### Ed Lu's Journal: Entry #6: Orbits

Status Report From: Johnson Space Center
Posted: Monday, July 14, 2003

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.

// end //