¤

Since there are 50 different sets of ballot-access laws, 3rd-party presidential candidates who are truly accessible to the entire electorate are almost unknown -- only the Libertarians have consistently jumped through the hoops in recent election cycles.

[ 20030216 ]

 
Shuttle Perspectives -- Good, Bad, and Ugly

Via Post-atomic, the endlessly entertaining Fred Phelps is at it again. Bad as he is, we will be poorer when he's gone, reduced to telling our progeny tales of the old days when things like this were actually produced with serious intent -- how will we convince them that Westboro Baptist "Church" (which consists entirely of the Phelps extended family) wasn't a satire?

On the good side, the rather orthogonal yet benign Bill Walker weighs in with The Loss of the Space Shuttle Was No Disaster, which title, taken properly, is likely to be true in the long run.

Ugly? Well, that's what I'm for. Reading through The Experience Economy, we find (p 177) Figure 9-3, "The Economic Pyramid," which I clumsily render as follows (not sure why the borders aren't complete):

What does this mean for space exploration and development?

First of all, notice that all private or semi-private activity in space today is in the "services" category, manifested as telecommunications and remote Earth sensing (which includes weather sats).

Second, notice that the predominant idea of the next major private market in space is in the "experiences" category, namely tourism.

Third, notice that all publicly-funded space activity also fits into either services (spysats, etc) or experiences (research and exploration), again with the "next" activity (Mars mission) being in the experiences category. (Pine and Gilmore define [p 30] the experience "realms" as entertainment, education, escape, and estheticism; popular space exploration events like Mars Pathfinder/Sojourner cover all four.)

The Experience Economy repeatedly stresses (see, for example, p 186), with supporting statistics, that the margins associated with commodities are less than those associated with goods, which in turn are less than those associated with services, which in turn are less than those associated with experiences, which in turn are less than those associated with transformations. What I think this means is that if Pine and Gilmore's model is correct, some long-time and fondly-held notions of space enthusiasts will turn out to be dead wrong.

In particular, things like asteroid mining and space manufacturing may never be very prominent -- not because they won't happen, but because most people who go to space will be going there for something analogous to Las Vegas or a golf course -- or a retreat center -- not to extract resources or build things.

My longtime readers will recognize a broad similarity to Rand Simberg's vision, which I note gives pride of place to "... coorbiting tourist hotels and resorts, with orbital sound stages and sports venues, for filming movies and broadcasting new types of dance and games." Me, I'm holding out for a monastery on the Moon. Perhaps one dedicated to the memory of the blessed Saint Leibowitz ... ;)

 
More On-The-Scene Columbia Reporting

Old Blind Dog has lots of on-the-scene reports from Nacogdoches. Graze on over there if you haven't done so recently.

 
Irony in Tennessee

Glenn Reynolds says: "You can count on Union County to embarrass itself this way every few years ..."

There's enough material here to keep a stand-up comedian in business for months.

First of all, Glenn's not kidding; this ain't the first time. In other news, Horace Maynard Middle School's principal is named Jimmy Carter. Its team name is the Red Devils. There is great emphasis on science education.

I stopped following the links at that point; it was just too much. My prayers, personally, are with any kid who transfers out of there into another middle or junior high school and has to tell his new classmates that he came from a school named Horace Maynard.

[ 20030214 ]

 
Proof that Machine Translation Isn't Quite There Yet

-- may be found here, as for example where "WARNING: Spoilers!" becomes -- "after being translated from English to French to English to German to English to Italian to English to Portuguese to English to Spanish to English" -- "this INFORMS: I scrape."

 
Inferior Asteroid Discovered

-- in the sense of "inferior planet," that is. 2003 CP20, as it is designated, is the third object known whose entire orbit is closer to the Sun than Earth's -- the only other two are Mercury and Venus! As this diagram shows, it's in a fairly elongated orbit (e looks like about 0.3) with i = 25°, and it's near aphelion now -- relatively close to Earth, but it can never get closer than about 0.19 AU, or 74 times lunar distance.

From that vantage point, the Earth-Moon system would appear as a bright double star, three-quarters of a degree apart (that is, a bit more than the diameter of the Moon as seen from Earth) and shining at magnitudes -7 (15 times brighter than Venus as seen from Earth) and -2.5 (about as bright as Jupiter). Earth would be 1.5' (arc-minutes) in diameter, the size of a quarter 175 feet away -- just large enough to show a tiny disk.

The Space.com article, however, notes that 2003 CP20 "will pass within 4.65 million miles (7.48 million km) of Venus more than once." This is less than one-fifth Venus' minimum distance to Earth; from the asteroid, Venus would appear 1/6 the size of a full Moon and shine at magnitude -8 or brighter.

The bright yellow line going off to the right in the diagram points to the vernal equinox, that is, where the Sun appears to be as seen from Earth on about March 21; so where it intersects with Earth's orbit is where Earth is on September 21. The somewhat dimmer yellow line going up to the top of the diagram points to the north ecliptic pole, that is, it is at exactly 90° to the plane of Earth's orbit.

 
As A Public Service on Valentine's Day ...

Advice for my single, male, churchgoing readership, and I know there are at least a few of you: this Sunday is just a couple of days past V-day. I want you to hand out flowers to all the single women at your church. Nobody else doing it? Doesn't matter; do it anyway. Broke? Carnations are cheap; do it anyway. Are some of them women you wouldn't date on a bet? Sorry, but this is like handing out valentines in grade school; everybody gets one.

Why? Because more of them than you can imagine have never gotten a flower from a man in their entire lives, that's why.

 
The Air Force Pictures (II)

Sure enough, the shuttle picture that got so much attention a few days ago was, as I calculated, taken with a modest instrument; in Supersecret Telescope Wasn’t So Super (free registration required for access), Mike Gudgell informs us that: "The picture was taken with a 3.5-inch telescope, similar to one you can buy in a hobby store."

 
Disruptions as Practice for Terrorist Incidents

Again via Glenn, this telling turn of phrase from Howard Kurtz: "An orange alert becomes like a snow alert, just another fact of life."

Without wishing to trivialize the entirely justifiable fear being felt by residents of NYC and DC, which remain the only likely targets, I would suggest that personal preparation for future incidents may be less burdensome than is often suggested. What sort of disruptions to daily life are actually in your experience? What did you do then? What did the society around you do? How did institutions respond?

Honest answers to these questions can help alleviate fear. Virginia Postrel has written that "... as an ex-Angeleno I don't find the idea of emergency supplies all that new. As I always say, nuclear war might. The Big One will happen." Around here, the Big One, contrary to stereotype, isn't a tornado; it's an ice storm. The one last year knocked out our electricity for five days, and we were lucky at that. Things got pretty squalid there for a while. But you know what?

It got fixed. And the institutions of civil society, like major retailers, transportation networks, and electric utilities, had a pretty good handle on things within about 36 hours. From then on, it was pretty much a matter of buying whatever we needed: there were pallet-loads of portable heaters, flashlights, and nonperishable food in the stores -- and waiting for the KCP&L crew to show up: they were working 12+ hours a day and getting neighborhood after neighborhood switched back on. And we had done no preparation beforehand.

To take a more recent local example, though one that did not affect us personally, the busiest bridge over the Missouri River had to be closed for 10 days due to structural failure. MoDOT had to locate, and work from, 50-year-old pencil drawings on graph paper to fix it. This is exactly the sort of disruption which figures so prominently in terror scenarios -- the severing of a main traffic artery in the heart of a major city (except that in this case the "terrorists" were generations of pigeons), with emphasis on the difficulty of recovering long-lost information and expertise to perform repairs. This is supposed to plunge the area into chaos. Actual result: a few days of minor annoyance for commuters.

 
Life Imitates the Onion (A Continuing Series)

Via InstaPundit, Letter from Gotham reports that "peace" protesters in NYC tomorrow will employ plenty of violence to get their point across.

Funny, I thought irony was supposed to be dead.

What's actually interesting about this, of course, isn't that a bunch of commies plan to smash things and hurt people -- what else is new? Rather, it's that the specific threat mentions this:

I now refer my readers to this post; discuss among yourselves.

[ 20030213 ]

 
NTP vs NEP, Round 3

Faithful readers will recall that at the end of the previous episode, our spaceship, the NSS Glenn Reynolds, was about to embark on an Earth-to-Mars trajectory which would take it only 1½ months to reach the Red Planet, but it was stuck in LEO while its astrogator (me) figured out how to calculate its flight-path angle j₁. This is the angle between a tangent to Earth's orbit around the Sun and a tangent to the transfer ellipse, a fairly eccentric (e = 0.667) orbit with a perihelion of 0.5 AU and and aphelion of 2.5 AU. Earth is assumed to be at its average distance from the Sun of 1.0 AU, and Mars is analogously situated at 1.523 AU.

Recalling that the true anomaly n of the intersection of Earth's orbit and the transfer ellipse is 2.892 rad = 165°42', and regarding Earth's orbit as a perfect circle, then the tangent to Earth's orbit is just n + 90° (p/2 rad), or 4.463 rad = 255°42'. But how do we find the tangent to the same point on the transfer ellipse?

Well, I did it by finding Prof Eduard Belinsky's Introducing the Ellipse, in which a key phrase, "focal radii form equal angles with the tangent," gave me the clue I needed. The tangent point and the two foci form a triangle whose sides add up to 5 AU (twice the aphelion). Its base is the distance between foci, which is 2 AU. Its right leg is the distance from the Sun to Earth, which is 1 AU. Therefore its left leg must be 2 AU.

Now what we want, first, is the angle (referring to the Belinksy webpage) F₁AF₂. We can then subtract this from 180° (p rad) and divide by 2 to get angles T₁AF₁ and F₂AT₂, particularly the former; adding it to F₁AF₂ and subtracting 90° should give us the flight-path angle (in this case, we don't even need to know the angle of a tangent to Earth's orbit).

Now to use the Law of Cosines. Call the base side a, the right leg b, the left leg c, and the corresponding angles opposite the legs a, b, and g. We know a, b, and c, and we want a.

Turning, I kid you not, to this source (p 32), we find

cos a = (b² + c² - a²)/2bc

So cos a = 0.25, and a = 75°31'; then (180° - a)/2 = 52°14'; 75°31' + 52°14' - 90° = j₁ = 37°45'.

Now that we've got the flight-path angle, what do we do with it? First, use the equations in "Appendix 1" of this post, with some additional complications:

1. Calculate the parameter p of the transfer ellipse as p = a (1 - e²)


2. Calculate the energy E_t of the transfer ellipse as E_t = - m (1 - e²)/2p


3. Calculate v₁ and v_CS1 as before.


4. Dv₁² = v₁² + v_CS1² - 2v₁v_CS1 cos j₁

Note that the final step is another application of the Law of Cosines. And the results are ...

p = 1.247 ´ 10⁸ km

E_t = 164.3 km² sec^-2

v₁ = 45.85 km sec^-1

v_CS1 = 29.78 km sec^-1

Dv₁² = 829.0 km² sec^-2; therefore Dv₁ = 28.79 km sec^-1

Add to this the Earth-escape-from LEO Dv of 3.17 km sec^-1, for a total of 31.96 km sec^-1, and the Reynolds is underway, no doubt with this playing over the ship's PA system.

But will its crew reach Mars alive? And if they do, how much Dv do they need to enter Mars orbit?

Graze on back tomorrow, or whenever I get around to analyzing the ship's mass budget, to find out whether they can carry enough consumables -- or even propellant -- with them to orbit the Red Planet. Also for some good ideas from Randall Parker of FuturePundit.

And someday, I'll post answers to the e-mail I've been getting about this.

Hey, it's a cliffhanger for geeks. Deal.

Jay Manifold [9:19 PM]

 
Because It Can Become Good (V)

Continuing this series -- via Glenn Reynolds, in a comment to this post, Sylvain Galineau writes (my emphasis):

... what makes the US special and successful [is that i]t's just a huge mix of people who know what not to do and are willing to try the rest and select the best no matter where it comes from.

Jay Manifold [8:50 AM]

 
Arcturus is a Loser

As explained by goatee, and I'm in good company -- I see, among other luminaries, Joanne Jacobs, Charles Murtaugh, Fritz Schrank, and John Weidner, none of whose sandals I am worthy to untie, on that list. But, hey, I'm at the top, and besides, it's all in how you look at it:

... this isn't to say that these sites are less popular in absolute terms. None of these sites have lost inbound links and most have doubled them over six months. Simply, some sites were pushed aside with the influx of the 330 new sites. In fact, this analysis doesn't even consider those sites from six months ago that are now below the 500 mark.

Must reading for anyone wishing to acquire a deeper understanding of the power law phenomenon in the blogosphere.

Jay Manifold [7:31 AM]

 
Your Daily Math Fix

Speaking of Joanne Jacobs, she points to Number 2 Pencil's blogging of a study which shows that "teaching to the test" might not be so bad after all (locals, one of the districts in the study is Blue Valley); conversely, grade inflation has rendered classroom grades worthless as a measure of achievement.

Jay Manifold [7:30 AM]

[ 20030212 ]

 
The Universe at 380,000 Years

"The microwave light captured in this picture is from 380,000 years after the Big Bang, over 13 billion years ago: the equivalent of taking a picture of an 80 year old person on the day of their birth." (source)

Jay Manifold [3:29 PM]

 
Risk Management: Foreign (cont'd)

(Ref this earlier post.)

Charles Murtaugh notes the possibility of a lengthy American occupation of Iraq and the disbelief this often evokes, at least in some American subcultures.

A history lesson is in order. Browsing USAREUR as NATO's Shield of Democracy, we find:

From a strength of about 79,000 in 1950, USAREUR grew to a strength of more than 250,000 ten years later. Its two corps, four divisions, and two armored cavalry regiments, the bulwark of NATO's Central Army Group, maintained a vigil on the borders of East Germany and Czechoslovakia.

By the early 1970s, as the war in Vietnam drew to a close, one-fifth of the Army's total manpower was in Europe. Seventh Army (consolidated with USAREUR in 1966) included one-third of all the Army's combat divisions. Additional units in the U.S. were earmarked for rapid movement to Europe as dual-based and rapid reinforcement forces.

With its current [as of Mar 99] strength of about 65,000, more than one-third of USAREUR'S soldiers are deployed at any one time on diverse missions, often as part of joint and multinational task forces. USAREUR also has expanded its contacts with the military forces of central and eastern European countries to assist those forces in making a successful transition to democracy and partnership with NATO.

Turning to Cold War History, we find that

The nearly 50-year sojourn of an entire American field army and American air forces in peacetime Germany was a hallmark of the era.

Whereas American military and naval deployments before 1941 had been confined to limited garrisons in Panama and the Philippines, military commitments now assumed a global defensive character. Defense appropriations were consistently the largest element of the annual budget and a large part of the nation's scientific genius and wherewithal went into weapon and other defense-related research. Direct defense outlays for 1989, the year that the Berlin Wall came down, amounted to $303.6 billion or 5.7 percent of the gross domestic product for the year.

If we assume that the US spent 3% of GDP for 50 years to defend western Europe, the costs of a 20-year occupation of Iraq seem modest by comparison. There is essentially no external threat analogous to the Warsaw Pact, and Iraq, while physically larger than Germany, is mostly flat, empty desert and has less than one-third Germany's population (and therefore less than ¼ its population density). The American role will largely consist of repairing or facilitating the creation of 1) public health infrastructure and 2) autonomous institutions (an independent judiciary, free media, peaceful transfer of executive and legislative power through free elections, etc).

Suppose that satisfying (1) costs as much as building modern water works for the entire Iraqi population (24 million people), and that per capita water use is 200 gallons per day (the usual American estimate is one acre-foot per family of four per year, which works out to 223 gallons per person per day; this is extravagant). This source indicates that water treatment plant construction costs are $~1 gal^-1 day^-1. We need a total capacity of 4.8 billion gal day^-1. In round numbers, $5 billion, which is about what we were spending on NATO every couple of weeks during the Cold War.

Satisfying (2) is, of course, a good deal fuzzier. Suppose it entails giving 100,000 people 1,000 hours of instruction apiece at a fairly high labor cost, $100 hr^-1. That's another $10 billion.

Not to overlook the obvious, there is the cost of the occupation force itself. Maintaining 20,000 soldiers on duty at all times -- meaning two or three times that number physically present in the country -- and again assuming a labor cost of $100 hr^-1 yields an annual expenditure approaching $20 billion. So if we did have to occupy Iraq for 20 years, the "nation-building" costs could come to less than 5% of the total.

Jay Manifold [10:08 AM]

 
Risk Management: Domestic (cont'd)

(Ref this earlier post.)

Courtesy of Elaine Monaghan in Times Online, All-America survival pack: What everyone needs, which references something called the Guide to Citizen Preparedness. I Googled this and found FEMA's eschatologically-titled Are You Ready?, the juicy part of which is National Security Emergencies (warning: 628 kB *.pdf). The entire document is also available in MS Word format here (483 kB). I'll comment on its risk-management quality one of these days ...

Jay Manifold [10:07 AM]

[ 20030211 ]

 
NTP vs NEP, Round 2

Nothing like pegging the needle on the old geek-o-meter to generate fan mail. -- To which I will post responses presently, but right now it's time to do an equally out-of-control follow-up to this earlier post, in which I employed some oversimplifications and crude calculations in an attempt to show that nuclear-electric, aka ion drive, is vastly superior to nuclear-thermal (ie NERVA) for a Mars mission.

My hypothetical rocket was flying to Mars on a Hohmann transfer, which requires the least energy but takes the longest (8½ months each way), thereby requiring lots of extra consumables. So it's a good thing that only about one-ninth of the mass of a nuclear-electric propulsion spaceship would need to be propellant, because a whole bunch of that other eight-ninths would be needed for anything that couldn't be recycled, or recycled efficiently enough, en route.

We will therefore consider more direct trajectories and determine their Dv requirements and flight times. Those of you who brought your copies of Fundamentals of Astrodynamics should turn to ch 4, "Position and Velocity as a Function of Time."

This is going to require some visualization, and I have not yet begun creating diagrams and ftp'ing them to my personal website, so you may wish to refer to Time of Flight in Classical Variables, especially the diagram at the top of the second page (this document is a 181 kB *.pdf). Those of you who are hopelessly intrigued by this topic may wish to procure pen and paper (and judging by my e-mail, quite a few of you will do just that).

Our spaceship, the NSS Glenn Reynolds, will be launched from LEO into a solar orbit which, were it to follow its entire circumference, would appear to be an ellipse with perihelion 0.5 AU and aphelion 2.5 AU. The only portion of the ellipse it will actually travel along, of course, is a segment connecting Earth and Mars, which as before are assumed to be at their average distances from the Sun, 1.0 and 1.523 AU, respectively.

We're going to calculate time-of-flight first. The formula is

TOF = Ö(a³/m) (E - e sin E), where

a = 1.5 AU = 2.244 ´ 10⁸ km
m = 1.327 ´ 10¹¹ km³ sec^-2
e = (aphelion - perihelion)/(aphelion + perihelion) = 2/3 = 0.667

and last, but certainly not least,

E is the eccentric anomaly

The eccentric anomaly is defined as "the angle measured at the center of the ellipse from pericenter to the point on the circumscribing auxiliary circle from which a perpendicular to the major axis would intersect the orbiting body." It's angle QOV on the diagram in the paper I referred to above.

Now, having spent a few minutes sketching the elliptical orbit as described and superimposing on it a circle representing Earth's orbit, I satisfied myself that the point at which they intersect has a true anomaly n of (2p - 0.5)/2 radians = 2.892 rad = 165°42' (yes, I'm too lazy to reproduce the entire chain of reasoning). We need to convert this into the eccentric anomaly, and the formula is

cos E = (e + cos n)/(1 + e cos n)

Since e is 2/3 and cos n is -0.969, cos E is -0.853 and E itself is 2.593 rad = 148°32'. Now repeating the mysterious process for determining the intersection point of the ellipse (let's just say I had to use the Law of Cosines this time), but with the orbit of Mars, I find n = 2.318 rad = 132°46'. The "Mars E" then works out to 1.594 rad = 91°21'.

The E we want, of course, is the difference between the two, which is 0.999 rad, or 57°14'. Plugging this back into the TOF formula yields an answer of 4,042,000 sec, which is 46 days, 19 hours -- 1½ months vs the 8½ months of the Hohmann transfer. So the Reynolds can carry less than one-fifth the consumables needed by the earlier (unnamed) spaceship. Perhaps nuclear-thermal, even with its prohibitive mass-ratio, is an option after all.

But how much Dv does the Reynolds need to get onto this trajectory in the first place? Will it be so much that only nuclear-electric can do the job? Tune in tomorrow (or whenever I figure out how to compute the flight-path angle j₁) for our next thrilling episode ...

Jay Manifold [10:42 PM]

 
Results of Latest Random Survey

Via Amygdala (indirectly), and sufficiently flattering to post ...

test yourself at fontlover.com!

Jay Manifold [1:29 PM]

[ 20030210 ]

 
Public Sentiment: Stay the Course

Perhaps unsurprisingly -- in a difficult time, significant public-policy changes not related to national survival don't get a lot of mental bandwidth. That's my interpretation of Gallup's Americans Want Space Shuttle Program to Go On. Realism is in the air: "Many Americans, while upset over the tragedy, felt that something like it was bound to happen, and only about 4 out of 10 have a great deal of confidence that NASA will be able to prevent future shuttle accidents."

Nonetheless, "Eighty-two percent say the United States should continue with the manned space shuttle program, while only 15% say the nation should not do so." And that's the way the question was worded -- "... do you feel the U.S. should or should not continue the manned space shuttle program?" -- not a vague "space program" or even "manned space program."

This support drops, but only slightly, in the face of the relatively inexpensive and successful planetary program: "Additionally, 73% of those interviewed ... believe the space program should continue to include manned missions in addition to unmanned missions like the Voyager probe." While I would have worded the question to mention Mars Pathfinder/Sojourner instead, it's difficult to imagine this lowering support for a manned program below 50%.

The American tendency to align in the wake of a crisis is evident in "... a rise ... in the percentage of Americans who want NASA's funding increased (now at 24%) and a drop to only 16% who want space funding decreased or ended altogether."

Meanwhile, a CBS poll found 4-1 support for continuing the Shuttle, but substantially more respondents thinking that the space program (manned/unmanned not specified) is good for "pride and patriotism" than "scientific advances."

What's missing from all this, of course, is any suggestion that things can be done differently: use non-Western launch vehicles, facilitate a competitive domestic launch market, fund science through NSF or the states, or any other alternative to a multi-billion-dollar annual public expenditure on space, the bulk of which goes to Shuttle/ISS. Those of us who advocate such changes need to prepare for the day when the public will be ready to consider them.

Jay Manifold [8:53 AM]

[ 20030209 ]

 
NTP vs NEP: the Tradeoffs

(Advance warning: longer and, if possible, even geekier than my usual material.)

At Randall Parker's suggestion, I followed a link from an earlier post of his to Bruce Moomaw's Media Hype Alone Cannot Fuel The Space Program (see end of post for excerpts). The question all this raises is, which propulsion method is better for a manned Mars mission: nuclear thermal, in which hydrogen is heated by a nuclear reactor and expelled via an otherwise relatively conventional rocket nozzle, or nuclear electric, in which the reactor powers an ion drive?

Nuclear-thermal rockets are high in thrust and short in duration, like the chemical rockets we have today, but two or three times more efficient. Nuclear-electric rockets are low in thrust but long in duration, like the ion rockets we have today, but ten to fifty times more efficient than today's chemical rockets.

In The Pre-Game Show, I showed that a nuclear-thermal spacecraft might be able to devote about one-fifth of its mass to all non-propellant items, whereas a nuclear-electric one could reserve nearly three-fifths, thereby carrying at least three times as much payload.

Alert readers, however, will recall that I specified a Dv of 15.6 km sec^-1 (approximate escape velocity from the Solar System, starting in low Earth orbit). What is the actual Dv requirement of a Mars mission?

Assumptions:

• The propulsion system in question will be used only to get from low Earth orbit (LEO) to medium Mars orbit (MMO), perhaps the vicinity of Deimos (23,460 km from Mars), and back to low Earth orbit. Separate shuttles carry the astronauts up from Earth and down to Mars.


• The baseline case will be one in which both Earth and Mars are at their average distances from the Sun.


• The trajectory chosen will be a Hohmann transfer orbit.

The changes in velocity are:

1. LEO (400 km) to Earth-escape: 3.17 km sec^-1


2. Earth-escape to Hohmann transfer: 2.95 km sec^-1


3. Hohmann transfer to MMO (Mars Orbit Insertion [MOI]): 3.21 km sec^-1


4. MMO to Mars-escape: 0.56 km sec^-1


5. Mars-escape to Hohmann transfer: 2.65 km sec^-1


6. Hohmann transfer to LEO (Earth Orbit Insertion [EOI]): 6.12 km sec^-1

Total: 18.66 km sec^-1. Plugging this back into m_bo/m₀ = 1/eDv/gI and setting I = 950 sec for nuclear-thermal leaves 13.5% of total mass for non-propellant items. But with I at 16,000 sec for advanced nuclear-electric, only one-ninth of total mass is propellant!

The objection to this scenario is obvious: a Hohmann transfer takes longer than any other orbit; from Earth to Mars, it's 259 days -- 8½ months -- each way. What about more direct trajectories? The next post in this series will consider some alternatives.

APPENDIX 1: How I Figured It

The equations are taken from pp 164-5 of Fundamentals of Astrodynamics, and the value of m from p 429:

E_t = -m/(r₁ + r₂)

v₁ = Ö[2 (m/r₁ + E_t)]
v_CS1 = Ö(m/r₁)
Dv₁ = v₁ - v_CS1

v₂ = Ö[2 (m/r₂ + E_t)]
v_CS2 = Ö(m/r₂)
Dv₂ = v₂ - v_CS2

m = 1.327 ´ 10¹¹ km³ sec^-2
r₁ = 149,600,000 km
r₂ = 227,800,000 km

Escape velocity from LEO (400 km) = orbital velocity ´ (Ö2 - 1) = 7.67 km sec^-1 ´ 0.414
Escape velocity from MMO (23,460 km) = Deimos' velocity ´ (Ö2 - 1) = 1.36 km sec^-1 ´ 0.414

I made a simplifying assumption regarding the MOI and EOI maneuvers, namely that the vectors would be lined up in such a way as to permit simple addition of the velocities.

APPENDIX 2: Excerpts from the Bruce Moomaw article ...

[NASA Administrator Sean] O'Keefe has spent the past year talking constantly about his hopes for a deep space mission using nuclear-powered propulsion within a decade or so -- while making it clear that he is talking about an unmanned, relatively small probe. NASA's Nuclear Electric Propulsion program -- for which it included $46.5 million in its FY 2003 budget request -- would have been just such a system.

... its actual rocket engines would be ion thrusters using several kilowatts of high-voltage electricity to electromagnetically hurl a trickle of ionized vapor out of the thrusters at extremely high speed, thus producing at most a few ounces of thrust, but for years rather than minutes.

This allows a spacecraft to gradually accelerate itself to very high velocities using a far smaller amount of onboard ejectable propellant mass than any chemically powered rocket engine can do.

A spacecraft with a nuclear-electric propulsion (NEP) system would therefore carry a miniature nuclear reactor weighing several hundred kilograms, and capable of turning out kilowatts of power for years on end ... It could thus accelerate itself to very high speeds in the outer System -- and also decelerate itself later to enter orbit around outer planets.

But this is an enormous distance from the tremendously larger and more powerful nuclear-powered rocket engines that would be necessary to accelerate a manned ship to Mars.
Indeed, these would probably not use NEP at all, but would instead use some form of "nuclear thermal propulsion" in which a large reactor would heat the propellant gas directly to thousands of degrees in order to blast it out of the rear exhaust.

Nuclear-electric exploration of the Solar System has tremendous scientific potential in the middle-range future -- and such reactors would use uranium-235, which is far more expensive than plutonium but also thousands of times less radioactive when a reactor is shut down, thus being virtually totally safe to launch into orbit.

Jay Manifold [7:11 PM]

 
Columbia Struck by Orbital Debris on Day 2?

CBS News space consultant William Harwood reports

... that something might have struck the shuttle about a day after launch.

... sources say data from Air Force tracking radar indicates the possibility that a piece of the shuttle may have come off. They see something that appears to be separating from the orbiter about five meters per second.

... perhaps the shuttle was doing a water dump at that time.

But sources have said that it looks as if the object might have been in orbit another two days before re-entering the atmosphere, and that's not consistent with a water dump.

See this earlier post for my assessment of the likelihood of such an event.

Jay Manifold [12:28 PM]

 
If You Choose Not To Decide, You Still Have Made A Choice

Via the usual source, Clay Shirky's Power Laws, Weblogs, and Inequality. Read the whole thing, and ponder these two questions:

Where'd I get the title of this post? And what happens when Glenn quits?

UPDATE: Semi-regular contributor Bill Walker is first past the post with: "The quote is from the Rush song Free Will. When Glenn quits, Postrel will take the One Ring, and all will love her and despair."

Second-order contest: Where did Bill get that line? Be specific.

Jay Manifold [11:46 AM]

[ 20030208 ]

 
Shuttle Pix

Via Pathetic Earthlings, a big page of ground-based shuttle photographs by Paul Maley; the external tank reentry over Hawaii is particularly impressive.

Jay Manifold [4:51 PM]

 
Educational Innovations in KC

Taking a brief break from my all-Shuttle-all-the-time format of the past week, here's a human-interest story, namely a follow-up to Kansas City Strip (-Search), which you may wish to read before continuing.

Now we have KC district principal, two teachers removed over alleged binding of kindergartners with tape -- and whaddaya know, it happened at Pitcher Elementary, the same school where the 3rd-graders were strip-searched last March:

... pupils from more than one class may have been taped to their chairs and their hands bound together with tape .... officials were also investigating reports that pepper had been placed in the mouths of pupils. Other officials said that at least one kindergartner had been threatened with a hot glue gun ...

Way over the line -- if it's true, that is. If the only witnesses are the alleged perpetrators and classrooms of kindergartners, then leading of witnesses is going to be just as big a problem as it was in all the bogus day-care Satanic abuse cases of the 1980s. And not all the patrons are upset:

"From what I heard of the incident, I don't see a thing wrong with it," said Victoria Levy, whose granddaughter is in kindergarten.

"You mean to say our teachers can't discipline the children?" Levy said. "I think if that's what it takes to make children behave, I believe that's necessary because our school is getting out of hand.

"Children are bringing guns to school; they're fighting and doing all kinds of things. Who's going to run the school?"

Reviewing the school report card doesn't leave a favorable impression: bizarre fluctuations in the Missouri Assessment Program test scores (which to my mind suggests either high turnover or facilitated cheating), less than half the K-3 kids reading at grade level (the recommended baseline is 85%), less that three-fifths of 3rd-5th graders demonstrating "one year of growth in one year of instruction," and marginal parental participation.

The school is not in a stereotypical "bad area," and minorities are not overrepresented. But as I know from personal experience, there are such things as white slums, and I think that's part of what we're dealing with here: a student body most of whose parents have low incomes and low expectations.

Jay Manifold [11:58 AM]

[ 20030207 ]

 
The Air Force Pictures

The image everybody's talking about has an apparent resolution of perhaps 0.5 m. What can we infer about the capabilities of the optical system?

The picture was taken from Albuquerque, and this story says "the shuttle ... passed somewhere between Albuquerque and Santa Fe." Its altitude at that point was about 65 km. All this works out to a slant range of ~80 km. Resolution was therefore 1 part in 160,000 = 0.00000625 rad = 1.3" (arc-seconds).

Once again applying a ~ 120/D (see this earlier post for explanation), we find that the minimum aperture required is only about 90 mm, so one of these could have taken the picture.

Alternatively, if the picture was taken from White Sands, the slant range would be more like 210 km, and the resolution 0.5", essentially the limit obtainable without adaptive optics. The telescope aperture would have needed to be at least 240 mm (~9½ inches), still well within amateur range.

In either case, however, the camera/telescope combination would have had to track the Shuttle's motion, as it would have been moving about 1/7 its own length even in a 1/1000 sec exposure!

Jay Manifold [9:36 PM]

 
Quote of the Day

From The Scene:

My optimism isn't a faith that the future will be better, only that it can be better. Making a better future possible depends not only on having, but on defending institutions and ideals that are always at risk from those who wish to destroy them. One of those ideals is that the ordinary joys and sorrows of individuals' earthly life are important, that "the pursuit of happiness" is so central to human life that securing that right is one of the reasons for government.

As a much lesser writer recently said, "a selection process is underway, at the level of the nation-state, favoring those who develop the most effective and enduring institutions."

Jay Manifold [10:59 AM]

 
Space Shuttle Economics

Is the shuttle worth it?, asks Richard Stenger of CNN, and the answer is painfully obvious:

"The [original] numbers that NASA gave to the White House were that shuttle would cost about $5.5 million per launch and the launch rate would be anywhere between 50 and 60 launches a year," said John Logsdon, director of the Space Policy Institute at George Washington University.

Shuttles have instead averaged about five launches a year, and NASA was way off on the cost.

"Most people use a figure like $400 [million] or $500 million [per launch]," Logsdon said.

Assuming a payload of 20,000 kg per launch, what was promised was around 1.1 million kg per year for just over $300 million. What we got was 100,000 kg per year for $2.5 billion. Cost per kilogram of payload to orbit was supposed to be $~275. It's actually $~25,000, that is, over 90 times more expensive (if Logsdon's figures are uncorrected for inflation, it's still over 30 times more expensive than promised).

Well, isn't this stuff terribly expensive anyway? Uh, no. The Saturn V put 118,000 kg into orbit for $431 million (1967 $), which (using these conversion factors) works out to about $19,000 per kilogram in current dollars -- cheaper than the Shuttle is now, and only 13 Saturn V's were ever launched, less than one-eighth the number of Shuttle flights!

Just to add to the irony, a Shuttle based on a reusable version of the Saturn V first stage, called "Flyback F-1," was designed (in detail, not just high-level) in 1971 (source: T.A.Heppenheimer, Colonies In Space, pp 85-96); it would have had a payload cost to orbit of about $165/kg today, over two orders of magnitude cheaper than the Shuttle we've got (or rather, had). And it wouldn't have had any solid-rocket boosters strapped to its sides, thereby eliminating a huge risk.

While I'm making comparisons, consider that Skylab had a total habitable volume of 361 m³, and cost less than $100 million (see page 5); for comparison, the ISS has a habitable volume of 425 m³, for a cost approaching $100 billion. In the Encyclopedia Astronautica Skylab entry referenced above, Mark Wade concludes that a second Skylab/Apollo-Soyuz could have been launched in the mid-1970s, "an International Space Station, at a tenth of the cost and twenty years earlier." I'd say more like less than 1% the cost and thirty years earlier ...

Jay Manifold [10:23 AM]

[ 20030206 ]

 
Shuttle Safety, and M/OD (again)

Over on FuturePundit.com, Randall Parker has a typically lengthy but fascinating entry comparing airliner safety to Space Shuttle safety.

Meanwhile, Glenn Reynolds states:

... the odds favor debris; in Low Earth Orbit there's about twice as much manmade debris as natural meteor flux.

But assuming the impact occurred during re-entry, the Shuttle was a bit low for that. It would have had to collide with something that was re-entering (or in the case of a meteorite, just entering) the atmosphere at the same time, which is far less likely than an on-orbit collision.

This depends on one's definition of LEO; my impression after reading through the NASA document referenced below is that the difference is much greater than a factor of 2, and that meteoroids may essentially be ignored. Glenn is correct, however, in stating that the lower the Shuttle, the less likely the impact, due to rapid decay of debris orbits as atmospheric drag decreases. The solar maximum of 2000 also helped remove debris by expanding the outer atmosphere.

Jay Manifold [1:44 PM]

[ 20030205 ]

 
Meteoroid and Orbital Debris Threat to Shuttle?

Jim Miller dropped me a line to point me to this post on his blog and politely hint that I might be just the guy to look into the possibility. Man, I should have thought of this already (interestingly, meteors and space debris are not mentioned in the FAQ). Anyway, a short search turned up NASA Reference Publication 1408, Meteoroids and Orbital Debris: Effects on Spacecraft (warning: 1.4 MB *.pdf).

To answer Jim's inquiry literally, no:

Measurements by Pegasus spacecraft in 1965 found that, in Earth orbits, the probability of collision with a meteoroid large enough (greater than 1 cm) to create significant damage is remote.

But "natural causes" are not the only way to get hit by something in orbit:

Orbital debris is not a naturally occurring phenomenon in the natural space environment. It is man-made space litter resulting from 40 years of space exploration. Released parts of spacecraft, unintentional explosions, and spent satellites have created this growing threat to space operations. Orbital debris includes rocket bodies, mission related debris, fragmentation debris, and nonfunctional spacecraft.

The cumulative mass of these objects is approximately 2 000 000 kg with an average velocity of 10 km/s.

The hazard is not just theoretical:

Significance of the meteoroid and orbital debris (M/OD) threat is evident in numerous spacecraft anomalies. Unexplained destructions of spacecraft are believed caused by impacts with large debris. A French military research satellite, Cerise, was struck July 24, 1996, by an Ariane booster fragment about the size of a suitcase. The Cerise began tumbling after the 6-m boom which stabilizes the satellite was cut in half. This incident was the first witnessed impact of two tracked space objects.

Examples of spacecraft anomalies caused by the M/OD environment include:

• A cracked Space Shuttle window from impact with a paint chip


• Penetration of high gain antenna dish aboard the Hubble Space Telescope (HST)


• Marred surfaces on the Solar Maximum Mission spacecraft.

A figure on p 4 of the document (page "13 of 27" in Acrobat Reader) shows the orbital debris flux for the Space Station. Assuming that a particle at least 1 cm in size would be required to significantly affect the Shuttle, as by striking it obliquely and damaging or dislodging several tiles, leading to a "zipper effect," then the flux in this orbit is ~10^-5 impacts m^-2 yr^-1.

The cumulative time spent in space by all the Shuttle orbiters is about 3 years. Taking the Shuttle as a large isoceles triangle, 37 meters tall and 24 meters wide at the base, we find an effective surface area (counting both sides) of about 900 m². Multiplying 900 by 3 and dividing by 100,000 yields a likelihood of 2.7% that an orbiter would have been struck by a medium or large piece of orbital debris by now.

This is higher than I expected, but hundreds of additional Shuttle missions would be needed to get the cumulative probability into double digits. So the short answer is: maybe, but probably not.

UPDATE: Rand Simberg points to NASA Considering Space Hit, which points out that the orbit Columbia was in was much "cleaner" than the ISS orbit (which would lower my probability estimate above) and that

... if something struck the shuttle with enough force to ultimately bring it down, many analysts say NASA, its crew and the craft's computers would have known instantly. NASA's test facility in White Sands, N.M., recently conducted a study of the potential impact of space debris. The conclusion: A piece of plastic the size of a walnut could tear a 5-inch-wide hole through aluminum as thick as the Los Angeles telephone book. In other words, one analyst said Tuesday, if the shuttle struck something, "everybody would know. It would be loud."

Jay Manifold [5:00 PM]

 
More Local Blogging on Columbia

Thanks to previously unknown (the best kind) reader Angie Schultz for pointing me to Old Blind Dog, a Nacogdoches (TX) blogger with several posts worth reading from over the weekend; start here and scroll up.

UPDATE: Angie has a fine blog, The Machinery of Night, herself.

Jay Manifold [10:44 AM]

[ 20030204 ]

 
Cross-Posting

I've received several kind mentions on other blogs recently, but both because almost anybody who reads Arcturus reads them too, and because (believe it or not) I try not to be too self-indulgent, I'm reluctant to call attention to such things, so I haven't listed them. I should, however, acknowledge Agenda Bender, whose proprietor not only has reached across several cultural divides but has also managed to post Columbia-related items about music and smell which are very much worth reading.

Jay Manifold [8:11 PM]

 
Columbia FAQ

-- is here. Thanks to Rand Simberg for the tip.

Jay Manifold [3:32 PM]

 
Debris Math

Independent Shuttle Panel Surveys Debris, reports AP Science Writer Joseph B. Verrengia:

Some 12,000 pieces of debris had been collected in the region by late Monday afternoon. Human remains have been reported at 15 locations in Nacogdoches County alone.

The pieces are being gathered from an area larger than West Virginia. The debris field stretches west to east 380 miles from Eastland, Texas, to Alexandria, La., and north-south 230 miles from Sulphur Springs, Texas, to metropolitan Houston.

Assuming this area to be elliptical, applying A = pab, we find that it covers nearly 70,000 square miles, or 180,000 km². Turning to Mark Wade's incomparable Encyclopedia Astronautica, we find that the mass of the Columbia orbiter was 104,328 kg.

Suppose the average piece of debris is 5 ´ 10 ´ 20 cm and has a density of r = 2 g cm^-3, giving it a mass of 2 kg. There would then be over 50,000 such pieces; their average separation from one another on the ground would be over a mile.

Fortunately, the weather has cooperated so far, but rain and freezing rain are forecast for later in the week. Today may be the last full day of an unimpeded search.

Jay Manifold [9:36 AM]

[ 20030203 ]

 
Spotting Shuttle Problems from the Ground

So, okay, suppose a bunch of tiles fall off an orbiter. What would it take for an amateur network of observers to monitor it and tell NASA there was a problem?

Suppose it's going to the International Space Station, as nearly all Shuttle missions these days are; that we need to be able to track it when it's as low as 30° above the horizon; and that we need 10-cm resolution to spot problem areas. The ISS is 390 km above Earth's surface (source), and slant range at 30° altitude would be twice this. It all works out to one part in 7.8 million, that is, 1.28 ´ 10^-7 rad, or 0.026" (arc-sec). Can this be done?

Applying a ~ 120/D (where a is the smallest resolvable angle in seconds of arc and D is aperture in millimeters) suggests that a 4.5-meter telescope would be needed; furthermore, "atmospheric conditions seldom permit values less than 0.5 [arc-sec]," nearly 20 times coarser than our requirement (source).

But there's a way around this. Referring back to this earlier post, we read of an existing adaptive-optics system getting 0.1" resolution with an aperture of only 1 meter. Well-equipped amateur observatories have telescopes in this size range. Were the Shuttle to fly directly over a facility with these capabilities, it could be imaged at a resolution of 19 cm, probably sufficient to diagnose serious trouble. So the question becomes one of the expense of the AO system. If I ran NASA, and I wanted to keep the Shuttle flying, I'd start handing out grants to organizations like this to upgrade their telescopes.

Jay Manifold [9:02 PM]

 
Space Exploration vs Shuttle/ISS

Numerous commentators, including some I greatly admire, are conflating "space exploration" with the Space Shuttle and the International Space Station. This is a mistake. Space exploration can and indeed must continue. But it can do quite well without the Shuttle or the Space Station, and perhaps without NASA altogether, at least in its present form.

Rand Simberg has done well by asking, in effect, what's the object of the game? -- and pointing out that there are, in fact, several different "games"; he mentions:

• "Building an orbital infrastructure that can both mine useful asteroids and comets, and deflect errant ones about to wipe out civilization"


• "Building orbital laboratories in which biochemical and nanotechnological research can be carried out safely"


• "A new leisure industry, with resorts in orbit or on the moon"


• "Establishing off-world settlements"

I would add, in order of distance from Earth:

• Inner Solar System: Further lunar exploration, especially of the polar regions, the far side (specifically the South Pole/Aitken Basin), and sites of relatively recent volcanic activity; near-Earth asteroid rendezvous; Venus balloon-borne probes and landers; Mars rovers, balloons, etc (several of these are in progress); Mercury missions (also planned) -- Mercury has only been visited by a single spacecraft, nearly three decades ago.


• Solar missions: If climate change on Earth is being driven by "solar forcing," greater understanding and better monitoring of the Sun is of the highest importance.


• Outer Solar System: Probes to main-belt asteroids of interest, including Vesta -- a geologically complex body -- and at least one metallic and one "carbonaceous" asteroid; follow-ons to Galileo and Cassini-Huygens to explore the Jovian and Saturnian systems; outer planet and Kuiper Belt probes.


• Solar Neighborhood: Advanced optical systems to search for planets around nearby stars and conduct an exhaustive census of everything within tens (or hundreds) of light-years of the Solar System.


• Galactic research: Infrared and other telescopes to examine the galactic center in greater detail.


• Cosmological research: Follow-ups to the Hubble Deep Field image to learn more about the early Universe.

Of course, Rand's list is intended to demonstrate a role for human spaceflight; mine is oriented toward space science, and few if any of the items on my list would require a human presence in space. Some things on my list, however, are precursors to substantial economic activity; in a paper I delivered at the Commercial Lunar Base Development Symposium in Houston in July of 1999, I stated:

A program of robotic sample return missions to various unexplored lunar sites can accomplish the definitive characterization of the geology of the Moon over a period of several years. In the course of doing so, such a program would develop much of the market and communications infrastructure necessary for returning human beings to the Moon, and would provide researchers with mineralogical and other data sufficient to identify locations suitable for human settlement.

and

Developing a greater understanding of the Moon and engaging the public are key parts of laying the foundation for a lunar base.

These statements apply to other locales for tourism, resource extraction, and settlement as well, notably near-Earth asteroids and Mars. There is therefore a complementarity, and often a logical sequence, of unmanned and manned activities in space.

But very little of what either Rand or I foresee can make much use of the Shuttle or the International Space Station. The inefficiency of the ISS is relatively well known, but few American taxpayers are aware of the gap between what was promised for the Shuttle program and what it has delivered. Turning to p 63 of this source, for example, we find:

Since the external tanks are not reused in a space shuttle mission, plans call for the manufacture of perhaps forty-five to sixty tanks per year in the late 1980s to accomodate the total number of planned flights of space shuttle through the 1990s, expected to be between five hundred and six hundred flights.

A wildly optimistic NASA diagram on p 106 shows a Shuttle orbiter being "turned around" in only 160 hours of ground maintenance, that is, being made ready for re-launch within one week.

Reality: browsing this table reveals only 94 flights through the end of 1999, with a peak of 9 in the busiest year (1985). There were only 3 each in 1998 and 1999, 5 in 2000, 6 in 2001, and 5 in 2002. Instead of being one week apart, launches of any given orbiter have been closer to a year apart. And as we now know to our sorrow, it is most unlikely that there will be more than one Shuttle launch in all of 2003.

On this basis, then, the program has performed at somewhere between one-sixth and one-fiftieth its intended level. The cost picture is even worse. The Shuttle, which was supposed to knock a digit off of the price of space travel, is by far the most expensive launch vehicle per unit of payload mass currently in service -- far in excess of $10,000 per kilogram to orbit (at the other extreme, the Ukrainian Dnepr booster, a converted SS-18 ICBM, is less than one-tenth as expensive). Manned spaceflight, American style, is the only technological endeavor I can think of that has actually gotten more expensive over the past generation.

And in so doing, has robbed every American from the baby boom generation onward of the patrimony we could have had. Every item on my space-science wish list could have been carried out simultaneously for far less than we have spent on the Shuttle and ISS. A competitive space-tourism industry -- not just the occasional flight for a multi-millionaire -- could have been a reality long before now.

The best memorial to the fallen is to learn from events. We can do so by thinking outside the box -- not only technologically, but politically.

Jay Manifold [8:12 PM]