[MUSIC PLAYING]
Have we finally discovered Planet X?
And I'm not talking about yet another Kuiper Belt ice
ball, like Pluto, Haumea, Makemake, Eris, Quaoar, Sedna,
et cetera, et cetera, et cetera.
This is a potential near-Nepture sized planet.
The catch, it hasn't actually been seen.
[MUSIC PLAYING]
Caltech planet hunters Mike Brown and Konstantin Batygin
have been the trail of something big out there for some time.
Now, Dr. Brown apparently wasn't satisfied
as accomplice to the murder of Pluto, which
was demoted to dwarf planet partly
due to Brown's discovery of Eris,
a distant planetary body that's larger than Pluto.
And presumably is just one of many such rocks orbiting
the Sun in the vast Kuiper Belt, out beyond Neptune.
You see, Brown also found Sedna, a minor planet, whose elongated
orbit takes it out way beyond the Kuiper Belt.
It looks like it's been dragged out of the Kuiper Belt
by the gravitational attraction of something.
It was actually competing planet hunters,
Chad Trujillo and Scott Sheppard,
who first noticed that several Kuiper Belt objects had
these elongated orbits, orbits that are roughly
aligned with each other in the axis of their elongation.
They suggested the possibility of a large planet
out there, dragging on these objects
with its gravitational pull.
But it was Brown and Batygin who first ran
the exhaustive computer simulations
and found a single compelling solution,
a very, very distant giant planet,
with a mass well over 10 times that of the Earth,
and a stretched out eccentric orbit
with a period, a year-length, of 15,000 Earth years,
and an average distance to the Sun of 700 astronomical units.
That's 700 times the Earth's average overall radius,
placing it far outside the Kuiper Belt.
Given its mass, the best guess is
that it would also be a gas giant, something
like Neptune or Uranus.
It could be smaller.
But it could also be larger.
However, until we spot it, we can only
guess what it looks like or even whether it exists.
Now, the alignment of those weird Kuiper Belt orbits
is pretty unlikely to have happened randomly, a 0.007%
chance, to be precise.
So it seems pretty likely that something is out there.
Now, people have claimed the discovery of Planet X before.
Apparent discrepancies in Uranus' and Neptune's orbits,
which have now been debunked, nonetheless led to the original
discovery of Pluto, which is way too small to affect the gas
giants anyway.
But did we really find Planet X this time?
To quote Mike Brown, "This is different
because this time we're right."
Existing telescopes should be able to see this thing,
even if we don't know exactly where to look.
But believe me, we'll be looking.
OK, time for the answer to our photon clock challenge
question.
We asked you whether according to your perception,
a clock, or a photon clock, traveling towards you
at 50% of the speed of light, would
seem to have a tick rate that was slower, faster,
or the same as one that's moving away
from you at the same speed?
The answer, faster.
Why?
Because of the relativistic Doppler effect.
The relativistic Doppler effect classically
changes the wavelengths of light,
blue-shifting approaching material
and red-shifting receding material.
But it also affects clock rate.
You see, special relativity tells us
that a clock that's moving relative to you
will have a slower tick rate compared
to a clock that's stationary in your own reference frame.
However, that's based on a sort of instantaneous comparison
of the timelines of the two clocks.
To determine the observed tick rate,
you also have to factor in the travel time of light.
The best way to illustrate this is with a spacetime diagram.
For a refresher on how these work, check out this episode.
OK.
So a photon clock that stationary
on the spacetime diagram moves straight up.
By definition, ticks correspond to intervals on our time axis.
Now, a clock that first moves towards the observer
and the stationary clock, overtakes, and then moves away,
will have ticks that occur at a less frequent rate
when viewed from the stationary frame.
That's regular time dilation.
But what does someone in the stationary frame actually see?
To understand that, you need to draw lights
like photon paths between the moving clock
and the stationary observer.
Where those paths intersect the vertical world line
tells you the observed time interval between the ticks.
You see?
When the clock is approaching, its ticks
are more clustered than when it's moving away.
So the approaching clock ticks faster than the receding clock.
And this is just a complicated way
of saying that the approaching clock sort of chases
after its own photons, condensing
the distance between the light signals that carry those ticks.
While the receding clock is backing away from the photons
traveling in your direction, stretching out
the distance, and hence the time, between tick signals.
I also asked an extra credit question.
Does the approaching clock appear
to tick faster, slower, or at same rate compared
to a stationary clock?
To answer this, you actually need some math.
One effect, time dilation, slows down the tick rate
of the approaching clock.
At the same time, the relativistic Doppler effect
speeds it up.
So which effect wins?
Time dilation will slow a moving clock down by this,
1 over the square root of 1 minus velocity
squared over c squared.
That's the Lorentz factor.
The relativistic Doppler effect will speed up
an approaching clock by 1 over 1 minus v on c.
Combine these and you get what we call the Doppler
factor, which looks like this.
The length of the observed second
decreases by this factor for an approaching clock
and increases for a receding clock.
Our clock is moving at 50% the speed of light.
So this comes out to D equals the square root of 3.
The approaching clock appears to tick around 73% faster
than your own stationary clock.
While the receding clock appears to tick
42% slower than your clock.
If you think of just the time dilation, and not the Doppler
effect, you get that the moving clock is always
around 13% percent slower than your clock,
whether approaching or receding.
By the way, this is an effect that we see out there
in the universe all the time.
Quasar jets, pointing towards us, appear crazily bright.
And they pulsate much more quickly
than they should because our sense of their time
is compressed.
At the same time, supernovae that
are moving away from us due to the expansion of the universe
appear to die away far more slowly
due to the combined effect of time dilation
and the Doppler effect.
OK.
So many of you got the first part of this right
and for the right reason.
We chose three random entries from those
to get brand new "SpaceTime" t-shirts.
Far fewer got both the first and the second parts right.
And so to reward the extra credit kids,
we selected three of you to also receive t-shirts.
So more work means a better chance.
If your name appears on the list below, please
email us at pbsspacetime@gmail.com
with your name, mailing address, and typical US
t-shirt size, small, medium, large, extra large, et cetera.
Also, let us know if you prefer an I'll Science Any Question I
Want t-shirt or a Black Hole Orbits t-shirt.
For those of you who missed out, we'll
have more challenge questions in the future.
But we'll also have more t-shirt designs.
So don't be shy about supporting the show
by clicking on the link below for your very own "SpaceTime"
t-shirt.
And I hope you'll join us next week for a brand
new episode of "SpaceTime."