Ed Lu’s Journal: Entry #6: Orbits

Lately, it seems like every time I look out the window I see Canada.
A few weeks ago it seemed that it was always the southern
Andes Mountains and Tierra Del Fuego. While I have nothing
against Canada or the Andes Mountains, I got to wondering
why that is. It turns out there is a fairly simple explanation
for the “Oh Canada!” effect and the “The Andes
Again!” effect, but you have to understand a little bit
about orbits first. Plus, many of the really neat things I’ve
been describing about living on the ISS are a result of being
in orbit – so it’s worth a mention.

You may
have noticed that I keep mentioning the speed we are traveling
at up here – about 18000 MPH. That is the key to what keeps
us from falling back down to the ground. In fact, we are always
falling towards the Earth, it’s just that we manage to keep
missing it. I’ll explain. Think of standing on the ground
and throwing a baseball. The harder you throw it, the further
it goes before gravity pulls it to the ground. Obvious. Now
imagine you are incredibly strong and can throw the baseball
all the way across the country, or even half way around the
Earth before it lands. Now reach back and throw it even harder
– perhaps it goes three fourths of the way around the Earth.
What if you throw it even faster? Then maybe it will fly almost
completely around the Earth and land right at your feet. Now
throw it just a bit harder. What will happen? If there was
no atmosphere and therefore no air resistance to slow the
ball down, the ball would fly all the way around the world,
right past your feet, and keep going. Since it doesn’t slow
down, it keeps right on going and continues around the Earth
again and again. The ball would be in orbit.

For the
physicists and engineers out there, you know the story isn’t
quite that simple, but the basic idea is correct. The trick
to being in orbit is to get going fast enough that you go
all the way around the Earth in the time it takes gravity
to turn your direction around. While gravity is pulling you
downwards all the time and making you curve around the Earth,
the curvature of your trajectory isn’t enough to actually
run into the ground. If you think about a bit you’ll see that
there are some complications, namely you have to throw the
ball at the proper angle so it doesn’t run straight into the
ground, and also you have to show that the trajectory doesn’t
diverge after repeated laps. Of course you also have to make
sure you don’t go too fast, or you will just fly away since
the Earth’s gravity won’t be strong enough to pull you back
again.

So that’s
all it takes, a lot of speed and initially a little bit of
aiming to make sure you don’t hit the ground, and as long
as you are high enough so you are out of the atmosphere you
will just keep going round and round the planet. For orbiting
the Earth at our altitude, that required speed is about 18000
MPH. That is the purpose of the big rocket that our Soyuz
spacecraft sat on top of on the launch pad, and is also the
purpose of the Space Shuttles main engines and solid rocket
boosters – they both serve to lift their respective spacecraft
high enough to get out of the atmosphere, and then to reach
orbital speed. Once that is complete, they are no longer needed
– the force of gravity will keep the spacecraft in orbit around
the Earth. The Space Station and everything in it (including
Yuri and myself) are just coasting along in orbit, much like
the moon also orbits the Earth.

The interesting
thing about orbits is that the closer you are to the planet,
the faster you need to go. This makes sense since the force
of gravity decreases as you move away from the planet. That’s
how Newton first figured out his law of gravitation, by reasoning
that the moon was in orbit and figuring out that the force
of Earth’s gravity pulling on the moon had to be much less
than it was on the surface of the Earth. The effect of this
is that if you momentarily speed up in orbit, you will climb
to a higher orbit where in fact your speed will decrease.
We make use of this fact during the rendezvous of the Space
Shuttle and Soyuz with the ISS.

Even
though we are above almost all the atmosphere, there are still
traces left at this altitude which do cause some drag on the
space station. This has the effect of slowing us down slightly
over time. This then has the effect of lowering our orbit
where in fact our speed will then increase again, but at a
lower altitude. In order to stay out of the atmosphere, we
have to periodically boost our orbit back up again. A few
weeks ago we fired the engines for a few minutes on the Progress
which was already docked to the Station in order to compensate
for this small drag. The engines of the Progress are small
compared to the huge station, so our acceleration was very
little, and in fact we only used it to increase our speed
by 1 meter/sec, about walking speed. We tried to watch out
the window to see the engine firing, but we don’t have a window
which can see straight backwards, so we couldn’t actually
see much. We were able to show that the station was very slowly
accelerating by letting a pen float in the air. It slowly
started to move towards the rear of the station. Actually,
it was the station wall which was slowly accelerating towards
the pen.

A common
misconception is that the reason we are weightless because
we are beyond the Earth’s gravity. In fact, the reason we
are in orbit is exactly because we are being pulled downwards
by gravity – as I said earlier it is only because we are going
fast that we manage to keep from hitting the Earth. The reason
we are weightless here is that the entire ship around is also
being pulled by gravity in exactly the same way, so we are
both falling around the Earth together. It is the same feeling
that you get when in a roller coaster going over the top,
you feel light in your seat for a moment because the seat
is falling out from under you.

In a sense the entire Space Station has been pulled out from
under us. In fact, when flying around and doing flips inside
the Space Station, I am just doing exactly what divers do
when they do flips as they dive off a diving board. They are
“weightless” also while they are in the air, it
is just that they only get a second or so until they hit the
water. We get 6 months.

As I
described in my last letter, our orbit path is like a big
hoop around the Earth that we circle round and round. Meanwhile,
the Earth is rotating on its axis once a day inside the hoop.
Since the Earth is pretty close to a perfect sphere (but not
quite), its rotation doesn’t affect our orbit very much (think
about how you would notice if a perfect sphere was rotated
around – answer – you wouldn’t). As I mentioned before, the
hoop of our orbit doesn’t go around the equator, but rather
is tilted by 51.6 degrees. You can figure out why that is
pretty easily; our launch site Baikonur is not on the equator.
Since our orbit has to start from Baikonur, it has to be tilted
relative to the equator in order to pass over that point.

I’ve
included a picture here of a computer program we use to give
us our current position and show the track of our orbit across
the ground. In the middle of the screen, the two small red
rectangles with the little white circle between them is supposed
to represent the Space Station. The white circle around it
is roughly the patch of ground you can see if you look down.
Right now the Space Station is over Western Sahara (you can
see the zoomed insert in the lower left) and moving southeast
towards the bottom right hand corner. The white dotted lines
show the path that the Space Station will follow in this orbit,
as well as the next two orbits. The reason the 2nd and 3rd
orbits are displaced to the left is that during the 90 minutes
it takes us to complete a lap around the hoop, the Earth has
rotated by one 16th of a revolution to the right, so our orbit
track is displaced to the left by that much each time. You
can see that we never cross over any point with latitude greater
than 51.6 degrees, so we never get to see the North or South
poles from here. You can also see that if we do go over a
point, we go over it twice a day: once going northeast, and
once going southeast.

The shaded
areas of the map are the areas in darkness, and the rest of
the map is in daylight. If you are wondering why the day-night
line curves up and down, it is for the same reason that our
orbit curves up and down – namely the sun isn’t over the equator
so that while half the Earth is lit up that half doesn’t line
up with the equator or one of the lines of longitude. You
can see that now in the summertime, very far northern points
will always be in daylight.

From
the map, you can also see that part of the solution to our
puzzle is that our orbit tracks at the far northernmost and
southernmost parts run due East. That means that on repeated
orbits we’ll get to see the same point again. That doesn’t
happen for points near the equator since as you can see our
orbit path is southeast or northeast so if you see a point
once, you won’t see it again on the next orbit, at least not
very well. So you are likely to see points near the southernmost
and northernmost parts of our orbit more frequently. But then
why Canada and not the Andes now, and why the opposite a few
weeks ago?

The answer
has to do with timing. The shaded portion of the map and our
orbit track both move left together over the course of the
day as the Earth rotates underneath us, so picture the map
as sliding to the right while the dotted lines and shaded
area of the screen stay in position. From the map you can
see that when Canada crosses under our orbit, it will be roughly
in the middle of the bright region, meaning in the middle
of the day in Canada. When we are crossing the southernmost
part of our orbit (i.e. the Andes) it is nighttime. At the
time this picture was taken the “Oh Canada” effect
was in full force. During our workday (we live on a timezone
roughly halfway between Houston and Moscow – Greenwich Mean
Time), we tend to look out and see Canada, especially since
we have free time in the evening, which is the middle of the
day in Canada.

This is a screen shot of the computer program we use to tell where we are. The places labeled EOS are locations that scientists have requested photos of. Godzilla is shown for scale.

It turns
out though that our orbit hoop slowly rotates due to the fact
that the Earth isn’t quite a perfect sphere. This turns out
to apply a torque to our orbit which makes it slowly shift
westward with respect to the sun, and therefore the lighted
part of the screen. It is the same effect that makes a spinning
top wobble. In effect our orbit is like a large top, and the
fact that the Earth has a bit of a bulge around the equator
causes our orbit hoop to wobble slowly. In a few weeks, the
southernmost part of the orbit will be in the fully lit section
of the orbit, and we will be back to seeing lots of the Andes
again. Actually I’m looking forward to our orbit track shifting
a bit since I am trying to take a photograph of the Great
Wall of China. Right now, of the two times a day we cross
over it, once is during our sleeptime when we are heading
southeast. The northeastbound crossing is during our awake
hours, but it is very close to sunrise in Beijing, so the
lighting is bad and it is difficult to take a photo.