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Lagrange Points

In orbital dynamics, there are very strange things that can happen.  One of those is the idea of Lagrange Points.  When you have two bodies that are orbiting each other (like the Earth orbiting the Sun or the Moon orbiting the Earth), you can get points in which the forces cancel such that you can put satellites there and they will basically stay in the same spot (mostly).  There are five Lagrange points, as illustrated below. These are very strange and sort of unexpected!  I thought that I would explain how L1 and L2 are created and wave my hands for the others, since the physics is exactly the same.

Lagrange_Points
The five Lagrange points between the Sun and Earth (from space.com)

To illustrate, we will consider the Earth-moon system, since that is a bit closer to home. Let’s start with the most basic thing: Earth’s gravity.  Earth has gravity that essentially goes outwards forever . Even Jupiter “feels” Earth’s gravity – it is just really weak.  Just to make sure that we are all on the same page, Earth’s gravity is towards Earth. 🙂

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Let’s switch to the moon. When you are standing on the moon, you are always being pulled towards the moon, but if you look at this from the Earth’s perspective, this “towards the moon” can be either “towards the Earth” or “away from the Earth”, depending on which side of the moon you are on.  If you are on the side facing the Earth, the moon is pulling you away from the Earth.  If you are on the “Dark Side of the Moon” (i.e., the side of the moon facing away from the Earth), then the moon is actually pulling towards Earth.  Weird, right? Take a look at the plot:

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So, if you next consider Earth’s gravity and the moon’s gravity together (plot below), you can see three things: (1) when you are close to the Earth, Earth’s gravity “wins”, and you are pulled towards Earth; (2) on the far side of the moon, Earth’s gravity and the moon’s gravity point in the same direction (towards the Earth), so they add together and you would be a little heavier on this side of the moon; and (3) when you are close to the moon, but on the Earth side of the moon, the moon pulls you away from the Earth and the Earth pulls you away from the moon, so you would weigh a bit less on this Earth side of the moon.  At some point between the Earth and the moon, there is a location in which Earth’s gravity (pulling you towards Earth) and the moon’s gravity (pulling you towards the moon) cancel each other and you have a gravitation null.

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Solving for this gravitational null (see below) is a pretty standard high school physics problem.

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Up until this point, we have only considered gravity.  This would be fine if Earth and the moon were fixed in place, instead of the moon orbiting around the Earth. But since this is not the case, we have to consider the orbital motion.  The moon goes around the Earth once every 28 days (roughly).  You can then ask the question about how much force is needed to keep the moon moving around in a circle instead of the moon flying off in a straight line.  This is the centripetal force.  You can experience this force if you go on a merry-go-round that is spinning fast. You have to hold on to something to keep from being flung off of it.  If you are standing at the exact center, then you don’t feel any force at all, but as you move further and further towards the edge, you end up feeling more and more force.  You should totally go and try this.

Well, the same force works in space.  If you have an object going around another object, it feels an outward force (well, the object wants to continue to move in a straight line, which we interpret as an outwardly directed force).  If we pretend that the moon is sitting on a gigantic merry-go-round at the position of the moon, and the merry-go-round is spinning exactly the same speed as the moon is going around the Earth (one revolution every ~28 days), the acceleration that you would feel at any point along the merry-go-round would be this:

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Notice that the acceleration is always away from Earth, just like on the merry-go-round, you always feel a force pushing you away from the center.  Now, the Earth and the moon are not sitting on a gigantic merry-go-round, so this is really a thought experiment, but you get the idea.

This ends up being a third force/acceleration that is felt in the Earth-moon system, and so it needs to be included in all of our accelerations that we talked about earlier:

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Notice that the centripetal acceleration is pretty much nothing compared to the Earth’s gravity until really close to the moon.  Is that a coincidence?  No!  What is the force that makes the moon orbit the Earth? Gravity balanced with centripetal acceleration!  If you trace the Earth’s gravity line (which turns into a dotted red line) and the centripetal acceleration line, they cross at the moon’s orbit (~60 Re)!  Physics!

But, we are really looking at the sum of the forces.  So, the centripetal acceleration becomes larger than all of the accelerations in the gravitational null point (since the gravity of the Earth and the gravity of the moon cancel so there is almost no acceleration there), and when you go on the other side of the moon and are far enough away, the centripetal acceleration becomes larger than the sum of the Earth and moon’s gravity.  Notice that the sum of the gravity is red (towards Earth), and the Centripetal acceleration is blue (away from Earth), which means that where they cross, the sum will be zero:

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The above plot shows the sum of all three of the accelerations: gravity from the Earth, gravity from the moon, and centripetal acceleration. Now you can see that there are two areas where the three accelerations cancel each other out: around 52 Re away from the Earth and about 71 Re away from the Earth, both along the Earth-moon line.  These are the first two Lagrange points (L1 and L2).

These Lagrange points exist in any system where you have one body orbiting another.  You can look at this plot and think of the sun as being the main body, and the Earth as being the second body, so that L1 is between the sun and Earth, and L2 is away from the sun on the dark side of the Earth. These Lagrange points are very useful, since we can place satellites near them so that they can look at the sun all of the time (this is useful for solar physics missions), or look back at the dayside of the Earth all of the time (for climate and weather missions), or be in the shade of the Earth all of the time (well, no missions really want this, since they need solar power to run, but they do want to be far away from the Earth and not have the sun be too large in their view).

There are three other Lagrange points that I have not discussed (as shown in the top picture as L3, L4, and L5).  All of these points result from the balance between the three accelerations, just like L1 and L2. L3 is very cool because it is on the opposite side of the sun, and we can’t really observe it.  Some people would argue that there could be a mirror Earth at L3, which is pretty funny.  We would be able to tell though, since the hidden planet would change the orbits of Venus and Mercury.  But, can we really trust science? 🙂

L4 and L5 are strange because they are in Earth’s orbital path around the sun, but about 60 degree behind and in front of the Earth.  The math is a tiny bot more complicated, since you have to consider two dimensions, but the concept is exactly the same. These two Lagrange points are really interesting, since you can observe the sun from unique vantages.

 

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Exploration

Mars vs Moon

Recently, the Trump administration discussed sending astronauts back to the moon, instead of on the Mars. It is well known that Space-X would like to send people to Mars. This has brought up a debate about whether the moon or Mars would be better to colonize first. Mars should obviously be the winner here, since, you know, Mars is awesome, but I thought that it would be interesting to look at both sides from a number of different points of view.

First let us look at advantages for Mars:

1. Mars spins at a pretty reasonable rate. Its day is just over 24 hours, so a day on Mars will be roughly a day on Earth. A day on the moon is 28 Earth days, which will take a fair bit of adjusting too. There is no need to readjust on Mars. Also, because Mars’s day is relatively short, the day-to-night temperature difference is not too dramatic, while on the moon, the day is very hot and the night is very cold. There is an almost 300C degree temperature difference between the day and night temperatures on the moon. Yikes.

2. Mars has an atmosphere. Not really a great atmosphere, but some atmosphere. It is all Carbon Dioxide (well, not all, but a hefty bit), which is great for plants, but really sucks for us humans. The atmosphere allows wind to blow, which helps to equalize the day-to-night temperature differences, but causes a lot of dust to move around too. We can pressurize domes and structures using air from outside. Having some atmosphere is better than not having any, which is roughly what the moon has. The side of the moon that is facing away from the Sun (the literal Dark Side of the Moon, not the metaphorical one), is one of the more vacuous places in the solar system, since the solar wind of the sun just plows into the moon, which leaves a giant wake of nothing behind it. We think of space as being pretty empty, but there are something like 12 orders of magnitude more particles per square meter where the International Space Station flies than on the dark side of the moon. That is pretty empty. (And dark – remember that the night lasts for 14 days on the moon!)

3. Mars may have a lot more water than the moon. There would only be certain places we could colonize on the moon and have easy access to water, while water may exist in the subsurface all over Mars. This is not really definitive, but is a relatively strong possibility. Of course, Mars doesn’t have much Oxygen to breathe in the atmosphere, but, hey, neither does the moon. We can make Oxygen out of water, though. So, it may be easier to sustain life on Mars, simply because of the (possibly easy) access to water. On the moon, we would have to live near the poles, which is probably ok, since you might not have as much of a day-to-night temperature difference.

4. Mars’s atmosphere could stop a bunch of harmful EUV and energetic particles from the sun. This would stop you from frying if you went outside. The moon doesn’t really have anything to stop you from getting zapped (technical term). So, really, you would have to definitely live in caves on the moon, but on Mars it might be possible to live above ground. You would still get a lot of radiation exposure though.

5. Gravity on Mars is much larger than the gravity on the moon. This keeps the atmosphere on the planet, and would help us keep things down on the ground and keep our bones a bit more robust.

6. Mars is really cool. It is red, and there are gods named after it (or it is named after a god? Not sure which…) Mars is capitalized, while the moon is not. Clearly, Mars is better. Heck, life could have formed there, then been transported to Earth and flourished here. So, if you are interested in science, Mars wins.

Advantages for the moon:

1. The moon is really close to Earth. In fact, it is orbiting Earth. So, we don’t actually have to leave the Earth system to get to the moon. This saves a HUGE amount of fuel (money). We have rockets right now that can land a lot of stuff on the moon. Like, we could start dumping supplies on the moon in months if we really wanted to. We would have to do a lot of research to really dump an equal amount of stuff on Mars (i.e., years away). Don’t get me wrong, we do have rockets that can land tiny amounts of stuff on Mars, but that is tiny. We had been talking about a sample-return mission to Mars, but NASA has basically dropped it, since it would be about $20 billion dollars, and we find Mars rocks quite often. It is really hard to get big things to Mars, while it is much (much) easier to get big things to the moon.

2. It only takes 3 days to get to the moon, while it takes 6 months to get to Mars, and you can only do that every 2 years. If you miss the two-week launch window to get to Mars, you have to wait another 2 years. In the two-week launch window to go to Mars, we could literally go to the moon and back. If we need to rescue people from the moon, it would only be a few days, while on Mars it could be years. Remember the movie “The Martian”??? Also, if you want to have a conversation with someone on the moon, it would only be a few seconds of time delay, while the delay to Mars is between 4 and 24 minutes, depending on whether Mars is on “our side” of the sun or the opposite side. Imagine trying to have a conversation with someone with a 24 minute delay. Ugh.

3. Because the moon is much smaller than Mars, it is easier to get stuff down to the surface and back up into orbit (i.e., it takes less fuel and therefore less money). In fact, shipping stuff from the moon to Earth is very, very cheap (read the Robert Heinlein book, “The Moon is a Harsh Mistress”) . So, if we mine the moon, we could get stuff back to the Earth for almost no cost at all. If we mined Mars, it would be incredibly expensive to get it back to Earth (harder to get off the planet, and it is much further away). So, from a purely commerce oriented stand point, a moon colony is a much better economical venture.

4. Remember the 6 month trip to Mars? That is on a tiny ship out in the vastness of space. If there were a large solar event that caused the radiation to increase significantly (happens a lot), then you would die unless there was significant (very heavy) radiation shielding on the ship. The space between here and Mars is not friendly at all. This is true of the space between here and the moon too, but it is only 3 days to get there, so it is easier to avoid times in which there may be bad solar events.

5. Earth-rise. That would be awesome. Unless Earth was a nuclear wasteland. Then it would just be a reminder of what used to be.

So, in summary, Mars is a nice idea, and could probably sustain life better and provide a much better scientific exploration opportunity, while the moon is a much more economically feasible location for a colony. Because of that, Mars will continue to be far off in the future unless the funding and political winds shift. If something horrific happens on the Earth, and it can no long sustain life, then Mars is probably a much better place to live because of the possibility of finding water, its higher gravity, and its atmosphere.  The moon is a bit too harsh to be anything but a temporary stepping stone to the future.

Engines

Liquid Fueled Rockets

The opposite of solid is liquid.

Back before the 1900s, the only type of rocket fuel used was solid. Then, in 1926, Robert Goddard flew a very small rocket named Nell, after his daughter. This rocket had the distinction as being the first rocket to use liquid propellant. It reached the amazing height of about 100 meters. Not super high, but it was really a “Wright Brothers” moment. Nothing would be the same.

Goddard_and_Rocket
Robert Goddard with his rocket Nell.

An aside on Robert Goddard: Goddard was basically the father of modern rocketry. When the press found out what he had done, they interviewed him and actually made fun of him, because they didn’t understand how rockets work. They thought that the rocket exhaust pushed on the atmosphere, enabling the rockets to go. They did not understand that you don’t need an atmosphere, or the ground, to lift something into space. In fact, the New York Times printed an editorial about Goddard that stated that he “does not know the relation of action and reaction, and of the need to have something better than a vacuum against which to react—to say that would be absurd. Of course he only seems to lack the knowledge ladled out daily in high schools.” Oops. That journalist didn’t read this blog, where I explain that rockets go because of Newton’s laws of motion. Goddard became very withdrawn and basically did his research in private. But, people still knew about him. In fact, German rocket scientists knew about him. They would call him up and ask him about different aspects of rockets. Being a scientist, he would share what he knew. Being an American, he told the government about the German’s interest in rocketry, which the government ignored. Robert Goddard died in August 1945. Just north of Washington DC, there is the NASA Goddard Research Facility, where scientists and engineers build many of the satellites that are in orbit today. The New York Times published an apology to Goddard the day after the launch of Apollo 11, which stated “Further investigation and experimentation have confirmed the findings of Isaac Newton in the 17th Century and it is now definitely established that a rocket can function in a vacuum as well as in an atmosphere. The Times regrets the error.”

An example of a liquid fuel for rocketry is hydrogen with oxygen used as an oxidizer. When these two molecules are mixed together, they release a very large amount of energy, and water results. I am sure that you all know that oxygen is a gas at room temperature, and I am sure that many of you know that hydrogen is also a gas at room temperature. Why, therefore, is this post about liquids and not gasses? Well, a gas takes up a huge amount of space compared to a liquid. Oh, sure, you could store gasses in pressure tanks, but have you ever tried to lift a gas tank? They are extremely heavy, since they have to hold the massive pressures of the gasses. So, the rockets would have to be very, very heavy in order to hold all of the gas. It is much easier to cool the gas down to extremely low temperatures and cause them to liquify. Then, you can store the liquids in relatively light weight tanks.

A liquid propellent engine typically uses two different liquids, a fuel and an oxidizer to create a large amount of energetic (hot) gas that is expelled at extremely fast speeds. The liquids need to be kept in separate tanks to keep them apart until they are pumped into the combustion chamber. The word “pumped” is important here, since, the flow rate of a pump can be controlled. This means that a liquid rocket engine can be throttled, such that the burn-rate of the propellent can be controlled, unlike a solid rocket booster. In fact, the liquid can be cut off completely, stopping all thrust. The flow can then be resumed at a later time, allowing the engine to restart. These are huge advantages over solid rocket boosters.

Liquid propellents are typically more efficient that solid propellents. This means that less fuel is needed, and since the amount of fuel exponentially increases as more is needed (see the rocket equation post!), any increase in fuel efficiency can dramatically decrease the size of the rocket.

Why would anyone ever use a solid propellent rocket, then? Well, there are a few disadvantages to liquid fueled rockets.

The first is that the liquids typically have to be stored at an extremely cold temperature. For example, oxygen turns into a liquid at -183 C (-297F). It is not super easy to store, nor is it super easy to fuel the rocket. Also, the rocket sits on the ground for a while before being launched into space, so there sometimes is insulation on the storage tank. For example, the large orange thing on the space shuttle is not rocket, but is a storage tank for the liquid oxygen and hydrogen. It is orange because that is the color of the foam insulation that wraps the entire tank. This insulation was the direct cause of the Columbia accident in 2003. I will talk about this in a separate post.

Close-up_STS-107_Launch_-_GPN-2003-00080
The Space Shuttle Columbia during its final launch. The orange thing that the shuttle is attached to is the storage tank for the liquid hydrogen and oxygen.  It is orange because the tank is completely covered in several inches of (orange) foam insulation.

There is one advantage of having super-cooled liquids on the rocket, though. The combustion chamber and the rocket’s nozzle can get extremely hot, since the whole point of the rocket engine is to make extremely hot gasses and direct them out of the nozzle. The combustion chamber and nozzle can actually melt because of this. But, because there is very cold liquid around, the rocket’s plumbing goes around the nozzle and combustion chamber before leading into the chamber. This cools down the extremely hot metal, and warms up the liquids before they are combined together. All of this plumbing and pumping makes liquid engines much more complicated than solid engines.

Another disadvantage of liquid propellents is the storage tanks. Imagine trying to ride a bike with a half-empty five-gallon bucket of water balanced on your handlebars. As the water slushes around, it moves the center of gravity around. If you are trying to go in a (relatively) straight line, and stay balanced, this can significantly complicate things. The same is true with a liquid propellent rocket. The tanks move from being full, to being empty, with every stage in between. All the while, the rocket has to stay on course. The tanks, therefore, need to have baffles and be specially designed so that the liquids won’t slosh. Yet another complication.

If you drove a car before about 1995, you probably remember having a carburetor. These were devices that combined the fuel with oxygen. Now, pretty much all cars have fuel injectors that automatically adjust the amount of fuel and oxygen mixture. So, imagine 50 years before the first automobile fuel injectors were built, building them for rockets. The fuel and the oxidizer had to be mixed just right in order for the burn to be as efficient as possible. On the Saturn-V, the fuel was being used at such a huge rate, that they couldn’t get the mixture to be very good, so they ended up having pockets of fuel and oxidizer, which would then cause explosions. The engineers didn’t have time to develop new fuel injectors, so they made the walls of the combustion chamber thicker in order to withstand the explosions. Engineering! Fuel injectors are complicated when you are using hundreds of gallons of fuel a second. Today, fuel injector technology is much better, but we don’t have many rockets that use fuel as quickly as a Saturn-V did.

In summary, liquid fueled rockets have some big advantages over solid rockets, namely the engines can be throttled and even turned off, allowing more precise orbital insertion; and the liquid fuels tend to be more efficient than solid fuels. On the other hand, rockets that use liquids as fuels tend to be more complicated, with lots of pumps, massive plumbing systems, and fuel injectors. Most rockets that launch satellites into space tend to have a main stack that is liquid with strap-on solid boosters that provide a bit of extra lift in the first minutes of the launch. That way the rockets compromise between the simplicity, but reduced performance of the solid rockets, while allowing the complex, but precise orbital insertion and raw power of the liquid fueled rockets.

Photos:

Satellites

News: QB50 and Space Debris Conference

Yesterday was a very long and a very busy day for me – I traveled to Europe to attend the 7th European Conference on Space Debris and we had two satellites launch into space as part of the QB50 mission.

QB50 is a European led mission that has about 35 CubeSats that have been launched to the international space station (ISS).  Each of the satellites, which are about 4 inches by 4 inches by 8 inches (like, really small), carries one of three different sensors that measure the space environment.  The Europeans provided the instrument and the launch, while each group provided the satellite.  University of Michigan build two satellites, called Atlantis and Columbia, that carry the FIPEX instrument.  FIPEX measures the atomic and molecular oxygen density in the thermosphere.  Oxygen is the main gas in the thermosphere, so, in effect, these satellites will measure the air density.  This is important for satellite orbit prediction and collision avoidance. Below is a picture of these two satellites with a bunch of the students, faculty, staff, and engineers that worked on them.

qb50_group_photo

On April 18, 2017, the satellites were taken up to the ISS on a normal resupply mission. They are in deployers called NanoRacks, which push the satellites out into space from the ISS. According to QB50 officials, this should happen in the first few weeks of May. The satellites will then turn on, deploy some drag panels, and start to communicate with the ground station at UM.  We will then command the FIPEX instrument to turn on and start to take data.

While the launch was happening, I was participating in the 7th European Conference on Space Debris.  This conference has about 350 people who are investigating all sorts of aspects of space debris: new techniques for discovering it, quantifying how much there is, and looking at ways of removing it, just to name a few.

A quick refresher on space debris: There are over 20,000 objects orbiting Earth that are about the size of a softball or larger. Since we have hundreds of active satellites, this debris cloud is a problem, since if a piece of debris hits an active satellite (or another piece of debris), it will destroy it and create even more debris. People talk about a Kessler Syndrome, which is basically where low Earth orbit becomes crowded with debris which leads to collisions, which leads to more debris, which leads to more collisions, etc.  This has the potential for running away and basically making low Earth orbit unusable.

I got to watch a talk by Kessler yesterday.  He is a retired NASA employee. Sort of cool to see such a talk.

So far, I have watched a bunch of talks on how to measure debris and some missions that are trying to raise money to remove debris.  Measuring the debris is very interesting, since you can sort of do this with a relatively inexpensive camera.  Just before sunrise and just after sunset, the ground is in darkness, but the sun is still shining on satellites. If you look up in the sky during these times, you can see this reflected light and observe the satellites. Which is pretty awesome.  If you take pictures with a camera, you can figure out the speed of the debris, which gives you its orbital characteristics and roughly how big the object is (from its brightness).  The better your camera, the smaller the debris you can see. I may try to do this with some students. It seems like a great project.

For the debris removal missions, there are a bunch of hurtles: (1) getting to space is very expensive, so it may cost so much to get the junk down, that it is not worth it; (2) rendezvousing with the debris is really hard, since it is quite difficult to automatically track and maneuver into position; (3) capturing the debris is hard, since it may be spinning and oddly shaped; and (4) deorbiting the debris is a challenge, since you have to rigidly attached the debris to some sort of thruster and then use a bunch of fuel to deorbit it.  This means that the missions are pretty expensive and have a LOT of technical hurtles to get over in order to be feasible.  But, they are pretty interesting to learn about!

 

Engines

Back to the Basics: Solid Rocket Engines

As you can probably tell, I tend to get ahead of myself.  This blog has talked about all sorts of crazy different ways of getting into space, except for the two most common methods, which are solid rocket engines and liquid rocket engines. The difference may seem to be subtle, but they are actually quite big. I will talk about solid rocket engines first.

Most people have probably seen a solid rocket engine (maybe even held one in their hands), since they are what are used in model rockets. In fact, they have been used for about a thousand years. The first fire arrows were arrows with a little solid rocket engine tied on to them.  Basically, people used to take gun powder, shove it in a tube, tie it to an arrow, and light it.  The arrow would travel at much higher speeds than if an archer fired it, but they were also very hard to aim. Before World War II, the largest improvement in the technology came when William Hale, in about 1845, packed the gun powder into a cylinder and had the exhaust come out in such a way that the cylinder would spin, which provided stabilization to the rocket. It also eliminated the need for a big stick.

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Korean Fire Arrows. 

Did you know that we launched rockets against Mexico City?  How crazy is that?

When the Civil War started, we started to use modern artillery, like guns, which were much more accurate and could be used by a vast number of the solders. Rockets basically went out of favor during this time, although there were a few people working on liquid propellant rockets (like Goddard in the early 20th century), just to try to get the ideas right. I will talk about this when I talk about liquid rockets.

Anyways, during World War II, the Germans figured out how to really use rockets. They used liquid propellant engines in order to launch rockets against the allies. Now, the liquid propellant technology was a huge breakthrough, but they also came up with a bunch of other breakthroughs, namely a guidance system to actually steer the rockets on their 200 mile journey as well as a telemetry system to see if they actually were headed in the correct direction. This sounds like a simple thing to do, but this was before computers were invented, let alone GPS.  But, that is once again, for another post.

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A revolutionary German V-2 Rocket from WWII

The lesson here is that the Germans developed the underlying technologies that allowed the rocket to go from being a spinning cylinder that would sometimes work, to a supersonic vehicle that could hit a target accurately from 200 miles away.

Once World War II was over, the US and USSR militaries wanted to used rockets for a couple of uses, but one of the most important was for launching atomic bombs at other countries.  This was because an airplane could be shot down when trying to deliver an atomic bomb. Also, it could take an airplane hours to get to a target. With a rocket, almost any place on Earth could be hit in 45 minutes or less.

What rocket scientists learned is that using liquid propellants on Intercontinental Ballistic Missiles is not really smart.  This is because liquid propellants can’t actually be stored in the rocket – they have to be stored in coolant tanks that keep the liquids very cold.  For example, liquid oxygen needs to be stored at about -300° F (-183° C), which is a wee bit cold. So, when someone wants to fire a liquid propellant rocket, they have to fuel it first, which can take a long time.

On the other hand, those old rockets from the 1840s were packed with gun powder and were stable for a many years, and could be fired immediately when needed.  A perfect solution for global thermonuclear war! Therefore, scientists developed solid propellant engines. These are pretty simple.  You take a solid fuel and a solid oxidizer and mix them together with something that will bind them.  You put it in a tube and shape it, and ta-da, you have a solid rocket engine. There is obviously more to it than that, but that is the basic premise. There are a lot of resources out there that will tell you the chemical makeup of solid rocket fuels.

minuteman_3
A Minuteman-III ICBM

When you pack the fuel (called grain) into the cylinder, where are a wide variety of shapes that it can be.  The simplest is packing the outer walls and leave a hole in the center (see wonderful drawing below).  The point here is that only the part of the grain that is exposed will burn, so when you ignite this, then a very small portion of the grain starts to burn. Then, as the grain burns away, more surface area is exposed, so more grain can burn. If you are looking up the rocket from the bottom, you will see a little circle of clear area at first, then as the grain burns, the circle gets larger and larger, with more and more grain burning. Since more grain is burning, the thrust actually increases as a function of time, until the outer wall is reached, and the thrust stops, since the fuel is completely depleted. This is called a progressive burn. Model rockets have this grain pattern.

progressive_burn
A progressive burn grain pattern.  This is viewing up the rocket from the bottom.

 

If you pack the grain in exactly the opposite way, with a big circle in the middle, and a thin shell of clear area at the outer shell, then as the grain burns, the circle of grain gets smaller and smaller, which creates a regressive burn.

regressive_burn
A regressive burn grain pattern, viewed from the bottom of the rocket.

Interestingly, you can do some strange shapes that will allow the burn to be neutral, where the exposed surface area of the grain remains mostly constant as a function of time.  (If you think about it, the area always has to roughly be the area of outer shell, since this is the final area.) This is what the space shuttle’s solid rocket booster engines used – an 11-point star configuration for a roughly constant burn for the entire 104 seconds that they thrusted.  More on the space shuttle’s solid booster in another blog post!

One huge disadvantage of solid rocket boosters is that once you fire them, you can’t stop them – they burn until all of the grain is used up. With a liquid propellant rocket engine, you can throttle the engine and even turn it off and back on. There is none of that control in a solid rocket engine. Engineers design the shape of the grain to give them the type of burn that they want, and when it is lit, it goes.  This can be somewhat mitigated by making the top of the rocket so that it can pop off, exposing the grain at both the top and bottom, allowing the rocket to thrust both down and UP at the same time. This creates a balance in the (upward and downward) forces, allowing the rocket to go nowhere. That is pretty insane, and, I would imagine, quite dangerous, but it is something.

Another disadvantage is that, because the rocket exhausts all of the fuel in one go, the rocket basically can’t do any final adjustments. Therefore, the uncertainty on where it will end up can be rather large. For nuclear weapons, being off by a few (10s of) miles is not a big deal, since there are a lot of warheads on each one and they all go sort of cluster-bomb at the end anyways. If you want to get something to orbit, being off by a few (10s of) miles can be somewhat bad.

Ok, let’s summarize. Some advantages of solid rocket engines:

  1. Solid rocket engines are dead simple and are therefore easy to design and cheap.
  2. You can store a fully fueled solid rocket engine for a long time and fire it whenever.
  3. Solid rocket engines can be strapped on to liquid propellant rockets to give them an initial boost. Hence, solid rockets are sometimes called boosters.
  4. Did I mention that they are so simple that you can buy them at Walmart?

Some disadvantages:

  1. Once you ignite the solid rocket engine, it will fire until used up.
  2. Because they can’t be relit, they are not super accurate.
  3. They are almost always not as powerful as liquid propellant engines. I didn’t talk about this, but it is true!

Solid rocket engines end up being used as strap-on boosters and intercontinental ballistic missiles, and are not used very often to put stuff into orbit on their own.  That is, unless you don’t have a lot of money and need to get to space for cheap. You can pick up a bottom of the line Pegasus-XL for about $28,000,000 from Orbital-ATK (and build a paper one for free!). And yes, they accept bitcoin.

Images:

 

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More Interstellar Travel

This week, researchers announced that they have found seven rocky planets around another sun that may be capable of having water – three of which are in the habitable zone of the solar system. The star, called TRAPPIST-1, is about 39 light years away.

pia21422_-_trappist-1_planet_lineup_figure_1
From NASA/JPL.

This discovery raises the issue, once again, of interstellar travel.  A while ago, I wrote a post that discusses how long it would take to get to our nearest neighbor star using modern technologies. Long story short: it would take a many thousands of years.

Since then, articles have been published that discuss getting to another sun using lasers. In the last post, I talked about using lasers to get to Mars. This time, I will talk about the idea of using lasers to get to another star.

The idea of using light to accelerate things has been discussed for a long time. Basically, light bouncing off of a reflective surface will impart some pressure on that surface.  There are two extremely interesting things about using light to accelerate things: (1) if it is sunlight, it is free, which is the cheapest type of energy; and (2) if it is not sunlight, the energy can be generated somewhere besides on the spacecraft (like on the Earth or the Moon), which means that the spacecraft can be much smaller and won’t need huge engines with gigantic fuel tanks. The big disadvantage of using light to accelerate things is that the efficiency is absolutely horrible, with a huge amount of the energy being completely wasted.

The general idea with using lasers for interstellar travel is exactly the same as using lasers for getting to Mars: bounce a laser off the spacecraft, or a gigantic sail, and accelerate it up to an extremely large speed, moving in the right direction. For a trip to Mars, you could imagine having a similar laser system on Mars, so the spacecraft could be slowed down. On an interplanetary trip, the spacecraft would simply (quickly) pass through the solar system of the other star.

So, why don’t we do this now? Well, there are a bunch of reasons:

  1. We don’t have lasers that are large enough and can operate for long enough to accelerate something (relatively large) up to close to the speed of light. The article above talks about using a laser array that is in orbit that would be about 6 miles across.  That is a pretty big array of lasers.  Basically, you would need a ton of lasers that would all fire for a very short amount of time, but combined, the array would provide a constant stream of energy that would rapidly accelerate the spacecraft.
  2. The article talks about accelerating the spacecraft up to speeds of 1/3 of the speed of light in 10 minutes. That would be an acceleration that is 17,000 times gravity. We don’t build spacecraft that can experience that type of acceleration – even 20-30 times gravity is pretty horrible for a spacecraft!
  3. Even with the huge laser array, the spacecraft that is getting the energy would have to be super tiny.  The article talks about a spacecraft that is something like 1 inch in size.  That is pretty small! Considering that the smallest satellites in orbit around the Earth are CubeSats, which are about 4 inches cubed (and that is REALLY hard!), it is unlikely that we will launch anything even CubeSat size on an interstellar trip.
  4. Since the spacecraft are so small, it is hard to imagine how we would get signals from it. Let’s take the New Horizons mission to Pluto as an example. New Horizons has a dish that has a diameter of 2.1 meters. At Pluto, it had a bandwidth of 4.5 kilo-Bytes/sec. Compared to a standard cable modem, this is about 1000 times slower. Ok, New Horizons is not going to stream Netflix – that is clear.  But, it has taken the mission over six months to stream all of the images that they took in their flyby of Pluto. That is a very slow bandwidth! Bandwidth falls off as the square of the distance between objects.  So, if we launched New Horizons to a solar system 39 light years away (which is about 62,500 times further away), the bandwidth would be 0.0000012 Bytes/second. Yikes!  That is slow!  If the spacecraft were really only an inch in size, then the antenna could only be about that big, which means that the bandwidth would decrease by a factor of 10,000. That is really not good.  So, this is the largest issues with this idea.  In some ways, it is like trying to use your cell phone to call someone on Earth from Pluto. “Can you hear me now?” “Uh. No.”

    new_horizons_transparent
    The New Horizons spacecraft.  The antenna is about 2 meters across. The black thing to the right of the antenna is the power source for the spacecraft.  It is a Radioisotope Thermoelectric Generator (RTG), which is just cool to say.
  5. Since the spacecraft would quickly move away from our own sun, it would not have a power source for the entire trip to the other solar system. Which is bad for two reasons: we wouldn’t be able to communicate with it, since it takes energy to send signals, and it would quickly cool down to the background temperature of the universe, which is -269°C. Not many electronic components will survive those temperatures! So, we would HAVE to have a power source that would last the trip, just to heat up the system. That would be big.
  6. It would take at least 40 years as a bare minimum to get there, and would pass through the system in about 10 minutes. On the first front, you would have to count on the scientific community to keep its eye on the prize for the 40+ years of the trip. And, it should be noted that 40 years is the absolute minimum, assuming that we can accelerate it up to almost the speed of light. If we can get it up to 1/3 of the speed of light, it would take 120 years. That is a fair bit of time.  Next, when it arrives and passes through the system, it will need to have an extremely fast camera, since it will be passing by the planets at >500,000,000 MPH. That is a good camera.  Not a cell phone camera.

Ok, I think that you get the point.  This is a really, really hard mission. We are not really close to having interstellar travel. It is great to think about these things, but they really are science fiction at this point.

But, if we just …..

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Using Lasers to Get Moving

In the chain of crazy ideas of how to get to space and how to get from one planet to another, there is an idea to use lasers. Actually, there are a couple of ideas on how to do this.  This is the first of a two-parter where I talk about this idea.  The first part will cover one project that has actually gotten off the ground (literally) and an idea on getting to Mars, while the second post will look at interstellar travel with lasers.

The first idea on using lasers makes a tiny bit of sense.  It is called Lightcraft (get it – light and craft?).  The general idea with this is that you have an object that has a very specific shape on the bottom side. Then you shoot a laser at it and the shaped bottom focuses the laser so that it superheats the air that is touching the object.  The air then is propelled away from the object, resulting in a net thrust that is towards the top of the object.

Interesting, eh?  They have actually tested this with some very shiny objects that are about the size of a fist and are pretty light. Here is a picture:

lightcraft

That is actually almost real size, too! These little things have flown about 75 meters into the air.  That is not, um, unimpressive, I guess. There are several problems with this technology, since it is hard to keep the Lightcraft pointed in the right direction and keep the laser pointed directly at it, and all sorts of other things. My guess is that they have not had the right public relations people and the large amount of funding that is needed to take a project like this from the tiny prototype stage to anything of real size.

Recently, another team has also been working on using lasers to move things about in the solar system.  This idea with this team is to use very high powered lasers in a similar way as we would use the sun and a solar sail.

A quick aside on solar sails (boy, I really need to write a post about solar sails):  When light hits an object, it actually imparts a super, super small amount of momentum.  When you feel the sun beating down on you on a very bright days, it is totally because it is actually beating down on you. Well, technically it is, but in reality, the amount of force on you by sunlight is less than a paperclip put on you.  Like, way less.  But, if you were out in space, and you had a huge reflective “sail”, the light would shine on it and impart a very small force – something like a pound for a sail that is about 1 km². But, imagine if you could turn the brightness of the sun up by a factor of 100. Or 1,000. Or 1,000,000! Then you could get some real force to act on your spaceship!

So, the general idea with using lasers is that you could have a reflective surface on your ship that you would point a really really really intense laser at.  This would impart a large force on the ship and accelerate it. The beauty of this plan is that the lasers all would need to be powered here on Earth, so we could generate it using a nuclear power plant or hydroelectric or even good old-fashioned coal.  The ship could be very small, since it wouldn’t need a lot of fuel to accelerate it, since that power is coming from Earth.

In the article that I linked to above, the researchers say that they could envision getting to Mars in 3 days using this type of technology. Please excuse me if you heard a cough that subtly masked my slight doubt of this claim.

The first (and most obvious) issue with this is that you would have to have some sort of a laser system that would be on Mars to slow down the ship.  So, you would have to build something like a nuclear power plant on Mars. I am sure that this is not really likely to happen soon, since we are so successful at building them here in the United States (sarcasm). But, there are probably less regulations on Mars, so it should be easier. But then there is the whole getting all of the (highly radioactive) materials to Mars to actually build the plant.  Well, any ways, we will get there eventually!

Ok, so now that we have a laser system on Mars and a laster system on Earth, how much acceleration would we need to get to Mars in 3 days?  Well, we would accelerate for half the distance and then decelerate for the other half of the distance.  If we make a very simple approximation that the acceleration is constant, the problem is easy to solve.  Let’s assume that Mars and Earth are the closest they can be together, which is 0.3 AU, or about 45 million kilometers. We need to accelerate through about half that distance in about 1.5 days. Do a little math and we get that the acceleration needs to be a constant 5.3 m/s², which is about half of the acceleration of Earth on the surface.  This is extremely reasonable!

The problem with this is that the power from the laser falls off as the distance squared. This means that the acceleration that the laser system could supply would have to start off extremely large, then would fall to almost nothing, or that the power that is consumed by the laser would have to start off relatively small, and would have to increase dramatically.

Let’s think about how high-powered of a laser you would have to have in either case. I am going to simplify the problem significantly, since I am a relatively simple person. The sun, for reference, exerts about 4.5667e-6 Newtons of force per meter squared of area. This is an incredibly small force! Like, really, really, really small.  In order to exert that much force, the energy in that light is about 1350 Watts, which is a LOT of energy.  So, this idea is not very efficient at all!

Let’s say that we want to send something to Mars that is a 100 kg, or about 220 lbs. This is an extremely small satellite. If we want to accelerate it at a rate of 5.3 m/s², like the example above, we would have to use 530 Newtons. If we had a sail hooked up to this object that was, say, 100m by 100m (about the size of a football field), how much force would the sun exert on it?  About 0.0457 Newtons.  That is not much! And that is taking about 1350 W, as described above.  So, we would need a laser that is about 11,600 times more powerful than the sun to give us our 530N of force.  That would require a 15.7 Mega-Watt laser.  And this would only accelerate it at the 5.3 m/s² for a little while, since the distance between the laser and the satellite would increase and the received power from the laser would decrease.

Let’s say that the laser delivered the 15.7MW (or 530N of force) at a distance of about 10 Earth radii away from the surface of the Earth (I had to choose a distance, and this was quite arbitrary, but whatever). If you wanted to continue to accelerate the satellite at 5.3 m/s² all the way to the halfway point between Earth and Mars, the power of the laser would have to increase by a factor of about 500,000 times while it was shining on the craft. This means that in order to accelerate it all the way to the halfway point, the laser would have to be a 7,800,000 MW (7.8 Tera-Watt) laser, and would have to fire (ramping up in intensity) for about 36 hours.

Practical?  I don’t know.  This website talks about a 2,000 TW laser that was fired for 1 pico-second (not very close to 36 hours). Another website talks about getting a 10 TW laser that fires for about a femtosecond (that is also pretty short), but fits on a desk.

Where could we get the power? Well, if the sun delivers 1,350W of power per 1m x 1m area, then we would need about 5,800 km² of solar panel area to get that much energy.  Oops, solar cells are not perfectly efficient (more like 25% efficient), so we would need about 23,000 km² of area, which is about 150 km by 150 km of solar cells. This is about the size of New Jersey.

Anyways, the idea is that power on Earth is very cheap, while getting that power into space is really painful.  So, it is ok to take a HUGE hit on efficiency to accelerate something up to enormous speeds in space using Earth-based systems, instead of trying to haul some sort of chemical rocket engine up to space. In fact, chemical rockets will never get us to another star, so it is a non-starter. But, that is a conversation for next week (I promise!)