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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. 🙂

Slide1

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:

Slide7

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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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.

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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!)

 

 

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Reinventing Innovation With Small Satellites

When NASA first formed, getting to space was extremely dangerous and no one really knew how to do it. Therefore, there was an acceptance of a large amount of risk. Part of the reason for this is that the amount of money invested in NASA was enormous – at one point in the late 1960s, NASA’s budget was 6% of the total federal budget. This allowed NASA to rapidly solve problems by trying new and innovative things and iterate on the design over and over until it worked. For example, the Atmospheric Explorer satellites, built in the 1970s, had four versions that each lasted only a few months until AE-E lasted for many years. The IMP series of satellites measured characteristics of space between the Earth and the Sun. There were seven satellites that lasted only a few months until IMP-8 lasted 30+ years. The reason that NASA could do this is because the ratio between the cost of a satellite to the total budget of the agency was quite small. Therefore, failing on a few satellites didn’t matter very much.

NASA today is quite different. The budget is 0.5% of the total federal budget and dropping every year. The total number of satellites launched is significantly smaller, and each one needs to succeed, since they cost so much compared to NASA’s total budget. While failure still happens at NASA, it is not something that is taken as a lesson; it is taken as a failure. Therefore, there are a plethora of lessons learned, sets of rules that need to be followed, and significant numbers of reviews that must be held to move the project to the next phase. While this helps to ensure success, and it is a natural outcome of a system with limited budgets, it stifles innovation and greatly increases the cost of each satellite.

When a satellite is launched, the rocket (or launch vehicle) has a certain capability. For example, a given rocket may be able to launch a satellite with a mass of 1000 kg to a 700 km altitude. If the satellite that is being designed is 950 kg, the rocket then has excess capacity and, in order to get the satellite to the exact desired orbit, 50 kg of ballast needs to be added to the rocket. Sometimes, this ballast can be another satellite.

The idea of a CubeSat was created when Bob Twiggs suggested that there could be a standardized deployer for very small satellites that could be used as ballast on almost any launch vehicle. The deployer could be very strong and could ensure that if anything went wrong with the little satellite inside it, the primary payload (i.e., large satellite) would not be affected. The P-POD deployer was invented to allow cheap access to space for extremely small satellites as secondary payloads. It created a standard for a tiny satellite, dubbed a “CubeSat”, that could fit into the P-POD deployer and be launched into space wherever a P-POD could be used. A P-POD accepts a satellite that is roughly 4 inches by 4 inches by 12 inches, or 3 satellites that are roughly 4 inches on a side (hence the name “CubeSat”).

The invention of the P-POD deployer has revolutionized space, since is allows cheap access to space for anyone who can build a satellite that can fit within its extremely limited confines. At first, it was considered too small to be of any use for any real science to be conducted. This has since changed, though. The National Science Foundation has embraced CubeSats as both an educational tool and a science tool. They have funded over 10 CubeSats that have been used to conduct science ranging from lighting detection to radiation belt monitoring.

CubeSats have been successful because that have placed the community into a place where the satellites are once again quite cheap compared to the total budget of the institution. This has allowed innovation and rapid technology development to reenter the satellite industry. Because of this, a large number of companies have been created to support such an industry, creating smaller and smaller supporting hardware for tiny satellites. For example, small, high-speed radios have recently been introduced that can be used to downlink massive amount of data. Without such radios, it would be extremely expensive to get all of the data from the satellite to the ground.

With the emergence of small-satellite hardware, agencies such as NASA and the Department of Defense could start to look at creating missions that are designed in a radically different way – instead of launching a single satellite that was quite expensive, they could explore how to get the same science return with two or more smaller, cheaper, satellites.

Another technology that has led to the creation of missions such as CYGNSS, a satellite constellation mission that I am involved with, is the Global Navigation Satellite System (GNSS), which is the general name for constellations such as GPS. These satellites were designed to provide precise position and time information for military systems, but their use has become significantly more general. GPS is ubiquitous, with everyone having a receiver in their phone, which has done two things – pushed GPS receivers to smaller and smaller sizes and lowered the price for those receivers.

In space, a GPS receiver can be used to do many different things. One of the most common is to use the delay between when the GPS satellite sent the signal and when the monitoring satellite received the signal to tell something about the atmosphere. This can be done because electromagnetic waves travel at different speeds in different medium. So, for example, if the waves travel through the ionosphere, they slow down a bit and take longer to reach the satellite. This difference can be measured and the amount of ionosphere between the two satellites can be determined. Just like the ionosphere, the waves slow down when they travel through water vapor, so, when the waves have to travel through the atmosphere, the amount of water between the satellites can be determined. This is the primary use of GPS on satellites today – radio occultation to determine atmospheric characteristics. Because of the inexpensive nature of GPS receivers, constellations can be launched that take advantage of this. The COSMIC satellites are an example.

The CYGNSS satellite mission uses GPS signals, but in a very different way than other satellites – it measures how much of the signal is reflected off of the ocean’s surface, which says something about the roughness of the ocean. The amount of scattered signal is dependent upon the surface roughness, which itself is dependent upon the winds over the water. Therefore, the scattered GPS signal strength that is measured by a satellite such as CYGNSS depends on the wind speed over the ocean. CYGNSS takes advantage of there being the GPS satellites in orbit around the Earth continuously sending signals towards the Earth.

Past satellites that have measured the wind speed over the ocean have had to both transmit a radio wave and receive the wave back. In order to measure the signal, the transmitter had to be quite large and powerful. Since CYGNSS does not contain the transmitter, it can be significantly smaller.

In addition, CYGNSS takes advantage of a number of components that were designed for very small satellites (like CubeSats), such as the radio for communication with the ground station, the star trackers that provide information on the orientation of the satellite, the momentum wheels, which keep the CYGNSS satellites oriented in the proper direction, and the computer systems that run everything on the satellites. This has allowed NASA to launch eight very small satellites for cheaper than a normally priced large satellite, and it is all due to the shrinking of space technologies and the global availability of the GPS network.

By pushing the boundaries of what can be done with extremely small satellites, NASA has started to shift to considering constellation missions that can give us an idea of what is happening over a large portion of the globe instead of in a single place.  It has allowed innovation and rapid development of cheap technologies to flourish. This will result in some amazing new science to take place in the next decade!

 

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Space Shuttle Atlantis

Here are some pictures from Kennedy Space Center of Space Shuttle Atlantis.

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A view from the front with a wide angle lens.
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A view from the side with a horribly distorting 8mm fisheye lens.  Interesting effect, but it makes you think that the shuttle is small, while it is gigantic.
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The three main engines. Feel the burn.

 

 

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Project SpaDE – Deorbiting Satellites with Bombs and Balloons

In 2011, a person from Raytheon called me up out of the blue and asked if I wanted to be involved in a project to help eliminate space debris.  I was interested.

A little background (the first): The majority of space is not really a vacuum.  There are particles pretty much everywhere in space.  The question really is what is the density of those particles – or how many particles are there in a given volume. The atmosphere of Earth is a relatively narrow shell around the Earth. We know that if we climb Mt. Everest there is not much air up there.  But, to us, “not much air” is still a whole lot of air.

We think of space as having no air at all. Astronauts have to wear space suits to protect them from the “vacuum of space” after all. There are a number of very interesting things about this, but it should really be a totally separate post.  Let’s simply leave it that there is, indeed, atmosphere up in space where the International Space Station (ISS) orbits.

Since there is air up there, objects such as satellites and the  ISS feel a drag force, as we have discussed in a few other posts. The density in the atmosphere up there is very very small, but the objects in orbit are moving extremely fast.  This means that the drag force that the objects feel is not really large, but it can strongly affect their orbital motion.

As a rule of thumb, objects that are orbiting below about 200 km (120 miles) will deorbit extremely quickly, in a matter of days to weeks, because of the atmospheric drag. The atmosphere is so thick there that the objects just can’t stay aloft and they ultimately decrease their altitude rapidly and (hopefully) burn up in the atmosphere around 70 km altitude.

Satellites above about 700 km (420 miles) or so will basically never deorbit because of atmospheric drag.  The atmospheric density there is so low that drag is not an important force on objects in orbit. Don’t get me wrong – there is still an atmosphere, but it is so tenuous that orbiting objects don’t care about it.

Between these two altitudes, drag is important. In fact, the ISS, which orbits at around 400 km (240 miles) altitude has to be moved up every couple of weeks, because atmospheric drag pulls it down.  The ISS is constantly being pulled back towards the Earth due to drag, and we lift it back up to 400+ km using propulsion to keep it in orbit.  If we didn’t do this, the ISS would fall back to Earth and burn up in the atmosphere in 6-12 months.

A little background (the second): Space is filled with a lot of crap. There are about 20,000 objects in orbit around the Earth that are about the size of a softball or larger. This stuff is pretty dangerous, since it is moving at speeds of 7,600 m/s (17,000 MPH). It can cause a lot of damage (Gravity, anyone?).  Here is a picture of the space shuttle window after being hit with a piece of debris that was significantly less than a millimeter in size:

space_debris_impact_on_space_shuttle_window

There is a realization that we need to do something about all of this space debris.  One of the worst things that has happened because of the amount of debris is that an Iridium satellite was destroyed due to a collision with a retired Russian spy satellite. This caused the creation of thousands more pieces of debris, which could then impact other objects. There is real concern.

I was called by this guy from Raytheon to see if I wanted to help solve this problem.  I said, sure, that would be great.  We wrote a proposal to NASA to see if we could get money for it.  They gave us some seed money to see if the idea could pan out.  The project was called “Space Debris Elimination (SpaDE)”.

The general idea of the project was to see if we could increase the atmospheric drag in front of an object in orbit around the Earth enough to cause it to deorbit. Here is a graphic to illustrate the idea:

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At first, this idea seems very interesting and plausible. My main profession is a modeler of the upper atmosphere.  A long time ago, I wrote a large-scale model of the atmosphere that looks at what happens when large amounts of energy is added to the atmosphere in the form of the aurora (i.e., the northern/southern lights). I continue to work on this model today, and have a bunch of graduate students who use the model to do research. For project SpaDE, I took the model and made it so we could run it over a very small area (like a couple of hundred kilometers by a couple of hundred kilometers) and inject a huge amount of energy quite low in the atmosphere. The model then simulated what would occur.

You might ask, what is “a huge amount of energy”?  Well, that is a good question.  The model can handle almost any amount of energy, but for this project we were looking at roughly nuclear bomb types of energies. The general idea would be to take a large explosive device to the stratosphere, or about 30 km, and explode it there.  We would use some sort of device to direct the majority of the energy upwards, creating a very large density perturbation that would propagate upwards to the upper atmosphere where a piece of debris would travel through the density enhancement and deorbit.

When people find out about this project, they always ask: why did you stop working on it? Well, this is really the point of this post – to describe why this type of debris mitigation strategy is unlikely to work.

Problem, the first: You have to take an extremely large explosive device up on a balloon and explode it in the atmosphere. That is unlikely to be ok with pretty much anyone.  Also, directing the blast so that the majority of energy would go upwards could be rather heavy, making the balloon quite big. Basically, there would be a lot of logistical problems.  You could envision that each balloon launch could run upwards of several hundreds of thousands of dollars or more. For comparison, if you wanted to do something like capture debris with a satellite and deorbit it, it might cost 10s of millions of dollars.  So, a balloon with a large bomb is much cheaper, but a logistical nightmare.

Problem, the second: This is somewhat more technical. The atmosphere breathes. When it warms up, it expands, and when it gets cooler, it contracts. The upper atmosphere absorbs a bunch of energy from the aurora. The aurora deposits about 40 Giga-Watts of energy into the  upper atmosphere continuously. During extremely disturbed times, it can deposit over 500 GW of energy for several hours. Those are big numbers, so what does it mean? Let’s say we have an extremely disturbed aurora (500 GW) for 6 hours. That is about 1e16 Joules of energy, which is 2.6 megatons of TNT, which is roughly 10 times LESS energy than a very large nuclear bomb. With the aurora, it is distributed over a very large region, and will cause an increase in density at around 400 km altitude of about a factor of 10. That is a pretty big increase in density. A coworker noted to me that a hurricane is caused by a density change of about 10%. This is a 1000% change in the thermosphere due to the aurora. The thermosphere is a pretty interesting place!

A nuclear bomb will cause a much larger change in the density, clearly.  But, the problem is that it will change is only in a very small volume. You get a mushroom cloud that goes up into the atmosphere and causes a (lets say) 100 times increase. By the time the mushroom cloud gets up to orbital altitudes, it will be about 200-ish km across. A satellite will pass through this mushroom cloud in about 25 seconds. Then the density is back to normal.  For a large auroral event, the entire atmosphere is increased by a factor of 10 for 6 hours, meaning that the satellite goes through 6 hours of 10 times larger drag.  This is enough to change the satellite’s orbit.  Definitely.  But, it will really only change the altitude of the satellite by a meter or two. Not much in the grand scheme of things.  So, a 100 times increase in the density for 26 seconds doesn’t change the orbit very much at all. Simplistically, you would need about a 1 million times increase in the density at satellite altitudes over the 26s in order to get the same effect as a 10 times increase for the storm over six hours.  That would be a very large bomb indeed. And it would only cause something like a meter or two altitude change.  Not deorbiting.  For that you would need on the order of a hundred or so of these events.  That is a lot of bombs.

Hopefully that was not too technical. Sorry if it was.

Problem, the third: In order to actually effect the single piece of debris, you would have to launch the balloon several hours before hand to allow it to get to a high enough altitude, and be over the pretty much the exact spot in which an object will be orbiting.  Then you have to time the explosion perfectly, so that the orbiting object passes directly through the shock front of the blast.  This is probably the easiest of the three problems, since with a model, you can pretty easily determine how quickly the blast wave will move through the atmosphere in all directions. Controlling the path of the balloon is more of a challenge, but I have actually written software that will allow you to figure out the trajectory of high altitude balloons, since this is a sort of a hobby or mine. (I will say that I have never exploded a nuclear device on one of our balloons!) Check out a video of one of our balloon launches where we launched two balloons at the same time.

What basically happened with Project SpaDE is that we did not get selected for funding for round two.  This was not too surprising, since the concept is just not very scalable.  You could actually see this working if you wanted to slightly nudge a small object that was going to hit a major satellite or something.  If you perturbed the orbit a couple of days before the collision was supposed to occur, it could actually change things.  Possibly. But, it would not be able to deorbit anything.

Sorry that this post was so long.  Hopefully it was still entertaining.

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The Craziest Way to Get to Space

Hopefully, over the past few posts, I have convinced you that using chemical rockets to get to space is a pretty horrible way of doing it. And, just as I am certain that I will continue to post about this technology, I am certain that we will continue to use them, since it is really the only way to actually climb out of this gravity well that we call home (at this time!). But, my friends, trust me when I tell you that there is something better.  Actually, there are a number of technologies that are being worked on that may be better.  All of them have some really major issues, but it is good that we are trying.

This is the first post in a series that is going to explore some alternate ways of getting around the solar system and off of this rock. And, because I like you guys, I am not going to start off with #10 and work up to #1.  I am going to start off with the craziest possible way of getting us into space. (There are crazier ways of getting around the solar system, though!) Let’s get started.

Once upon a time, there lived a guy named Gerald Bull. Yes, he was sort of short and stocky.  And Canadian.  Here is a picture of him:

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Gerald Bull

Gerald Bull came up with a fantastic idea. In 1961 he bought a 16-inch battleship gun from the US Navy for about $2000.  That isn’t 16 inches long, that is 16 inches in diameter. He moved it to Barbados and started running tests with it. He put atmospheric sensing instruments into the noses of the shells, and then fired them into the atmosphere.  These shells were about 150 kg and could go to altitudes of about 100,000 ft, or about 20 miles. In the air. By the way, these “rockets” were called Martlets. His program was called the High Altitude Research Program, or HARP.

Ok, let’s step back for a minute and think about this.  Bull was firing a gigantic cannon straight up in the air with things that weighted about 300+ pounds. I launch weather balloons.  These go up to the same height with packages that weigh 12 lbs.  Bull was doing some crazy stuff! Interestingly, there is really not a great way of sampling this part of the atmosphere, since it is really hard for airplanes to fly this high. Satellites can’t orbit this low because the atmosphere is incredibly “thick” there. So, rockets are about the only good way to take in situ measurements in this area (well, above about 100,000 ft, or 30 km to about 200+ km) of the atmosphere. Bull fired about 1,000 of these Martlets into the atmosphere in just a year or so.

But it really doesn’t stop there.

In 1963, Bull created the Martlet-3, which reached over 100 km altitude. He could launch a “rocket” that could go up to space for about $5000. Considering that rockets can cost over a million dollars that do the same thing, this is super freaking cheap.

He then extended the length of the cannon to about 110 feet with the ultimate goal of launching things into orbit. (The reason that you extend the length of the cannon is because you can get the force of the expanding gas for longer, allowing the projectile to accelerate for longer.) His idea was to build a rocket that would be shot up to about 100 km, and then the rocket would fire and take the payload into orbit.  This would be extremely cheap, since the majority of the mass to get something into orbit is used up just to get up to the right altitude.  If you can get the “third-stage” of a rocket up to 100 km altitude with a big gun, then it is super cheap to get to orbit! His Martlets got up to 180 km altitude for a world record that is still in existence.

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The HARP 16″ gun firing a Martlet-3

Unfortunately, Bull never reached this goal. There was a ton of red tape, with the US and Canadian government involved.  Bull did not really believe in red tape and so he left the program. Bull continued to love big guns and started working for some shady people, developing highly accurate guns that could be used by one country against another. Ultimately, he worked for Iraq in helping them develop the Scud missiles that were supposed to be used against Israel. It turns out that Israel doesn’t really like this type of behavior, and Bull ended up with a few bullets in him in March of 1990.

The moral of the story (besides “don’t screw with Israel”) is that we could actually use a big gun to get us to outer space and ultimately into orbit. We don’t even need gunpowder to do this anymore – we can use the same technology that drives super-fast roller coasters and trains: linear induction motors. This technology has led to the development of rail guns by the Navy.  You seriously have to watch this video. This is a massive increase in our technological capabilities.  Basically, you accelerate the “bullet” up to speeds of about 4,000 miles per hour in the barrel of a gun. Serious horsepower.

If we can use this technology to knock things out of the sky, why aren’t we using it to put things into orbit?  That is a fantastically good question!

There are two problems with this idea (beyond Israel killing you for trying):

  1. If you got something up to orbital speeds as it left the gun, it would slow down extremely quickly because of atmospheric drag.  Really, you want to have it launched upwards, and when it gets well above the atmosphere, have it accelerate up to orbital speeds using fuel. This is somewhat complicated.
  2. The accelerations that take place with this are just unbelievably horrendous. A human would be a pancake if they were launched like this.  So, humans will NEVER be launched into space using a bug gun.  Maybe a very very very long runway, but never something super efficient like a gun.  But, supplies and fuel and other things like instruments could be launched into orbit using this technique.

There are researchers who are working on techniques that could be used independently or in conjunction with a big gun, so that you wouldn’t have to actually take fuel to get to orbit either.  While that is interesting, it is no where as cool as the Martlet. Seriously.  Gerald Bull. What a guy.