--FIRST -PREV NEXT-
One of our satellites is missing. Sort of. Life might actually be easier if it had gone missing, but it's more like it's suddenly decided that it's done with its current job and wants a new career. Maybe it wants to be a sculptor. Or a dentist. Or just about anything except what it was built to do, which is sit in geosynchronous orbit and relay TV signals. I can't really blame it. If I had to hand off Survivor reruns for a living, I'd go nuts, too.
Galaxy 15 was, for five years, a perfectly unremarkable satellite. A standard product, almost identical to its siblings, it had functioned perfectly for nearly five years before wandering off to stretch its legs. No one really knows why, since it's no longer on speaking terms with ground control. But it's rapidly becoming a menace to navigation. At or around the end of May it's going to come close by the AMC-11 satellite, which is going to have to do some fancy dancing to avoid signal interference. Where Galaxy 15 goes from here is anyone's guess.
What we really need is a garbage truck. Unfortunately, no one seems to have built one yet. Which gives me an idea...
Over the next couple of weeks, we're going to go through a very basic, somewhat simplified vehicle design procedure. I honestly have no idea exactly what we'll end up with. But I expect to end up with something sufficiently detailed that I can "build" and fly it in Orbiter.
The first step is figuring out what kind of performance you'll need. This part isn't terribly difficult, as mathematics goes. Basically, you can figure out how much of a velocity change you need for each maneuver, and then add them all together to get a total performance budget.
To summarize: there are three equations we'll need, and one rule of thumb. Two of them involve the specific mechanical energy (SME) of the spacecraft. The SME is the sum of the spacecraft's kinetic and potential energy, divided by the mass.
(1) (SME) = (V)^2/2 - (MU)/(R)
V is the velocity, R is the distance from the spacecraft to the center of the Earth, and MU is the product of the Earth's mass and the universal gravitational constant. We can express the SME another way as well.
(2) (SME) = - (MU)/(2*A)
The variable A is the semi-major axis of the orbit. It is half of the sum of radius at perigee and the radius at apogee, and for a circular orbit it's equal to the constant radius of that circular orbit. Combining (1) and (2) above gives us three pieces of information: V1, the circular velocity of the parking orbit; V2, the required velocity of the low side of the transfer orbit; V3, the velocity at the high side of the transfer orbit; and V4, the velocity of the higher circular orbit.
It isn't necessarily obvious from (1) and (2) above, but one interesting thing about orbital mechanics is that even though higher-altitude orbits have more energy, the actual orbital velocities are smaller. Remember this, we'll use it later.
The third equation is the Law of Cosines:
(3) (Vc)^2 = (Va)^2 + (Vb)^2 - 2*Va*Vb*cos(G)
Here, Va and Vb are the velocities before and after a plane-change maneuver, G is the angle, and Vc is the required velocity change to go from Va from Vb. Note that if you're going from one circular orbit to another, Va = Vb. Plane-change maneuvers are incredibly expensive in terms of fuel. They are often unavoidable, though.
The rule of thumb I mentioned is that, to a good first approximation, launching into low Earth orbit requires as much fuel as accelerating 10,000 meters per second. Orbital speed is actually about 7,700 m/s, but you burn about 2,300 m/s worth of fuel overcoming gravity and atmospheric drag.
That said, the details of those computations make for tedious reading, so I'll simply present the results.
First, the ground rules. One: the vehicle will launch from, and recover to, Kennedy Space Center in Florida. Two: the vehicle will have a return payload of 8 tons, big enough to handle any current or projected communications satellite. Three: provision will be made for a crew of two, a commander and a pilot.
My first sequence of maneuvers went something like this:
(1) Launch into Low Earth Orbit (LEO): 10,000 m/s
(2) Plane Change into Equatorial Orbit: 3,804 m/s
[Loiter: up to 24 hours]
(3) Boost to Geostationary Transfer Orbit (GTO): 2,426 m/s
[Time of flight: 5h 16m 30s]
(4) Circularize at Geosynchronous Earth Orbit: 1,465 m/s
[Time on station: up to 13h 27m]
(5) Brake into GTO: 1,465 m/s
[Time of flight: 5h 16m 30s]
(6) Brake into LEO: 2,426 m/s
(7) Plane Change to KSC: 3,804 m/s
[Loiter: up to 24 hours]
(8) De-Orbit: 65 m/s
Total: 26,727 m/s (includes 5% reserve)
Now, the first thing we see here is that the plane change maneuvers eat up a huge part of our velocity budget. This is because the magnitude of a plane change maneuver scales directly with the velocity. They drink gas like nobody's business, which is why you avoid them whenever possible. However ... why am I doing it in a low orbit, when I could be doing it higher up, where the speed is lower? Partly because this first method was the obvious way ... and partly because I'm not sure I trust my ability to actually fly a fancier maneuver. Still, here's how the pros do it:
(1) Launch into LEO: 10,000 m/s
[Loiter: up to 24 hours]
(2) Boost to GTO: 2,426 m/s
[Time of flight: 5h 16m 30s]
(3) Plane Change and Circularize: 2,106 m/s
[Time on station: up to 13h 27m]
(4) Plane Change and Brake to GTO: 2,106 m/s
[Time of flight: 5h 16m 30s]
(5) Brake into LEO: 2,426 m/s
[Loiter: up to 24 hours]
(6) De-Orbit: 65 m/s
Total: 20,086 m/s (includes 5% reserve)
By combining the plane change and circularization at the top of your GTO ellipse, you save a whole 6 kilometers per second. That's huge. That's a tremendous amount of fuel you don't have to plan on hauling along with you. And when most of your weight is fuel, that adds up in a hurry.
Some of the times above are somewhat arbitrary. You're going to spend some time in low earth orbit waiting for the right launch window, and you're going to spend some time on your way back waiting to line up for re-entry. And you may or may not want a rest period in between your outward and inward GTO orbits. So, I'm planning on a nominal mission duration of three days. The absolute minimum would probably be 12 hours, but everything would have to line up perfectly. I'm going to budget a reserve here too, and allow for an extended duration of up to 7 days.
Here's the first fork in the decision tree: do we have a crew on board, or not?
There are good arguments both ways. On the one hand, hauling a crew along means you also have to haul along the stuff to keep them alive for the duration: food, water, oxygen. I was about to mention thermal control as well, but you'd have to do that for your electronics even in an unmanned craft. But an unmanned craft would be much, much lighter for the same mission specs.
But, since the point of this exercise is to design a simulator joyride anyway ... I've opted to include pilots. At least, for now. When we pick this up again next time, we'll see why orbit-capable rockets tend to be pretty big.
Monday, May 24, 2010
Sunday, May 16, 2010
Sesquicentennial, Part II: RNC 1860
--FIRST -PREV NEXT-
American politics in the 1850s were very chaotic. The Whig Party had enjoyed some modest success as a bulwark against the Democratic Party, electing two Presidents, but began to unravel in 1852. The Compromise of 1850 was the proximate cause. The Kansas-Nebraska Act sealed it. Whigs could not settle amongst themselves the question of whether or not to allow slavery in the new territories, and the question tore the party apart. Pro-slavery Whigs found a natural home among the Democrats, while anti-slavery Whigs had nowhere to go. Yet.
Another of the era's many splinter parties was the Free Soil Party, whose name tells you all you need to know: they were dead-set against the expansion of slavery. In 1854, ex-Whigs met with Free Soilers and anti-slavery activists in Jackson, Michigan to discuss how they might be able to work together. They had few differences, easily reconciled, and the Republican Party was born. Only two years later, John Fremont stood for the Presidency as the first Republican candidate for that office. Fremont only won New England and the northernmost states, but he polled 33% of the popular vote, an extraordinarily strong showing for what was to all intents and purposes a new party.
The Republicans convened for their second convention in May of 1860 in Chicago, having been handed what looked like a golden opportunity. The fratricidal disaster that was the Democratic convention of the previous month was all over the papers. To put it bluntly, they smelled chum in the water. With a divided opponent, they need not poll a majority nationally, a mere plurality would do, provided that they got their Electoral Votes in all the right places. To seal the deal, all they needed to do was select the right candidate.
Three men were favorites going into the convention: William H. Seward of New York, Salmon P. Chase of Ohio, and Edward Bates of Missouri. But a funny thing happened on the way to the nominating floor. For one, Seward, Chase, and Bates had each alienated important factions within the Republican party base. For another, this being Chicago, the convention was taking place on the home turf of an opponent that none of the three took seriously. Seward was ahead after the first ballot, but holding on at a strong #2 was one Abraham Lincoln. Two ballots later, Lincoln was the nominee. There was a vicious rumor to the effect that Lincoln's campaign had packed the venue with supporters using counterfeit tickets. I do not know if this rumor has any truth to it or not ... but, if true, it highlights something of Lincoln's character that we would see later on: he would do what was necessary, ruthlessly, and without compunction.
The party platform was almost a foregone conclusion: the party stood four-square against any expansion of slavery into the territories. They also supported a tariff in protection of domestic industry, and a homestead law to grant free land out West to settlers. None of these provisions were greeted with much joy down South. In the event, the Lincoln-Hamlin ticket wouldn't appear on the ballot in any Southern state.
The stage was set now for what would be at least a three-way race in November: Lincoln representing the Republicans, Douglas representing the Northern Democrats, and Breckenridge representing the Southern Democrats. What remained to be seen was if the loser would abide by the decision of the electorate...
American politics in the 1850s were very chaotic. The Whig Party had enjoyed some modest success as a bulwark against the Democratic Party, electing two Presidents, but began to unravel in 1852. The Compromise of 1850 was the proximate cause. The Kansas-Nebraska Act sealed it. Whigs could not settle amongst themselves the question of whether or not to allow slavery in the new territories, and the question tore the party apart. Pro-slavery Whigs found a natural home among the Democrats, while anti-slavery Whigs had nowhere to go. Yet.
Another of the era's many splinter parties was the Free Soil Party, whose name tells you all you need to know: they were dead-set against the expansion of slavery. In 1854, ex-Whigs met with Free Soilers and anti-slavery activists in Jackson, Michigan to discuss how they might be able to work together. They had few differences, easily reconciled, and the Republican Party was born. Only two years later, John Fremont stood for the Presidency as the first Republican candidate for that office. Fremont only won New England and the northernmost states, but he polled 33% of the popular vote, an extraordinarily strong showing for what was to all intents and purposes a new party.
The Republicans convened for their second convention in May of 1860 in Chicago, having been handed what looked like a golden opportunity. The fratricidal disaster that was the Democratic convention of the previous month was all over the papers. To put it bluntly, they smelled chum in the water. With a divided opponent, they need not poll a majority nationally, a mere plurality would do, provided that they got their Electoral Votes in all the right places. To seal the deal, all they needed to do was select the right candidate.
Three men were favorites going into the convention: William H. Seward of New York, Salmon P. Chase of Ohio, and Edward Bates of Missouri. But a funny thing happened on the way to the nominating floor. For one, Seward, Chase, and Bates had each alienated important factions within the Republican party base. For another, this being Chicago, the convention was taking place on the home turf of an opponent that none of the three took seriously. Seward was ahead after the first ballot, but holding on at a strong #2 was one Abraham Lincoln. Two ballots later, Lincoln was the nominee. There was a vicious rumor to the effect that Lincoln's campaign had packed the venue with supporters using counterfeit tickets. I do not know if this rumor has any truth to it or not ... but, if true, it highlights something of Lincoln's character that we would see later on: he would do what was necessary, ruthlessly, and without compunction.
The party platform was almost a foregone conclusion: the party stood four-square against any expansion of slavery into the territories. They also supported a tariff in protection of domestic industry, and a homestead law to grant free land out West to settlers. None of these provisions were greeted with much joy down South. In the event, the Lincoln-Hamlin ticket wouldn't appear on the ballot in any Southern state.
The stage was set now for what would be at least a three-way race in November: Lincoln representing the Republicans, Douglas representing the Northern Democrats, and Breckenridge representing the Southern Democrats. What remained to be seen was if the loser would abide by the decision of the electorate...
Thursday, May 13, 2010
Stupid Nuke Tricks, Continued
This is a continuation of a list I made a few months ago. I got to thinking about it the other day, and realized that I'd left some interesting projects out. And, in the interests of full disclosure, there is ... well, a bit of a confession to make.
Operation Plowshare: Alfred Nobel, the inventor of dynamite, never intended his invention to be used for warfare. In a weird reversal, the Atomic Energy Commission got the idea of trying to find peaceful uses for atomic explosions. Of what possible use could atomic explosions be in the non-city-destroying sector of the economy, you ask? Well, they use dynamite in mining, don't they? You can move a whole lot of earth with a bucket o' sunshine. The first few tests were mainly along the lines of proving how big a hole you could dig. The Sedan shot in 1962 dug a hole 300 feet deep and 1,200 feet wide. This was the second test of the series. The moratorium on above-ground explosions put paid to some of the more ambitious plans, such as using nukes to dig out a harbor, but even up to the end of the program in 1974 there were plans to use atomic explosions to stimulate natural gas recovery. The gas companies didn't like the plan much. They had two main objections. First, even over 25 years of gas recovery they might only recoup less than half of the cost; and second, customers would probably take umbrage at the delivery of slightly radioactive product. After 1974, the AEC gave it up as a bad idea.
Program #7: Given that the Soviets never really had to sell their government programs to their legislators or to the public, they kind of mailed it in when it came to project names. This program was also referred to as "Nuclear Explosions for the National Economy", but the program could just as easily have been called "Anything the Americans Can Do, We Can Do Bigger." And yes, it was bigger ... and even more useless, if such a thing were even possible. They tried to create an artificial lake. And they did ... but the artificial lake was radioactive, having been dug out by a nuclear explosion. They tried to open up a new diamond mine. And they did ... which produced radioactive diamonds. They conducted 115 detonations over the 24 years between 1965 and 1989, when Mikhail Gorbachev asked, "Why in the world are we still doing this?" No one had a really good answer to this question. For that matter, no one could remember why anyone ever thought it was a good idea to begin with. So, they just kind of gave up.
Spot the Asteroid: Earth-crossing asteroids are a serious threat. We're doing a better job these days of finding them before closest approach, but back in the day, we only found out about them when one of three things happened: (1) it had already zipped by and was going away, (2) it clipped Earth's atmosphere and someone saw the streak as it passed, or (3) WHAM! No one wanted to open Door #3. So, the question was, how do we find them? Well, Sir Arthur Clarke had an idea once. He claimed that an atomic explosion in outer space would allow us to detect every Earth-crossing asteroid in the inner Solar System by using the bomb like the biggest flash bulb in the known Universe. On the one hand, I have a lot of respect for Sir Arthur's capability. But on the other, I'm not really sure how this would have worked in practice. No one else was, either, which is probably why it was never tried.
Deflect the Asteroid: Spotting the asteroid is one thing, doing something about it is another thing entirely. For most of history, men threw their hands up in the air and appealed to the good Lord's mercy, because really, what else can you do? Starting in 1967, people started figuring out what their choices were. There was a brief scare earlier that year about the impending close approach of the asteroid Icarus. MIT Professor Paul Sandorff took that as inspiration, and directed his senior-level system engineering class that spring to find a way to push Icarus out of the way should it come too close. The result of that class project was published as Project Icarus, the only senior thesis ever to become a major motion picture. Basically, they would hijack the Apollo program to use their Saturn V boosters to deliver a series of nuclear warheads to explode near Icarus, pushing its trajectory away from Earth. That was the last word in asteroid defense for quite some time, until Johndale C. Solem of the Los Alamos National Laboratory started crunching the numbers to figure out exactly what a nuclear explosion would do to an asteroid. His report found its way into some conference proceedings, and that was that.
This is more or less where I came in.
Shoemaker-Levy 9 scared the Hell out of me. I really started worrying about what we could do in the event that we were treated to a duck's-eye view of a shotgun blast. I was a doctoral candidate in Aerospace Engineering at the time, and my research advisor gave me considerable latitude when it came to side projects, so I decided that I'd find out. A brief search led me to Dr. Solem's paper, and I was off to the races. So, here's the situation: we spot an asteroid in-bound with only weeks to a couple of months of lead time. What sort of last-ditch defense could we pull off? Well, just about the only thing we can do is pelt it with ICBMs and hope it goes away. Putting together some information on the ranges of our ICBM force, and some knowledge about ballistic trajectories, and Dr. Solem's formulas, I was able to calculate that you wouldn't be able to shift the trajectory enough to make it worthwhile. You can move the impact point by a crater's diameter, and that's about it. But, you can pulverize it. If you can bust it up into pieces 35 meters or smaller, the fragments will burn up in the atmosphere on the way in... And a time-on-target salvo of four Peacekeeper ICBMs can blast a half-mile-wide asteroid into pea gravel. I presented the paper at the 1997 AAS/AIAA Space Flight Mechanics conference. The reception was, as they say, mixed. A small group of Air Force officers in the front row was very interested ... and if there's a top-secret point-defense office in the Pentagon these days, odds are that's probably my fault. Everyone else basically said I was mad. Mad! And I can't really argue with them. I never thought it was a particularly good idea, just possibly the least bad one. It's a plan born of desperation, not of foresight. But if you spot a mountain falling on you with only eight weeks' notice, your options start at horrible and gurgle noisily down the toilet from there.
Still. It's gratifying to know that I earned my "Mad Scientist" title fair and square.
Operation Plowshare: Alfred Nobel, the inventor of dynamite, never intended his invention to be used for warfare. In a weird reversal, the Atomic Energy Commission got the idea of trying to find peaceful uses for atomic explosions. Of what possible use could atomic explosions be in the non-city-destroying sector of the economy, you ask? Well, they use dynamite in mining, don't they? You can move a whole lot of earth with a bucket o' sunshine. The first few tests were mainly along the lines of proving how big a hole you could dig. The Sedan shot in 1962 dug a hole 300 feet deep and 1,200 feet wide. This was the second test of the series. The moratorium on above-ground explosions put paid to some of the more ambitious plans, such as using nukes to dig out a harbor, but even up to the end of the program in 1974 there were plans to use atomic explosions to stimulate natural gas recovery. The gas companies didn't like the plan much. They had two main objections. First, even over 25 years of gas recovery they might only recoup less than half of the cost; and second, customers would probably take umbrage at the delivery of slightly radioactive product. After 1974, the AEC gave it up as a bad idea.
Program #7: Given that the Soviets never really had to sell their government programs to their legislators or to the public, they kind of mailed it in when it came to project names. This program was also referred to as "Nuclear Explosions for the National Economy", but the program could just as easily have been called "Anything the Americans Can Do, We Can Do Bigger." And yes, it was bigger ... and even more useless, if such a thing were even possible. They tried to create an artificial lake. And they did ... but the artificial lake was radioactive, having been dug out by a nuclear explosion. They tried to open up a new diamond mine. And they did ... which produced radioactive diamonds. They conducted 115 detonations over the 24 years between 1965 and 1989, when Mikhail Gorbachev asked, "Why in the world are we still doing this?" No one had a really good answer to this question. For that matter, no one could remember why anyone ever thought it was a good idea to begin with. So, they just kind of gave up.
Spot the Asteroid: Earth-crossing asteroids are a serious threat. We're doing a better job these days of finding them before closest approach, but back in the day, we only found out about them when one of three things happened: (1) it had already zipped by and was going away, (2) it clipped Earth's atmosphere and someone saw the streak as it passed, or (3) WHAM! No one wanted to open Door #3. So, the question was, how do we find them? Well, Sir Arthur Clarke had an idea once. He claimed that an atomic explosion in outer space would allow us to detect every Earth-crossing asteroid in the inner Solar System by using the bomb like the biggest flash bulb in the known Universe. On the one hand, I have a lot of respect for Sir Arthur's capability. But on the other, I'm not really sure how this would have worked in practice. No one else was, either, which is probably why it was never tried.
Deflect the Asteroid: Spotting the asteroid is one thing, doing something about it is another thing entirely. For most of history, men threw their hands up in the air and appealed to the good Lord's mercy, because really, what else can you do? Starting in 1967, people started figuring out what their choices were. There was a brief scare earlier that year about the impending close approach of the asteroid Icarus. MIT Professor Paul Sandorff took that as inspiration, and directed his senior-level system engineering class that spring to find a way to push Icarus out of the way should it come too close. The result of that class project was published as Project Icarus, the only senior thesis ever to become a major motion picture. Basically, they would hijack the Apollo program to use their Saturn V boosters to deliver a series of nuclear warheads to explode near Icarus, pushing its trajectory away from Earth. That was the last word in asteroid defense for quite some time, until Johndale C. Solem of the Los Alamos National Laboratory started crunching the numbers to figure out exactly what a nuclear explosion would do to an asteroid. His report found its way into some conference proceedings, and that was that.
This is more or less where I came in.
Shoemaker-Levy 9 scared the Hell out of me. I really started worrying about what we could do in the event that we were treated to a duck's-eye view of a shotgun blast. I was a doctoral candidate in Aerospace Engineering at the time, and my research advisor gave me considerable latitude when it came to side projects, so I decided that I'd find out. A brief search led me to Dr. Solem's paper, and I was off to the races. So, here's the situation: we spot an asteroid in-bound with only weeks to a couple of months of lead time. What sort of last-ditch defense could we pull off? Well, just about the only thing we can do is pelt it with ICBMs and hope it goes away. Putting together some information on the ranges of our ICBM force, and some knowledge about ballistic trajectories, and Dr. Solem's formulas, I was able to calculate that you wouldn't be able to shift the trajectory enough to make it worthwhile. You can move the impact point by a crater's diameter, and that's about it. But, you can pulverize it. If you can bust it up into pieces 35 meters or smaller, the fragments will burn up in the atmosphere on the way in... And a time-on-target salvo of four Peacekeeper ICBMs can blast a half-mile-wide asteroid into pea gravel. I presented the paper at the 1997 AAS/AIAA Space Flight Mechanics conference. The reception was, as they say, mixed. A small group of Air Force officers in the front row was very interested ... and if there's a top-secret point-defense office in the Pentagon these days, odds are that's probably my fault. Everyone else basically said I was mad. Mad! And I can't really argue with them. I never thought it was a particularly good idea, just possibly the least bad one. It's a plan born of desperation, not of foresight. But if you spot a mountain falling on you with only eight weeks' notice, your options start at horrible and gurgle noisily down the toilet from there.
Still. It's gratifying to know that I earned my "Mad Scientist" title fair and square.
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