star's atmosphere. 
So in principle, the transit method is a 
very constructive method, which gives us 
a lot of information. 
Some 300 planets and over 200 systems 
have been detected. 
There's a dedicated space telescope, the 
Kepler Space Telescope, which is doing a 
survey of the sky and already has over 
2,000 candidate planets and over a 1,000 
candidate systems. 
But the transit system the transit method 
is not considered a complete detection 
until verified by some other means, so 
these are undergoing verification. 
The sample of planetary systems that we 
have outside the solar system is 
certainly growing very quickly and we 
should have a lot of information. 
Ideally, when detects the same planet 
both using radio velocity and transit 
method and then one can extract lots and 
lots of information. 
We will talk more about transits when we 
talk about binary stars and light curves. 
There are a few other methods that have 
been used. 
The lights of a star can be intensified 
by the place, presence of the planet, 
and some sixteen planets have been 
observed this ti-, this way. 
If we have one transiting planet, we can 
study its, orbit and find protobations to 
its orbit, and describe them to another 
planet, and learn about the existence of 
the other planet in the same system. 
Some planets have been detected this way. 
In all, we're compiling the collection of 
solar systems and it helps us to see, 
well, 
how do they stand to our understanding? 
How does this match our understanding of 
our solar system? 
We developed sort of a good theory that 
describes the one solar system in the 
universe, 
but now that we suddenly have thousands 
of them, you can ask does this theory 
work? 
And so, what have we found? 
well this, as this image clearly shows, 
we haven't looked very far. 
We've looked to about 300 light years 
around the solar system, 
that's a tiny fraction of the galaxy. 
We have all these thousands of planets, 
depending on how exactly you make the 
estimate, and as I said, this is a young 
science between one and 40% of sunlight 
stars have planets. 
Either number means that in a galaxy with 
a few hundred billion stars, there are 
lots and lots and lots of planets and 
planetary systems all over the place. 
no, the solar system is not unique. 
Now, the methods that we've used, both 
the, the most constructive ones, both the 
transit method and the radial velocity 
measurement method are most sensitive to 
what we call hot Jupiters planets that 
are very massive and orbit very near 
their star. 
Remember, we saw that with the radial 
velocity measurement. 
It's also true that it's more easy to 
arrange an alignment if the planet is 
close or methods are sensitive to hot 
Jupiters. 
Maybe that's not, it's not surprising 
that mostly we find, at least initially, 
lots of planets with masses similar to or 
larger than Jupiter's orbiting at 
Mercury-sized orbits. 
Now, 
well yes, there is a sample bias going on 
here, clearly a selection bias. 
if one had a detector that was only 
sensitive to unicorns and one found no 
coyotes, this would not be a surprise. 
But if one had a, a detector sensitive 
only to unicorns then found unicorns, 
that would still be a discovery. 
Discovering all these gas giant planets 
orbiting within a half an astronomical 
unit of a sunlight star should still be 
jarring, because, remember we explained 
that great length, Y, it is impossible 
for such planets to form so close to the 
star, because the solar nebula is too 
warm and 
volatile materials are not solid. 
What we learn from the fact that they 
exist is presumably they did not form, 
did not position, 
they formed farther out where the nebula 
was colder, and migrated in. 
So the kind of migration that the Nice 
model proposes for the solar system 
apparently is occurring all over the 
place. 
And this indeed, seems to be a ubiquitous 
feature of the solar systems we're 
finding the kind of sedate stability that 
we see in our solar system is not 
actually the standard. 
There's lots of strongly interacting, 
very resonant orbits, instabilities 
in that sense, at least, the orbits we 
are find, we find in our solar system are 
a little bit uncommon. 
What are the planets like? 
Well again most of the planets we find 
are very massive and lots of them are 
very closed in. 
If you look at this logarithmic plot 
right in the center of the plot over down 
here is our Earth with 
and then the horizontal axis is the 
distance from the star, 
the vertical axis is the mass of the 
planet. 
Both of these are logarithmic. 
So most of the planets that have been 
found are much more massive than earth. 
In fact, much more massive than Jupiter 
up here. 
And many of them orbit very close in, 
these are these hot Jupiters that, we 
spoke of, 
but we're also finding planets that orbit 
out at far larger distances from their 
stars and we've even found some planets 
that are on the order of magnitude of 
earth's mass or less. 
And so if you take the selection bias 
into account, the prediction is that the 
fact this data suggests that there are 
earth-like planets in much larger numbers 
than there are Jupiters or gas giants. 
Because, the fact that we're detecting 
them at all means they are far more 
common. 
we also find some super duper Jupiters, 
some gas giants with masses, 
15, 20 times the mass of Jupiter. 
Much larger than one thought planetary 
systems could create. 
And some interesting, strange cases like 
a planet called Kepler-16b that orbits a 
binary system. 
So two stars orbiting each other with a 
planet in an almost perfectly circular 
orbit around the center of mass of the 
system. 
this had been thought to be impossible to 
arrange in a stable orbit and Kepler-16 
shows us that nature manages to find a 
way. 
So, the field of extrasolar planets is 
despite the fact that it's been a few 
decades since we first discovered the 
first ones. 
This is really a field in its infancy, 
we're just starting to learn what we can 
learn from these exciting systems. 
And well, I anticipate a lot of news, 
both in terms of discovery and in terms 
of insight into how solar systems work in 
the coming decades. 
Let's sum up a busy week. 
Well, we found a lot to learn, 
right, in our own solar neighborhood. 
A lot of it, both in our solar system and 
certainly beyond is just being learned. 
I hope you're starting to develop an 
appreciation for the fact that we tried 
to understand some of the fundamental 
physics, because whatever we can, we can 
apply, we can actually understand what is 
going on, 
we can make calculations, that tell us 
what to expect and match them to 
experiment. 
I think understanding the physics, 
roughly of the greenhouse effect might be 
a good example of this. 
And, as I said exoplanets are probably 
going to eventually completely change the 
way we think of solar systems and so stay 
tuned. 
we've not covered many of the interesting 
topics in the understanding of our solar 
system. 
I want you to think of this week more as 
a hunting license. 
You now have 
the tools to go and read about the moons 
of Jupiter and why it is bizarre that 
Neptune has a moon that orbits completely 
outside the ecliptic, what that probably 
tells you about Triton and so on and so 
forth. 
And so I think you are equipped with at 
least the tools to go and acquire 
information. 
next week, we aim for the stars.