Tuesday, October 13, 2009

Orbital Mechanics Extremely Simplified

After reading this, you’ll understand how is it that something stays up there and doesn’t come crashing down unexpectedly.

An orbit is, as taken from a dictionary, “the path of a celestial body or an artificial satellite as it revolves around another body”. IT is exactly what it means. Something just going in circles around something. No, not your kids when they attempt to burn you at a makeshift stake. A CELESTIAL body or an artificial satellite. An example of a celestial body is… our very own planet Earth!

Why? Because it’s going in circles around the sun. It’s a 365.25 day long circle, but a circle nonetheless. An easier example is the moon, going around the Earth.

An example of an artificial satellite is, well, one of many satellites you might be using to watch your favorite TV channel. When a shuttle launches and performs its mission in orbit, it is, well, IN orbit, so it’s considered an artificial satellite at that point. The International Space Station, or ISS, is also a perfect example of an artificial satellite. The ISS typically has a roughly 90-minute orbit, meaning it can do 16 laps around the Earth in a day. They have 16 sunrises and 16 sunsets per day. Talk about a ‘fast-paced environment’!

So how does it stay up there? Is it because there’s no gravity?

NO. Even at 200 miles above the Earth, there’s 80% gravity. So, how come the space shuttle, satellites and ISS stay up there without using any engines to stay up?

Two words. Permanent freefall.

Grab a transparent plastic cup. Put 2 or 3 colored paper clips. Cover the cup. Now throw it up, but not too hard. You’ll notice that when it reaches the top part of the climb, when it drops down again, the clips inside seem to float before flying towards the top of the cup. It all happens extremely fast, but you should notice that. In that micro-instant, the clips were floating as their falling speed matched the cup’s. That instant is known as free-fall, or as others would recognize the term, the feeling of weightlessness.

When astronauts go up to space, they have already experienced weightlessness so they know what they’re dealing with, but how do you recreate that feeling on Earth? Simple. Grab a plane, go up real high, then let the plane drop. Anyone inside the plane will immediately feel weightless, and everyone inside will float… until the plane runs out of altitude to keep dropping from, so it’ll have to pull up to avoid crashing into the ground, and immediately, everyone will feel heavy and drop down. NASA has a contract with a company called Zero Gravity Corp that does exactly this. They also give shorter rides to paying customers for around $5000 a ride (go http://www.gozerog.com if interested). They’re shorter because the sensation of going weightless and going back to weighting a lot again will cause nausea to people with queasy stomachs (hence, the airplane’s name, the Vomit Comet). Astronauts are trained to bear this so their training rides are longer.

Now, we threw the cup straight up. The same can be achieved if you throw it up at an angle, which would be similar to a shuttle blasting off into orbit. The harder you throw it, the more time gravity takes to pull it down to the ground. Even harder, and gravity takes even longer. Do you notice a pattern?

…eventually, throw an object hard enough, and gravity will take from almost forever to forever to pull it down, and this object is considered being in orbit around the Earth. This is how the shuttle achieves orbit. It accelerates to insane speeds, speeds where gravity will never be able to pull it down, but still has a sufficient hold on it to keep it going around the Earth. Thanks to the upwards of 17,000 MPH speeds acting against the 80% pull of gravity, the shuttle remains in orbit, and doesn’t slingshot away from the Earth. Higher speeds will result in higher, longer orbits, until you reach what is called “escape velocity”, in which you’re going so fast, the Earth’s gravity can no longer pull you back and you just keep going into space. We don’t want that to happen, so they stay within 17,250~17,500 MPH.

A quick note. If the shuttle can stay up without engines if travelling fast enough, why does it have to be at such a high altitude?

Atmospheric drag and friction.

Run a car to 65MPH. Crank the window down and put your hand out, the palm of your hand aiming at the airstream. You will feel that the air is pulling your hand backwards. The air, when one is going fast enough, actually acts as a braking force. At higher Mach (faster than sound) speeds, the air then causes heating due to friction of the air particles running through the object. The shuttle would be a fireball if it were travelling at such speeds at a low altitude. Not good. That’s why it must ascend (climb) to where there are no air particles whatsoever: above 400,000 feet. THEN it can accelerate undeterred AND stay in orbit.

Alright, so now we know how the shuttle stays up there. Quick notes on 2 orbit terms. There are usually some variations in the orbit altitude, and these are identified as “apogee” and “perigee”. Very simple terms. The apogee is the point in orbit where the altitude is highest. The perigee, always on the opposite side of the orbit, is the lowest point. Quick example, an orbiter reaches its apogee at 150 miles above the Earth. It then slowly decreases altitude until it reaches perigee on the other side of the planet, at around 135 miles above the planet. It then increases altitude until it again reached apogee, again on the other side, once again at 150 miles above the Earth, and the cycle repeats.

So, how does it change its orbit? Just accelerate and that’s it?

No. A simple rule applies. If you want to change an orbit, you must increase or decrease your speed precisely at either the apogee and/or perigee. Changing your speed in perigee will affect the apogee’s altitude. The other way around is also true. Changing speeds at apogee will change the perigee altitude. Increasing speeds will increase the other point’s altitude, and decreasing speed decreases the altitude at the other point. There might be irregular burns done at a point other than perigee or apogee, but these are rare, thanks to NASA programming their launches in a way that taking off at one point will identically match the orbit they’re trying to get to, meaning they only need to make certain adjustments to altitude in order to catch up to what they’re trying to reach (thus, saving fuel). The changes in speeds are measured in feet per second, since the changes in speed are subtle, but it affects the altitude greatly.

There’s another rule applied here when trying to catch an object in orbit. It’s called Kepler’s Law, actually, the third law. Basically, and as an example, an object travelling at 17,250 miles per hour at an altitude of 125~150 will actually travel faster than an object going at 17,300 MPH, but at an altitude of 225~230 miles. In other words, higher orbit means longer orbit, lower orbit means faster orbit.

To view this, it’s simple. Draw a small circle, and draw a bigger circle, and then an even bigger circle. You’ll end up with 3 circles, one inside the other. The smallest one is the Earth, and the bigger one is orbit 1, and the largest one, orbit 2. Then, trace with your finger at a slow speed, so you take 10 seconds to make a lap on orbit 1. Now, using that same speed, trace your finger around orbit 2. You’ll notice it took you longer than 10 seconds to make a lap.

That’s Kepler’s Law in effect. Assuming both objects on both orbits are going at roughly the same speed, give or take a few hundred miles, the wider the circle (the higher the orbit), the more time it will take to go around the Earth.

A ground example of this is a race. There are 5 tracks on a racetrack, and the racetrack has curves. However, the ones running on the inner tracks have a starting position that is behind the ones who are on the outer tracks. This is done because the ones on the inner track have less of a curve to go around than the outer track, so they clear these curves faster. The race coordinators calculated how far back each of the inner track racers need to start so if they all run at the same speed, when they come out of the final curve, everyone will be evenly matched.

This is used as an advantage to NASA to catch up to satellites or the ISS. The ISS is in an orbit of roughly 225 miles, give or take a few miles. When the launch window opens for the shuttle, it takes off, MATCHING the ISS’s ground track. Therefore, it only needs to go a bit faster to catch up to the ISS if it’s too far ahead. So the shuttle remains at a lower orbit, going slightly “faster” than the ISS in relation to the Earth, until it catches up. At this point, the shuttle changes its altitude, in a series of burns designed to roughly match the shuttle’s altitude with the ISS, precisely at the point where the ISS is very close to the shuttle, around 40,000 feet away. The shuttle then uses its RCS thrusters to close the distance and fine-tune and match its speed with the ISS, before it docks with it.

In orbit, the shuttle has several dimensions of movement that are unavailable/impossible for us who are at gravity’s mercy. It can roll, it can pitch, and it can yaw, and it can translate up, down, left, right, forward or back. Those movements are divided into 2 categories, Rotation and Translation.

For rotation, grab a tennis ball. Roll it forward or backwards. Now imagine it doing that while staying at the same place. Now imagine the shuttle doing that. That’s the pitch up and pitch down. Now, same exercise, but make the ball roll left or right. That is the roll of the shuttle. Once more, but this time, SPIN the ball to the left or right. This is the yaw of the shuttle. The rotation controls of the shuttle affect the attitude of the shuttle.

For translation, use the same tennis ball, only now, imagine the shuttle remaining in the same direction it’s pointing at, and that it’s simply drifting to the directions given. The shuttle can move forward, it can back up, or move backwards, just like a car. The difference is that it can also move left and right, unlike a car which can only go forward or back. And of course, it can move upwards and downwards like an elevator. The translation controls affect the position of the shuttle.

Rotation and Translation are combined to affect the attitude and position of the orbiter, and it can get to places like that. Usually, when docking to the ISS, it must maintain a precise attitude so the docking adapter can latch into the mating adapter of the ISS precisely and without any angles. And of course, it must be positioned exactly so that the mating adapter is centered with the orbiter’s docking adapter, before slowly closing in to dock.

Well, I guess that’s it. For my next blog, I’ll explain the abort modes available during ascent of the shuttle, and after that, descent and landing. I need to finish this before STS-129 Atlantis takes off in November…

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