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The Mathematics of a Trip to Mars?
hakonhaugnes wonders: "Since trips to Mars seems commonplace (NASA has sent one every 26 months), I thought it made sense to try to understand how the interplanetary trajectory is calculated. NASA's page is deploringly void of intricate details. I found this
excellent page, but it still left me feeling that I was missing something. Surely the calculus must go beyond two bodies (mars/earth)? (It seems there are commercial MATLAB scripts available but at $150 it went beyond the defensible to satisfy my curiosity). Are there any curious Slashdot readers with the usual great insight into how to calculate a trip to Mars?"
What with all the epicycles and all;-)
If brevity is the soul of wit, then how does one explain Twitter?
Nasa has probably built a nifty model that will tell them the best launch times and dates. And I highly doubt that this model is as simple as 2 bodies. Everything out there has gravity, hell even the moon could be a problem.
I'm willing to bet what ever they use has a TON of factors build into it.
snowulf.com
I see more budget cuts have caused NASA to outsource to the open-source
Try Google maps.
(G*M1*M2) / R^2
Earth(+moon), Mars, Sun...I think that will get you there, as long as you dodge the moon on your way out
Are there any curious Slashdot readers with the usual great insight into how to calculate a trip to Mars?
Come on, this ain't rocket science, people. Oh, wait...
Guess and check!
having the entire Earth jump at the same time?
;)
I am sure that can get you to Mars.
I love deadlines. I like the whooshing sound they make as they fly by. - Douglas Adams
You sure that's not Marvin? :^P
The eternal struggle of good vs. evil begins within one's self.
Since trips to Mars seems commonplace (NASA has sent one every 26 months)
Was I the only one to think... Slashdot... commonplace... once every 2 years....
"Having Sex is commonplace for me"... the new Slashdot definition of commonplace.
An Eye for an Eye will make the whole world blind - Gandhi
Point it in the general direction, and launch.
It's like a message in a bottle, but so much cooler.
XaNk: now I remember why I hated the girls in high school
XaNk: because none of them would talk to me
Ok ok...I understand some of you will be rolling your eyes at this stage, struggling to understand how on earth a piece of command line software designed for the installation and maintenance of Debian packages could even be remotely applicable to designing a robust mission control interface for missions to the Mars. I will explain. Basically, think of the Earth as a large Debian mirror, equipped with many astronaut 'files'. Imagine the space ship as a .deb package, safely protecting all the astronauts from the harsh vacuum of space. The Mars (or Mars...this solution is cross-platform after all) is your local host. The Sun is...well...that creaky old Sun Ultra 5 from yesterday's OSnews article that no one wants to go close to lest they get burned or flamed by Sun zealots. OK...now how does the system work?
Basically, a mission controller wants to 'install' a 'package' of astronauts from the Earth 'mirror' onto the Mars 'host'. It's 5am, the mission controller hasn't slept for 3 days, and every command sent from Houston is critical. Enter apt-get. The initial launch command would be something like:
apt-get install astronauts
Great! The launch vehicle is on its way! Since the 'link' between the 'mirror' and the 'host' is quite slow (imagine an old school 9600 baud leased line), the 'package' 'download' may take a few days to complete. This is where the mission control staff go to work on getting their Gentoo boxes compiling KDE. When the 'package' is 'downloaded', it's important to check that no astronauts were hurt along the way. The mission controller enters the following command:
apt-get check
This wil check for 'broken dependencies'. So far, so good! The '.deb package' will now successfully 'install' onto the 'host', meaning the astronauts can land on the Mars, and perform their critical experiments. However, all good things must come to and end, and the 'package' will need to be removed from the host. Mission control to the rescue.
apt-get remove astronauts
Excellent! Tom Hanks, Gary Sinese and that other guy are now on their way home. Again, this is a slow link, so our 'host' may take a few days to remove it from it's 'hard disk'. Once the capsule has landed back on Earth, it will be ready for the next group of astronauts to make their journey. But no-one would want to spend 10 days locked up in a small space filled with cast-off cans of Jolt Cola and empty Penguin Mint containers. The capsule will need to be tidied up! Mission control enters one last command to complete the mission:
apt-get autoclean
Done! Another successful Mars shot. Mission control is a breeze with the new apt-get mission control system. No more complicated GUIs, voice recognition or toggle switches. apt-get to infinity and beyond!
It's simple, this is a point A to point B problem. Well, except that point A is moving...and point B...and they are not moving in straight lines...and they are not even circles...and, of course, there's the gravity issue...um, maybe IT IS complicated.
There has been a very long tradition of making source code developed by Government projects available to the general computing public. This is the true "public domain" software that has existed since the beginning of computing. I believe many bits of code from NASA made it into the public domain over the years.
I would bet that the information you desire is now considered to be highly classified and thus not available. You could produce trajectory information for ballistic missiles and who knows how it might be mis-construed as useful to those "terrorists" of whom the US is so fearful these days.
Besides... you might find a units of measure error or two if you got to see this code.
Yeah, but that still doesn't explain what happened to Jon Katz. I suspect he was behind the whole thing.
Several of the people I work with in Caltech's Control and Dynamical Systems department work on celestial mechanics and calculating space flight trajectories -- and I can assure you, it's some pretty complicated stuff, involving invariant manifolds and (IIRC) patching together different three-body systems. There's a good popular article about this in Science News, and you can find more info (in as much detail as you'd like!) on Shane Ross' homepage.
Cheers,
IT
Power corrupts. PowerPoint corrupts absolutely.
Maybe I can dig up an old F77 program from my undergraduate days ;)
I was an intern at JPL a couple of decades ago, and they always started with a "porkchop plot" (or "butterfly plot") of possible trajectories and their energy requirements. Here is a webpage that documents that to some extent:
p All.html
http://marsprogram.jpl.nasa.gov/spotlight/porkcho
I recently had a NASA guy come to speak to my research group at my medical school in Houston. We were talking about the long term effect of micro-gravity on human physiology (round trip to Mars). Anyway he told us that most of the mathematical calculations that the Space Flight Center here in Houston use are the "simple" Newtonian laws of motion. He claimed they were suitable for calculating trajectories to the Moon, Mars, etc...
Argh. The laws of science be a harsh mistress.
Orbiter is a great way to learn how those trips are done. It is a free simulator for windows and is available at www.orbitersim.com.
It has tools for calculating all sorts of interplanetary transfers and you can actually perform the flight from launch to landing on mars with all kinds of spacecraft.
I've never taken the class, but this problem is assigned as the final project in a senior level Orbital Dynamics class at the Univ. of Notre Dame. A numerical simulation is done, and it's my understanding that the physics are non-trivial. Maybe the prof will see this article and lend some insights.
The key here is the energy required. Space travel is still dominated by propulsion. That is, the engines and the fuel they need, and the fuel needed to launch that fuel to orbit, etc., is where most of the cost is.
It is important to travel on a trajectory, called the transfer orbit, that requires the least energy. For a high thrust spacecraft, the minimum energy trajectory is called a Holman transfer. Simply, it is an orbit that just touches the orbits of both planets. The periapsis, the closest point to the sun, touches the orbit of the one planet and the apoapsis, the furtherest point, touches the other planet. For this to work, the destination planet needs to be half an orbit away when the spacecraft arrives. This is a lot easier to see in a picture.
For Earth to Mars, the spacecraft launches and then the thrusters fire to change the spacecraft's orbit of the sun from Earth's orbit to the transfer orbit. It then travels half of the transfer orbit and fires its thrusters to change its orbit to match Mars. This can be done by aerocapture, aerobraking or propulsion. The opportunity for a Holman transfer to Mars occurs every 26 years. It is based on the length of the orbit for the bodies being transferred between. The return trip also needs to be a Holman transfer to save fuel. The opportunity does not occur until many months after arrival. I forget the actual number. That is why Mars trips will have a long stay on Mars before returning.
Low thrust is different. Low thrust spacecraft thrust all or most of the time during the trip and the trajectory is more complicated. It is not usable for manned flight because it is to slow but is useful for unmanned spacecraft sometimes.
This is called Celestial Mechanics. When you add propulsion, it becomes Orbital Mechanics.
The best site I have found is NASA's Spacefligh Basics.
Also good is this site.
For explanation of gravity assists see this site.
Also see, Science World at Wolrram
Check out the Basics of Space Flight page at NASA's Jet Propultion Laboratory.
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I've been doing lots of numerical work (graphics stuff) involving numerical optimization lately and one of the techniques I've been using to compute derivatives for optimization is Automatic Differentiation (AD). Along the way I came across a few papers on applytng the technique to trajectory optimization. So I'm guessing that people choose something to optimize (a function of how close they get to the target, the journey time and fuel costs among other things) and use AD methods with a simulator and numerical minimizer optimize the path.
Doesn't it make you feel good to know that our freedoms are protected by politicans, lawyers and journalists.
(Honestly, I'm not sure how you intend to work the punchline in to this.)
Editor, A1-AAA AmeriCaptions
Are there any curious Slashdot readers with the usual great insight into how to calculate a trip to Mars?
Planning to move out of Mom's basement soon? I mean, come on, can't be THAT bad... Unless you're living with a mother in law or something...
The purpose of life is to find the purpose of life.
Skip doing all the math and even the funding part by simply doctoring up a few satellite photos and a research paper calculating with near certainty that near limitless petroleum exists on mars, and they are protected by a heathon god.
sit back and watch all the funds get diverted to a new space program.
** "It's not my job to stand between the people talking to me, and the ones listening to me." -- Pego the Jerk
Taht seems to be the american way.
go ahead, mod me troll, but you i am right and the parent is (a) an idiot and (b) an american.
The best info I've found so far is actually a do-it-yourself exercise... there's a space-travel simulator that you can use to try to figure out how to get to mars, along with some helper apps that do some math for you.
In terms of starting, basic data... you can ignore the effects of the MRO on the two planets, since it's so small. But the positions of the two planets can be gotten from here. To understand the coordinates used, study here.
I'd like to find some decent open-source apps to visualize the orbits in 3D... at least a static diagram, if not an animation.
With his illudium PU36 explosive space modulator.
I helped judge the Canada-Wide Science Fair a few years ago, and the person my judging team ranked the highest had set himself precisely this problem: how do you really calculate the trajectory of a spacecraft from Earth to Mars? His solution was a wonderful exploration of the gory details of the problem--he had parts of the orbit that could be approximated reasonably in closed form (basically when the spacecraft was far away from everything, especially Jupiter) and other bits where there were three-body and more calculations.
He understood error estimation and the importance of computing the same quantity several different ways so that they act as a check on each other. He also had modeled aspects of the spacecraft itself, the rotational moments, effects of changing fuel mass, etc, etc, etc. In short, he understood that science is more of an art than a science. It was really nice work.
Blasphemy is a human right. Blasphemophobia kills.
The web page the OP found looks pretty cool..though I agree it's a little too condensed to be useful for a complete beginner. While I don't want to imply that orbital mechanics is out of the reach of intelligent, math-oriented folks without some sort of formal instruction....a course in the subject matter can definitely help. I took a class with the author of this book http://www.amazon.com/exec/obidos/tg/detail/-/0292 751052/qid=1124147579/sr=8-2/ref=sr_8_xs_ap_i1_xgl 14/102-9094747-8542529?v=glance&s=books&n=507846
With a decent mathematical background, the book could be followed fairly well to get an idea of what it takes to calculate the trajectory for a Martian mission. There are other books out there too...but I am familiar with this one since I used it in college. Dr. Szebehely was an awesome prof, by the way...everyone should have the privilege of learning from someone like him at least once in their lives.
Of course, in the "real Solar System", the gravity of Jupiter can be a real factor, in addition to the other planets (depending on how close you need your calculations to be)...and unfortunately only the 2-body problem can be easily solved in a general closed form. For other scenarios, numerical methods that calculate the trajectory "step-by-step" must be employed.
Good Luck!
For my mission planning software we never considered more than two bodes at a time. For the real stuff, they probably consider more than two bodies at a time, but the other bodies are just correction factors.
The Mechanical Universe, is an excellent way to learn this stuff. It comes on in reruns from time to time.
Whomever modded this guy Offtopic should be flailed with MetaMod death rays. Or something.
The Spoon
Updated 6/28/2011
I bet you'll also never devirginize anyone, must keep it intact.
Duncan Sharpe's TransX
C'mon Orbiter fans, you were thinking the exact same thing when you read this article... Planning a trip to Mars? Just hit Shift-J and start plotting your Hohmann transfer orbit insertion burn.
For those who are lost:
ORBITER is a free flight simulator that goes beyond the confines of Earth's atmosphere. Launch the Space Shuttle from Kennedy Space Center to deploy a satellite, rendezvous with the International Space Station or take the futuristic Delta-glider for a tour through the solar system - the choice is yours.
But make no mistake - ORBITER is not a space shooter. The emphasis is firmly on realism, and the learning curve can be steep. Be prepared to invest some time and effort to brush up on your orbital mechanics background. A good starting point is JPL's Space Flight Learners' Workbook.
also...
TransX is [Duncan Sharpe's] eXtended Transfer MFD. It's designed for planning trips across the solar system, or even just to the moon. It's full-featured, with support for complex flight plans, including slingshot trajectories. And naturally, there's a manual that comes with it.
maybe this is a question for marketing?
The other bodies' gravity pull is very negligent. Because they are inverse prortional to the square of how far you are away from them.
Mainly there's just four significant factors.
1. How much to get off this heap of dirt we call Earth.
2. How fast we want to get there, which basically directly related to the next question...
3. How much does it take to slow down once you get there. (Since there's no friction in outer space...)
4. All the previous in reverse order, knowing that you don't need to get back to Mars again.
==========
You throw in the factors of survival. As you extend trip, your survival supplies costs more.
As you speed up trip, the bigger your fuel tank needs to be.
As you make things bigger, you increase costs. Oh, precious cost!!!
This is classic Linear Programming.
-====
In the end, the answer isn't how much it's going to cost.
The answer is a question.
How much can you spend?
You go from there.
by Roger Bate.
A fun physics exercise is to model a slingshot maneuver and then try to figure out *why* your rocket burn is more effective if you dip inside gravity well when you do it.
hahaha of course you just proved my point. i rest my case
To get this approximately right, you need to consider just 3 contributions to the gravitational potential that determines the ship's motion: the sun, the earth, and mars. If you are a programmer, and your physics/math isn't sufficiently good for you to write a simple simulation of motion in this potential in your favorite programming language, then you are out of your depth. I'm an ex-physicist, and it would take me about 30 minutes to write such a simulation in any programming language I know.
Consider an elliptical orbit around the sun (aren't they all...) with a major axis where perihelion is earth's distance, aphelion is Mars' distance from the sun. I don't know the formula, but you should be able to find it on the net.
Now calculate the orbit time. You start your trip tangent to the earth, and blast away faster than the earth is circling the sun (but in the same direction). You catch up to Mars as the top of your orbit is tangent to (grazes the inside of) Mars' orbit. Therefore, total trip time is 1/2 the orbit period (full orbit time shoould be somewhere between Earth's year and Mars' 2 earth-years - I guess about 16 months?).
This ignores secondary effects like the slowdown escaping earth's gravity, and the acceleration reaching Mars. These should be minor adjustments - you would have to adjust your departure velocity from Earth to include extra for escape velocity from your starting point (presumably Low Earth Orbit). As you depart, Earth will slow you down somewhat, but past a million miles the effect should be negligible. It also ignores the ellipticity(??) of both Earth and Mars orbits, which change the distance an path - more second-order calculations. (Earth's orbit varies from 92m mi to 94m from the sun.) The second-order calculations shouldn't make a big difference...
Then you need braking power at Mars, or you can use the atmosphere to brake (or break, if you miscalculate Km vs. Miles).
So, the launch windows occur when Mars is in such a position that it will be 180 degrees ahead of Earth's current position when you get there...)
Let's say the orbit time above is 16 months (a guess). So if today is a launch window, Mars has to be 180 degrees away in 16 months. Next window? 12 months from now, we're back here (360 deg) but Mars is 180deg away(2-year-long year) from where it was last launch time. 4 months more(16), we're 120 further, Mars 60 more, 180+60 = 240, or only 120 ahead now...etc. 18mo. and we're 360+180, Mars is 180 degrees; bingo - press the launch button again, and in 16(/) months, mars will be where you need it to be.
Basically we're solving for integer solutions of: y= 2x (mod 360); but of course, the Martian year is not exactly 2 earth years. Look that up too.
You can only launch in the same direction as Earth (and Mars) travel around the sun. This is the minimal amount of rocket fuel. It's like throwing a ball in the air so the top of its arc is just as high as the spot you want it to hit... Launch counter to Earth's orbit, other way, and instead of using the speed of the earth's solar orbit to boost you to Mars, it is a detriment. You'd be better off with a more direct route, if you have the fuel to burn.
For faster transits, you just need an arbitrary chunk of an ellipse which intersects both orbits at the correct time. As for slow, steady propulsion like ion-drive or solar sail - well, that's why calculus exists.
Rotsa Ruck.
This is a stellar (pun intended) example of what I visit /. for.
If you forget about the future, the future will forget about you.
I hope we don't send humans there, at least not until we're ready to inhabit other worlds. It's ridiculously expensive and NASA et al go hysterical when humans are at risk anyway. Machines can get plenty of data, even more than humans in fact! Sending humans is mostly just nationalism and something for the media to latch on to (because their audience can't/won't understand science).
You sound like the guy in the cave 10,000 years ago shaking his head complaining about people fiddling about with flint and fire when you know there are rats to be flayed for dinner.
The mathematical models for ballistic missiles isn't what's stopping "terrorists" from making them. What stops terrorists is that it's so much cheaper, faster, more reliable and easier to load a truck full of fertilizer and fuel oil, then blow up a skyscraper or maybe a bridge. Or just release a $25 video "around election time", which is about 18 months every 2 years (75% of the time). Both of which create terror, which is the entire point of terrorism.
There was a time when such math was secret, and strategic. But we caught up to the Soviets shortly after they tested that ballistic missile math on Sputnik, in the late 1950s. A half century later, our open society has proven more than a match for such "proprietary" losers. If we can stay that way, despite the exaggerated bugbears that people throw around to justify the secrecy that kills both science and liberty.
--
make install -not war
gravity, radial motion ect.. unfortunatly it's layer-upon-layer of simple rules that make a ver complex puzzel + Solar winds.
Second star to the right and streight on till morning.
In the not too distant future, next Sunday A.D.
If memory serves, the very first issue of Game Developer Magazine had an article on this and the author used genetic algorithms to calculate the most optimal thrust force vectors and durations to use. The simulation arrived at a very optimal solution in almost no time at all -- and it was for simulating an n-body problem, where n is much greater than 2. Maybe someone can find the original article somewhere, but here's some links which seem to be quite relevant.
Want to improve your Karma? Instead of "Post Anonymously", try the "Post Humously" option.
As another former student of the late Dr. Szebehely's, I second that one. His Theory of Three Bodies can be worked out without too much difficulty from the beginner's text above (for the nitty-gritty, you'll need his sadly out-of-print magnum opus, "Theory of Orbits").
Szebehely (pronounced sh-EBB-uh-hay) was quite a guy (and unlike a lot of geniuses, a genuinely nice guy as well). He was one of the engineers who worked out the detailed trajectory calculations for Apollo, among many other things. LabRat's right, it was a privilege to be in his class. Ditto for Wallace Fowler, who's still on the faculty at Texas.
Are there any curious Slashdot readers with the usual great insight into how to calculate a trip to Mars?"
How about the mathematics involved in financing a manned trip to mars. Surely this problem is even more complex?
Seven puppies were harmed during the making of this post.
you must be talking about anal? correct - you can have all the gheyse.cx/goatse.cx you so desire - i have enjoyed the virgin poontang, kthx. in other news, iraq is arabic for vietnam and mars is martian for dead f*cking planet - lets move along
lol u sure showed them
I find recent work on low thrust trajectories the most fascinating. I was made aware of it in Science News a few months ago. Although the combined influence of the Sun and all the planets form a chaotic system (in principle not predictable beyond certain time limits), there exist stable transfer lanes which function like chaotic attractors (thanks mainly to the stabilizing influence of Jupiter). Once you get your unmanned craft into the lane, it needs only to apply corrections now and then to stay in the lane - and gravity will take it all the way to its destination! The time required is measured in years rather than months, but it makes unmanned missions much more economical.
The "slingshot" trajectories of earlier out planet explorers were similar, but had to be calculated in full for each mission. This new technique creates a 3D (orbital plane plus time) map of the space lanes - which looks like a maze of twisting tubes of varying diameters. To plan your trip, you find a lane near earth that goes to your destination. You need fuel for getting to the lane, course corrections while travelling, and exiting the lane.
As described in the Novel Oxygen , we could send unmanned supply ships to Mars via the economical low thrust space lane routes. The manned mission would come later, when the supplies have and/or will have arrived, and will be lighter and cheaper since it will only need food, water, etc for the trip, and not for the extended stay required by Holman transfer trajectories for the speedier manned trip. Fuel for the return trip would also be sent ahead. (Clearly, I would want some reduncancy, and robot surveillance to ensure that said supplies have truly arrived safely.)
Re the novel: of *course* something goes wrong. Think Apollo 13, but on a *much* longer trip. That's all I'll say.
The saying is "From low earth orbit, you are halfway to anywhere in the solar system." The delta-V (change in velocity) required to get to low earth orbit is about 7.6 m/s neglecting gravity and drag losses. The velocity to escape is about 13 m/s. Add in a little bit of velocity to correct your orbit to make it to Mars and it's about right, 14 m/s. (actually it'll be a bit more if you're launching from Kennedy, you have to get rid of that pesky inclination and that's an expensive maneuver, even combining it with the trans-martian injection it's expensive.
Here's the actual procedure.
1. surface to low earth orbit.
2. circularize low earth orbit. [hohmann transfer]
3. correct orbital parameters (longitude of ascending node, argument of periapsis, orbital inclination)
4. low earth orbit to trans-martian-injection [hohmann transfer]
(3 and 4 can be combined, to a point, in order to save delta-V.)
5. burn to circularize martian orbit [hohmann transfer]
6. correct orbital parameters (Same as 3)
7. Burn to descend to surface
The actual math is too much for a slashdot post. Sorry. If you are truly curious check out "Elements of Spacecraft Design" by Charles D. Brown.
-everphilski-
Yup. You have to do trade studies with lots of iterations. On one axis you have launch date, on the other you have arrival date, and you start plotting. You can then vary your trans-martian-injection burn, and what your get are called Porkchop plots, cause they look like porkchops.
-everphilski-
Any orbital mechanics textbook will give you more than enough information to calculate this for yourself. One of my final exam questions in spacecraft design was to design a moon mission, in about 15 minutes. Mars isn't much harder, just further away, it's the same problem.
:P
"Elements of Spacecraft Design" by Charles D. Brown has a few good chapters on orbital mechanics. Check a local university library, cause the book cost me nigh unto $100
-everphilski-
Sounds like Lander or Thrust on the beeb. What are the graphics like? Mode2? Better?
As to how NASA actually does it, they probably use numerical integrators that take into account the basics (Earth, Sun, and Mars gravity), but also the gravity of the moon and maybe the other planets, and the solar radiation force. When you're calculating mid-course corrections these little things really start to matter (especially if you're going to be landing on the surface!). And if you're going to be orbiting Mars, then you would also take into account the fact that Mars is not a perfect sphere and how this affects your orbit. You could even use atmospheric drag to change your orbit like the Mars Odyssey spacecraft, cool stuff.
I'll just add my "for what it is worth" to this.
You can solve the main problem with sophmore-junior level physics. Any good undergrad Classical Mechanics book will have the basics. One on my shelf that has it is:
"Classical Dynamics" by Marion and Thorton - section 8.8
Advanced books generally have all the inner workings - Goldstein or Fetter and Walecka. Or even a specialized book like others have recomended.
I see no point, we can open a gate to Hell here on Earth. I assure you the research I've done proves that the risk is perfectly acceptable!
If you would just increase my funding and personnel there would be fewer accidents.
--Dr Bertregur.
Check out ioquake3.org for a great, free, First-Person Shooter engine!
It depends on what type of mission it is. For most missions (in which time is not an issue), the most energy efficient trajectory is one called the Hohman transfer. It involves an elliptical orbital transfer mechanism (which you can easily find on google). It works by conical patching of elliptical orbits (requiring only two delta v burns/ one to enter and one to exit the transfer). The time between mars-earth on a hohman is i think on the order of 300 days. the calculations are relatively simple and im sure you can find the equations anywhere on the net vince
check out STK, http://www.stk.com/ from AGI. It's pratically an industry standard.
Want to plan a trip to Mars? no problem using the Astrogator plug-in you're in buisness. However it will set you back several thousands of dollars....
1. Convince Americans that Mars is somewhere near Texas, and it needs a big highway.
2. Vote Republican.
If a 100 ton spaceship one boosted to 7 miles per second had a ion drive capable of 1% of mass or 1 ton of thrust and it could thrust at this 1/100 G rate continuously, one can calculate that after 20 days the spaceship will have increased in speed by 1 mile per second or 14%. Thus a 7 month voyage could be reduced by 14% or 29 days less. If accelleration can be done for 40 days, the time to arrive will be 60 days less. If accell for 60 days then time to mars will be 4 months. The spaceship will have to deaccelerate at a faster rate of 1/100 G to arrive at mars or would pass by.
Future ion drives may be in this thrust ranges
This isn't like dusting crops, boy! Without precise calculations, you could fly right through a star or bounce too close to a supernova, and that'd end your trip real quick...
I would mod you troll (I've got some mod points) but since I'm an American and you're not, you're not worth the dog shit on the bottom of my shoe.
Don't be a looter...and yes, I know that it's spelled with an "A" instead of an "E".
The easiest way to conceive of interplanetary orbits is to first pretend that they lie in a single plane (the plane of the ecliptic) and then pretend that the planets themselves are insignificant for most of the trip -- so you consider only the gravitational field of the Sun. Then your orbit is an ellipse. It's pretty easy to show that, if you're going at Earth's orbital velocity, the ellipse that gets you from Earth's orbit to any other nearly circular orbit with the least change in velocity (ie rocket fuel) is an ellipse that is tangent to both orbits.
Once you've figured that out, you have to figure out when to launch to get to Mars's orbit in the same place that Mars happens to be. Those times happen at a particular phase of Mars's and Earth's orbit.
You can do pretty well by pretending that you can neglect the Sun entirely until you get far enough from the Earth, then you can neglect Earth and Mars entirely until you get close enough to Mars. That is the technique that was used for Apollo trajectories -- the "method of spliced conics". You can hear some evidence of it in the Apollo 13 movie, when they talk about "entering the Moon's gravitational field" or something like that -- the Moon's gravitational field extends throughout the Universe, of course, but to simplify the calculations they neglected everything but the mass with the strongest gravitational force on the capsule.
Nowadays you can get really, really good orbital elements for each of the planets online, which lets you calculate exactly where each planet is at any given time. You can just code up an insanely cheesy inverse-square-law integrator in PDL or one of the other free languages -- or even a spreadsheet -- and find a good orbit by trial and error using the gravitational fields of all the large bodies in the solar system.
epicycles are still a useful expansion for perturbations around a circular orbit. I work with a bunch of planetary physicists, and some of them still use epicycles to this day to calculate weird effects like wave phenomena and density perturbations in protoplanetary nebulae, the rings of Saturn, and the like.
This dude starts to look at the two-body problem and see things aren't going anywhere.
And then, he considers the three-body which many approach but which is in effect much more difficult.
Finally, he goes for n-body -- and that, my friends, is the beginning of the end...
Take a look at the book "Mining the Sky" by John S. Lewis. Without getting into a deep mathmatical treatment, he does lay out what goes into calculating sending missions to and from Mars, Earth orbit, the moon, and the asteroid belt. If I am not mistaken, somewhere in there he even explains the significance of the oft heard NASA term "launch window". (It's basically when your launch site (Florida, for instance) and your target (Mars or the ISS) share a favored geometerical relationship in space-time.) While it is lite on the equations, I think this will have most of what you are looking for.... Now if I can just find my copy. BTW.. Lewis' books are a must read for anyone interested in what's up there, whether it's the moon, Mars, or beyond.
How China does it's space research department.
How come the guys name links to the Chinese space agency?
how to calculate a trip to Mars?
1) Leave Earth
2) ???
3) Arrive Mars
4) PROFIT!!!
Setting aside all the hot talk about longitude of ascending nodes, arguments of periapsis, orbital inclinations, and trans-martian-injections, why worry about this at all?
Wander out to the desert late at night and wait for Them to take you there.
the future is here, it is just not evenly distributed - w. gibson
expresses the gravitational force on a body
(2) F = m*a
expresses how the acceleration on a body depends on the sum of forces acting on it.
You can work out the path of a space probe by iterating these equations over short periods of time (to find out how short, keep making them smaller until the answers don't change).
To answer the question "what starting velocity do I need to get from eath to mars?" is more complex, but probably no more so than a few hundred lines of Python.
...it has something to do with metrics.
This page is a good start for learning about all the fun stuff that you have to do. Not quite the math you're looking for, but it covers stuff other than just orbits.
Because that approach would take too much fuel. I believe that NASA tries to calculate a launch pattern that more or less "slings" the object in an arc that will meet up with Mars after the necessary months of travel.
The Hohmann transferr orbit is based on a few simple ideas. 1. You only want to do two short "burns". 2. Your orbit in between is an ellipse. 3. The most efficient way to increase your kinetic energy is to push yourself forward. This means that you'll be leaving Earth tangentially to our orbit. By the same token, you'll arrive at Mars tangentially to their orbit (the math is the same backwards). All orbits have constant energy (no slingshots considered here), so you'll go from orbit near Earth at one energy, to an in between energy, to an orbit near Mars energy. Note that the final burn near Mars should actually *increase* your kinetic energy. If you didn't do the burn, you'd "fall" back down to near Earth's orbit. So both burns are "forward". Once you accept these concepts of the Hohmann transfer, the timing is just math.
main(O){10<putchar((O--,102-((O&4)*16| (31&60>>5*(O&3)))))&&main(2+ O);}
LN2 is cool!
In short, he understood that science is more of an art than a science. It was really nice work.
Unless you have some sort of zen of judging thing going on this makes no sense.
Science must be more Science than art, if it was more art than science one would suggest science is only partially science creating a recursive depreciation of science.
If what you meant to say was the solution was a "work of art" that makes sense.
I don't care how well/badly Doom 3 is faring in the stores... I think you can afford a measely $150.
Yeah, a pure F/OSS Mars trajectory solution would be nice, but once in awhile you have to bite the bullet, and splurge a little.
OTOH, you could probably justify a Phobos shot as R&D for Id,
if you can just keep those engines from burning out...
I thought it made sense to try to understand how the interplanetary trajectory is calculated. NASA's page is deploringly void of intricate details.
Math+Physics+Astronomy = Orbital Mechanics.
This persons statement makes you wonder how we ever reached the moon to begin with. A good example of government sponsored education at its finest.
No flame intended, just a statment of fact.
Enjoy,
It's just the normal noises in here.
Atomic Rocket has some interesting reading. It's a nice mix of (as far as I can tell) good physics and some science fiction theory.
Basically, the whole site was designed to help new sci-fi authors make their stories closer to scientific reality. So there's a lot of info not only on the various requirement for a mars trip with different types of engines (everything from chemical thrusters to ion drives to nuclear rockets to the sci-fi only torch ships) to what the requirements would be for a crew living on such a ship and what sort of person defense would actually be reasonable.
It's a fun read, and quite educational as well, if not as hard-core science-y as some of the replies.
He's lying; he must be French.
The second result is pretty good introduction
Other results include more details.
Truck bombs are actually far more frightening than most people think. Think about it for a moment - the IRA's attack on Manchester in the late 1990s was a 1,000 lb. truck bomb - probably fertilizer. The Oklahoma City bombing was about the same sort of size. The biggest conventional bomb in the USA - about 14,000 lbs. - could be felt from 20 miles away.
Those large trucks on the Interstate that you see every day have a weight limit of about 65,000 lbs. The main problem would be it wouldn't combust too well at that volume from a lack of oxygen, but all that would take is a LOX cylinder or two.
This is the main reason I'm convinced most of the threats out there stupid, overblown or both. If they were THAT smart, THAT rich and THAT psychotic, London and New York would be fond memories and not much more.
I'm not into conspiracy theories (I think those are a Plot by Them to Control The World by inciting paranoia), but I simply can't find any way to make the observations match the claims, which tells me that some component of the claims is exaggerated.
It's a small world and it smells funny; I'd buy another if it wasn't for the money; Take back what I paid (SoM)
You honestly believe preventing a plague would help this planet? Personally, I'm hoping a plague will wipe out at least 3 billion of us. (We could be our own plague, too.)
As to the reason to go into space, humans only need one: "Because it's there."
It does not matter how dangerous, difficult or expensive it is - it is human nature to expand, like the plague we are, we will expand into the rest of the Solar System, Galaxy, and eventually, the Universe. Or else humans will be rapidly consigned to the dustbin of history.
Human survival is only possible if we continue to expand - and the only place left to go is out.
Your stance assures that you will survive comfortably, but your descendants will die horribly, or simply fail to be born at all.
How many escape pods are there? "NONE,SIR!" You counted them? "TWICE, SIR!"
Dude, if you find this post I know your brain must be totally fried after reading all this. So please calm down, drink a glass of water, 5 cups of coffee, 3 red bulls, smoke a pack of cigarettes, and GO GO GO!
Our class was given this exact same problem for Physics 201. It was worth 25% of our grade. I used this site as a resource. Giving due credit of course. Our assignment had the efficiency of the rocket and the fuel supply given. We had to calculate the most efficient way to get there and back and how long it would take. We were told to research it and not given any hint on where to get the information. I plugged the info into these formulas and got 100%.
aim high, light fuse.
A mission scenario for a human mission to Mars from the European Space Agency: includes a detailed analysis of advantages and problems for the three typical trajectory solutions.
There's a hidden treasure in Python 3.x: __prepare__()
How is it done? First you have to realie the "NASA" is not just one person. It's a huge agency and theyhire contractrs too. SO there is not one program on a PC some place. These are hundreds. THe technique used depends of the purpose. So what are you trying to do? Do a "what if" calculation while you are still designing the system and trying to do a trade study of weight, fuel, time and so on, or are you trying to compute the burn time for a mid course correction? For the best accuracy the method is NOT closed form. You simulate little slices of "delta t" using (typically for earth orbit missions) Earth,moon, sun,jupiter. I suppose if you were going to mars you'd add mars too. Then you chosewhat is Delta t based on allowed error.
Earth and Mars have to be in a specific alignment for a Hohman transfer orbit to work. About how long is it between these alignments? The math is fairly simple.
Mars orbits the Sun every 1.88 earth years, so its orbital rate is 1/1.88, or 0.532 orbits/year. That means after they transit, Earth overtakes Mars by 0.468 orbits per year, and so it takes 1/0.468, or 2.136 years for Earth to catch up to Mars again. This is 25.6 months, the period between NASA's launches to Mars.
If you are really a nerd, consider a genetic algorithm. You could create a virtual model of the solar system (out to jupiter probably) and establish realistic gravitational physics, the thrust of a delta-VH launch vehicle, and the basic charicteristics of a launch. Then have the algorithm run through many iterations changing variables until it finds an optimal solution. More optimal settings spawn more test fires and less optimal fire fewer. After a series of runs, (a few thousand?) you will have an optimal launch solution. The math isn't easy, but it's fun!
People who think they know everything really piss off those of us that actually do.
The three main articles to look at for the transfer are the sun (largest gravity well involved) The Earth and Mars.
its generally used the homan (sp) transfer for calculating the orbit to orbit transfers but it goes a bit beyond that there are general windows available where the earth and mars are comparable to certain times of the year which depends on if you have to circle back.
and yes this is something aerospace engineers do in a freshmen course.
well calculating the force due to gracity would be important which can be calculated with F=GmM/r^2 where G is the gravitational constant. Force centripetal can be calculated F=mv^2/r . THe velocity and object needs to stay in orbit above a body can be calculated using V=sqrtGM/r.
any questions? email me at joe6600@yahoo.com
I once ported a program called "QuickTOP" to the Macintosh, back in the Mac OS 6.0.2 days. It was a NASA trajectory optimization program, which let you choose what planet you were going from and where you wanted to go, the dates of the window in which you wanted to leave or arrive, whether to optimize for least time or least reaction mass, whether you were using rockets, nuclear ion drive or solar ion drive, and many many other things you could tweak.
The program also included an ephemeris table for all the planets, and several well-known asteroids and comets that covered the twentieth and twenty-first centuries.
I didn't do the math, but I know that the underlying calculation engine was solving Chebyshev polynomials to converge on the solutions. FWIW, a typical Earth-to-Mars solution took about an hour to calculate on a Mac II CI.
-jcr
The only title of honor that a tyrant can grant is "Enemy of the State."
... Earth-to-Mars calculation packages and, more importantly, who's buying them? I mean, that got to be a niche market if there ever was one.
In a former life, I worked for a group that did some work for the Naval Research Laboratories. Some of the work involved LEO satellites. When asked what software package they were using (knowing that there were several available through COSMIC) to do the calculations, I still recall the answer: ``Oh, we just write our own.'' (As though they do it whenever they need such a program, probably while eating their corn flakes in the morning. Heck, they probably did just that. :-) Being mere mortals, we bought the sources for one of the nicer COSMIC packages. Name of it escapes me.)
So is there really a market for doing interplanetary orbital calculations that someone's actually able to sell a package for $150 a pop? The folks that are actually able to send something from Earth to Mars I suspect are already able to whip out this code in short order. (Dang, I wish I'd watched `The Day the Earth Stood Still' over the weekend like I wanted to. Then I'd be able to include that nifty quote that Klaatu uttered about ``being good enough to get me from planet to planet''.)
CUR ALLOC 20195.....5804M
In the land of the blind, the one-eyed man is king.
Ahahahaha.
:)
And I thought only trolls were funny.
If anyone wants a decent (and cheap) textbook, check out Fundamentials of Astrodynamics. The math in it is remarkably accessible, and most of it does not require derivative calculus. It's a bit dated by now, but still the book of choice at most universities for undergraduate astrodynamics.
(The book was written by U.S. Air Force Academy professors, and has an almost amusing discourse on ballistic missile trajectories as well.)
You have a torrent link?
(2) Get russians to agree to take Mark Shuttlebutt to mars
(3) ?
(4) Profit!
Can you imagine a beowolf cluster of trips to mars?
It is your personal duty to fight for what is right on a daily basis. Ignoring injustice is identical to approving
But I'd imagine its much worse before the g's come back and it's all just floating, suspended in the air you suddenly would rather not have to breathe.
Can you be Even More Awesome?!
Consider if NASA used accessible build web logs to track the developement of a space probe or mission.
It would definitely increase public interest and be educational, bring a window into the everyday world of engineering.
Also imagine the wizkid who finds the odd metric-to-english conversion problem and saves the day.
Marie Sharps is hot
very technical interesting article just found, Lo interview, a 2002 NASA press release, another cool description with nice illustrations, and the wikipedia.
...designs such as old-school ion thrusters, (which NASA only uses because they are scared to death of actually flying anything really innovative such as a VaSIMR or a magsail)
Is "innovative" some keyword for "speculative" or "not actually working yet"?
Note that NASA don't fly with Santa Claus thrusters or Tooth Fairy engines either.
They are also calculations of the same orbit but for different purposes. If you just want to make a simplified simulation and use a simple 2 body problem for educational purposes, then you ignore many variables and just use college calculus to solve it. If you calculate the same orbit but for a possible distant future, then you account for more variables, use more complicated math, and probably a more complex program (algorithm). Then you have the calculations for an actual launch, where you would account for a lot more variables, these would be a lot more complicated and will be very complex.
Now that is just speculation, I have never worked at JPL. If I get close enough with my dark skin and thick accent I'll probably be shot on sight..., at least that is what my friend from Caltech told me who works there...
If you don't mind paying for a book you might find http://www.astrobooks.com/index.asp?PageAction=VIE WPROD&ProdID=887 (Orbital Motion (Third Edition) by A.E Roy)
Deploringly?
Ten thousand thundering typhoons, stop making up words!
After the war, while helping the US Army launch liberated V2s in New Mexico, Wernher continued to screw off, and eventually scribbled enough material for a small book, Das Marsprojekt. It was quickly offered in English translation as The Mars Project, and is still available in paperback. It's only 90 pages cover to cover, and covers all of the basic math, engineering concepts, and logistics of loading up the wagon for a trip.
In particular, the orbital calculations are laid out and illustrated in such a way that anyone with any faculty in math can come to grips with it. THEN, you can go apeshit with tomes such as Introduction To Space Dynamics.
Luke, help me take this mask off
Yeah, there's this thing out there called "the Sun". I'd take it into account.
Sarcasm aside, though, I salute your quest for knowledge. This sort of thing ought to be better understood by the reasonably intelligent public.
"Those large trucks on the Interstate that you see every day have a weight limit of about 65,000 lbs."
0 .html to a story of an explosion caused when a semi overturned and caught fire in a canyon about 35 miles from my home. It occurred last Wednesday. The semi was hauling 38,000 lbs. of explosives. Not one person died! That stretch of highway is highly-travelled and pretty dangerous on its own without exploding vehicles. If you look at the images of the road, you'll likely agree that it's quite an amazing thing that no one died. Nearly the entire semi and trailer were gone. The explosion left a crater about 20 to 35 feet deep and 60 to 80 feet wide.
h tml to a Salt Lake TV station that received a video taken by someone travelling on the highway during the explosion. (The streaming video worked quite well on my Mac - Tiger & Safari - , so I'm pretty sure it'll work for most anyone)
Here's a link http://deseretnews.com/dn/view/0,1249,600155076,0
Here is another link http://kutv.com/topstories/local_story_226191800.
I plan to give those truckers an even wider berth from now on.
From a theoretical basis its not as hard as you would think it is, as long as you can simplify the problem. That is, the mechanics point of view of it, and doing it all analytically. I myself am studying orbital mechanics at the moment, and in just 3 weeks you can learn the BASICS(i strecth the word basic here) for a interplanetary transfer.
Here is a list of the sort of maths you would encounter in orbital mechanics:
- Conic Sections (parabolas, hyperbolas...etc)
- Calculus (pretty much have to know it all, a good understanding of differential equations (including partial D.E.), differential vector operator, even series calculations and their sums (eg Taylor series)...etc.)
- Linear Algebra (Vector and matrix operations, also applications with calculus, eg coupled differential equations come up in 3d rigid dynamics problems which can be solved using diagonlization matrices)
- something I missed !!
NOW TO THE ACTUAL PROCESS.
There are three main segments:
Earth escape (hyperbolic)
Heliocentric transfer and
Planetary encounter.
You use two- body mechanics to approximate trajectory of a spacecraft between two attracting bodies (its a 3 body problem, but you have to simplify it). This means you have to ignore all attracting bodies except the one with the most influence. Bodies with great masses have an "Attracting Sphere"(also known as 'sphere of influence') around them, when you leave the radius of that sphere you perform your 2-body calculations with the next body that has the greatest influence. Eg for Earth the radius for the sphere is 9.25 x 10^5 km. But don't forget that on the 'surface' of the sphere the influences of the 2 large bodies are equal, it's essentially a cosmic 'tug of war'.
With interplanetary transfer you have to start to think in reverse, first you have to think as to what is the purpose of the craft, do I want it to
a) send it into an orbit around the planet
b) use the planet as a slingshot for the craft
c) use the atmosphere of a planet to slow down my craft
d) or just crash it! (War of the worlds?!)
Then you need to calculate a HOHMANN TRANSFER that will give you a final approach velocity which will let you do one of those options (a,b,c or d). But for that final velocity you will need a certain initial velocity approach into the Hohmann transfer from a low Earth orbit(LEO).
After you have set the spacecraft into a LEO(because before any orbital manoeuvres can be made the properties of the initial orbit must be known), and the right moment in time comes, you apply an impulse 'shot' to the spacecraft of around 20 seconds and assume that to be infinitesimal in comparison to the 18 months required to reach Mars. The impulse is applied tangentially(to LEO) to generate the initial velocity of for the Hohmann transfer. Make sure you fire in the right direction and use the Earths velocity as an advantage, you would not want to make it any harder by fighting the velocity of Earth too. While on the Hohmann transfer to Mars it is wiser to make small adjustments now in thrust and directions so that you can save on energy and thus propellant rather then having to make adjustments when arriving there. A small change in angle at some large distance can save the trouble of having to make big changes when arriving.
From Earth to Mars the Hohmann transfer is a heliocentric transfer orbit ( the sun at the focus). The tough bit is having to think of it as a hyperbolic passage when approaching the planet. You have to think of the planet as a focus in your hyperbola where your flight of travel is the hyperbola and you are approaching the perigee form the asymptotes of the hyperbola( ie assume u are approaching from infinity, r~= infinity). For this, you initially assume that the velocity of your planet(the focus) is zero. Through the focus are two lines passing through and intersect there, these lines are parallel to the asymptotes. Give them the spacing 'delta'. Now if we know the velocity at which we a
At a first approximation, you can make the calculation with several 2 bodies system. 1 of which is the spacecraft, Not Mars and Earth.
You get ~ 3 orbits 1)around earth, 2)around the sun (to go from the earth orbit to the Mars Orbit) and 3) around Mars.
Then you have to make sure that the orbits interconnect, take into account all those pesky perturbations (moon, sun, Jupiter, mars atmosphere, ...) and the limitations of your spacecraft.
What if we were to invent time travel? How would we go about it? Who would be the contractor for it?
What if we wanted to travel in space? How would we go about it? Who would invent the ships?
Can anyone else publish an article with more What if's and theoretical BS than Business 2.0?
Mod Redundant.
Dammit.
octave is a free clone of matlab. http://www.octave.org/ it is compatible with most matlab scripts...
Good luck. I hope you out grow it.
After all, I am strangely colored.
In Germany we teach invariant manifolds to undergraduate students.
On the other hand, Germans invented rocket science, so it's not surprising that you need full-grown researchers for such things in forgein countries.
This explanation is too simple! How refreshing! Does your curiosity extend to ( steady now) reading a book?
http://en.wikipedia.org/wiki/Hohmann_transferh oth ighwayc s
http://en.wikipedia.org/wiki/Gravitational_slings
http://en.wikipedia.org/wiki/Interplanetary_Super
http://en.wikipedia.org/wiki/Category:Astrodynami
"A great democracy must be progressive or it will soon cease to be a great democracy." --Theodore Roosevelt
My dad does earth-mars trajectories all the time, he was on the Viking team, etc.
As for the earth-mars 2 body system, you're forgetting a pretty important other one, THE SUN. Come back and ask again when you at least are ready to ask about earth-mars-sun and maybe I'll pass along one of dad's programs for how to get there.
stuff |
You must have a very small penis.
Slow Down Cowboy!
Slashdot requires you to wait between each successful posting of a comment to allow everyone a fair chance at posting a comment.
It's been 9 minutes since you last successfully posted a comment
btw the site is missing the "slingshot" using other planets. this uses the fact that a hyperbolic orbit leaves the planet at the same speed as it entered, *in the planets frame*. so in the spaceships initial frame the speed when leaving can be larger or smaller. (i restrained from explaining further, isnt complicated but find it difficult to write clearly about in this form)
(http://www.mathpages.com/home/kmath114.htm seems good, but its missing how to aproach the planet to head out a certain direction (if you know a better sites, post!))
I've always thought they use the methods like in the given website for a first estimation, and then use simulation to determine more exactly the orbit. Is this true? they may use Monte Carlo simulation (simulate slightly differently many times) to account for errors that get into thrust direction and strenght, but these are probably small.
i know that explicit analytical formula's for trayectories for more then three planets are not known (or dont exits in form of normal arithmetic). (all of which have non neglible mass)
so everything yielding an analytical result uses aproximations. (are these really good enough?)
also the website doesnt say anything about how the position of the planets and spacecraft are measured, by earth or spacecraft. and how all this data is processed. (this isnt the fault of the website, its just about the mathematics of it)
It uses Verlet integration. It seemed adequate for the kinds of orbits involved in a tether, where the time span of interest is only a few hours. A trip to Mars will take months unless you go powered the whole way, which you probably can't afford to do (although a solar sail might help).
It would be best to come up with analytical solutions. If you never need to solve the 3-body problem these will be ellipses. A cheesy semi-solution to the 3-body problem could be piecewise-elliptical. Again, details are left as an exercise for the reader.
WWJD for a Klondike Bar?
Yes!
This is much easier than the "Linux From Scratch" method that is currently being used.
Those who sacrifice security to condemn liberty deserve to repeat history or something. - Benjamin Santayana
There's a new approach to the n-body problem part of this. They're using quantities related to impulse instead of time to step between iterations of simulations. This can yield O(N) computational cost.
http://www.cs.unc.edu/Research/nbody/
Verbum caro factum est
They don't use two-body approximations for the NASA missions to Mars!
They use high-precision numerical integration for the trajectory of the spacecraft, using one of the standard high-precision general ephemerides as background data. (Textbooks mentioned by posters elsewhere in this thread decribe in general terms the astronav. techniques used for mission planning, but as soon as they get down to mapping the trajectory as precisely as possible, they need the background ephemeris as well.)
For the recent Mars missions, the background ephemeris is a very highly refined ephemeris "DE410" produced by the JPL, this appears to be a local improvement intended especially to reduce errors in the neighborhood of Mars and Saturn, relative to the DE405 ephemeris which remains the world standard for official ephemeris publications. It seems they got an accuracy in the region of Mars as close as only "a few meters"!!!
See details of DE410 on the public JPL site here, and especially you might want to look at the background report on DE410.
-wb-
Cost of renting shuttle: $$$$$$$$$$$
Cost of fuel: $$$$$$
Cost of mission control: $$$$$$$$
Cost of training everyone: $$$$$$$$$$$
Cost of hiring everyone: $$$$$$$$$$$$$$
Cost of 100million things I cannot think of: $$$$$$$$$$$$$$$
Cost of short stay parking on mars: ASTRONOMICAL (HAHAHAHAHAHAHAHA ba-dum-pssssh)
Selling the right to the launch could net you about 1% if you are lucky, and have a team of lesbians covered in BRANDNAMEX chocolate sauce as the pilots, who are going to be doing 0 G lesbian experiments in space...streaming live over the intarspacewebnet.
haha.
Lameness filter encountered.
Your comment violated the "postercomment" compression filter. Try less whitespace and/or less repetition. Comment aborted.
#hostfile 0.0.0.0 primidi.com 0.0.0.0 www.primidi.com 0.0.0.0 radio.weblogs.com
Computers are bigger now so we no longer need the simplicity of Hohmann. There is a large class of optimization algorithms (genetic algorithms, gradient descent, simulated annealing), any of which could be thrown at this problem. And there are, dare I say it, several Beowulf clusters sitting around that could implement these algorithms.
This would allow us to choose the parameters to be optimized. Maybe there is a safe, quick trajectory involving a steady low-level burn (not the impulse used for Hohmann). A specially optimized trajectory like this wouldn't be as analytically tractable as Hohmann, but with cheap computers, analytic tractability is not the precious commodity it was in the slide rule days.
WWJD for a Klondike Bar?
The mathematical models for ballistic missiles isn't what's stopping "terrorists" from making them. What stops terrorists is that it's so much cheaper, faster, more reliable and easier to load a truck full of fertilizer and fuel oil, then blow up a skyscraper or maybe a bridge
But you're missing the point.
It's hard if not impossible to stop a terrorist from doing these things. It's easy to stop a terrorist from build a Mars base, from which they can plot world domination, safely out of reach of our cruise missiles.
If you are an official, when something bad happens, you have to be able to say in all honesty that you did everything within your power to prevent it. Or everything within your budget, which for the sufficiently unimaginative amounts to the same thing.
Post may contain irony: discontinue use if experiencing mood swings, nausea or elevated blood pressure.
www.orbitersim.com
Fly the mission yourself, as many times as you like. There are those who have made the flight using pencil and paper. For those less math-enthusiastic, there are 2 main navigation tools available - TransferX and I-MFD.
Enjoy!
http://wombat.ods.org/cgi-bin/lambert.pl?p1=Earth& p2=Mars&sd=0&tf=90
;)
The interface is kinda rough, but the calculations use coplanar, cicular planetary orbits to find a least-energy transfer orbit using Lambert's method and Battin's (the guy who wrote the Apollo Guidence Computer) continued fraction interation. Velocities are in km/s.
Simon
If you wish to calculate one's own pork chop plots, and one has access to a Windows machine, go to Jaqar and download their freeware utility Swing-by Calculator. It generates the datafile, the plot can be visualized with MS Excel, Matlab or Mathcad
Since trips to Mars seems commonplace (NASA has sent one every 26 months) Launching things to Mars might be "common place," but I wouldn't say succesful trips to Mars are common place. Nearly two-thirds of the 30+ spacecraft sent to Mars by the U.S., Russia, and Europe have either crashed, exploded, or othewise malfunctioned. Maybe those NASA bums need a little more practice before sending some live cargo.... I for one would be pretty pissed off if I was going to be lost in space because somebody didn't read the spec or forgot to convert pounds to newtons.
Oxygen availability is irrelevant for high explosives, such as fertilizer and dynamite. One of the reasons that they react so vigorously is that all the needed materials are already mixed in. For the curious, there have been various major accidents caused by far larger quantites than what will fit in a truck.
and the person my judging team ranked the highest had set himself precisely this problem
Are you bit by the illiteracy bug? The person in question was a "he".
You know if terrorists really wanted to "get our goat" they should start their own space program. I here there are lots of caves to hide in on Mars...and god knows we wouldn't put put much effort into searching a place we new them to be hiding. ;)
Don't ya hate it when the correct spelling of your favorite screen name is taken?
I know that the government is porpusly promoting as many wacked out conspiracies as it can in order to help cover up the true ones. It's a conspiracy to flood the world with conspiracies to cover up the nonconspiracies. I know, I'm part of this branch.
Paying taxes to buy civilization is like paying a hooker to buy love.
I need help calculating a trajectory to Uranus.
The problem of calculating the gravitational effects of _all_ bodies that affect trajectory is well, astronomical. The earth, sun, moon and mars are the major contributing factors. Once these are calculated it's enough to do the trip. Space agencies know this isn't accurate and would miss the target but they are close enough. At one or more points on the way they calculate the difference between their actual position and the calculated one, factor in the difference and their back on course. We couldn't even go to the moon our nearest neighbor without doing this.
To calculate more bodies takes an incredible amount of computing power. That kind of processing power didn't exist decades ago when probes to mars and beyond began. So, NASA did what mariners have done for centuries, plot your best course and then fix it on the way to get where you're going.
Everyone who's up in arms over the idea of simplifying the problem needs to calm down. As in most cases, taking into account anything and everything that could effect the trajectory of the spacecraft midflight in mathematical terms creates an overwhelming problem. Science, and good science at that, is constantly conducted using mathematical simplifications (or conducted accepting some form of error... even the most basic measurements, for example, are not accurate in the truest sense). The trick is knowing when and where to make those simplifications and understanding both what you are including the equations and what you are leaving out.
Trying to understand multi-body, multi-plane interplanetary transfers taking into account the effect of radiation pressure, atmospheric drag in LEO, blah blah blah is really not necessary (and becomes extremely complex, as has already been discussed numerous times in previous posts) if all you're trying to do is understand the basic mechanics of a trip to Mars or any other planet, for that matter. Even the mathematics related to bodies that would have an effect on a Mars mission can be simplified through the use of ideas like sphere of influence (SOI; which celestial body has the prevailing gravitational influence on a spacecraft at which points in its trajectory) and the like.
If you're just trying to begin to understand how interplanetary travel works, start with the basics. Then work your way out into Lagrange points, the effects of dark matter on deep space missions, and gravitational assist trajectories.
I am talking about the article poster, not the parent/grandparent:
- first off, he delivers us the NASA page where the trajectory and course corrections are described. There's 5 correction, of which the first is the "strongest". You can also see there the form of the trajectory ;
- then, the initial poster also delivers us the link to the orbital mechanics page, where you can see various orbital mechanics facts, including the tiny bit where "Hohmann transfer orbits" are described.
For the "slow" guys, here's a small digest that will answer ALL of your questions...
1. The only reason why NASA launches spacecraft to Mars only every so many days is FUEL EFFICIENCY.
If you look in second link, you will notice this small phrase: "Hohmann transfer orbits are interplanetary trajectories whose advantage is that they consume the least possible amount of propellant.".
Also, "To reach a planet requires that the spacecraft be inserted into an interplanetary trajectory at the correct time so that the spacecraft arrives at the planet's orbit when the planet will be at the point where the spacecraft will intercept it. [...] The interval of time in which a spacecraft must be launched in order to complete its mission is called a launch window."
Well, it doesn't get any more clear than that.
2. The calculations are VERY simple, actually. And that is because you will need course corrections anyway, as the combination of observation / measurement errors and thruster imprecision will make them more important as any gravitational interference when it comes to fuel efficiency.
In other words, there's only a handfull of factors, and those are:
- the Sun (i.e. potential energy, orbital speed decrease as you go away from the Sun)
- Earth's position at launch
- Mars' position at launch/arrival
All the other factors are so small, that they can be ignored completely in all calculations and compensated in the trajectory adjustments (which are needed anyway).
By reading this signature you agree to not disagree with the post you just read.
A book called Fundamentals of Astrodynamics. It was mentioned a few posts before mine.
And you can look for a set of equations called Hill's Equations. They're a set of non-linear differential equations that use orbital elements to describe the motion of a satellite (or interplanetary vehicle). Hohmann transfers are used only when you want to conserve fuel, they take the longest time too.
Once you find the equations, you can write a script to integrate them, or you can look for pre-compiled packages that are already set up for them, you just need to put in the satellite info.
Here's a plug for my favorite introductory book on the subject, Fundamentals of Astrodynamics by Roger R. Bate, Donald D. Mueller and Jerry E. White.
Amazon link
Barnes & Noble link
I didn't even have to special-order my copy. I walked into my nearest B&N and it was on the shelf. Your mileage may vary.
The book is Copyright © 1971, during the heyday of the Apollo moon missions, but its content was developed during the 1960s as part of US Air Force Academy classes for astronautics or aerospace engineering students. It covers computing orbital elements from various combinations of knowns/unknowns, refining initial estimates with additional observations, prediction problems, intercept problems, targeting problems, orbital perterbances, orbit changes, mission planning and more. Many of its chapter-ending problems are intended to be solved with a slide rule.
No one book can cover all of orbital mechanics. This is, after all, rocket science. But this is the best introductory book I know.
IAATA (I am a trajectory analyst)
p -image01.html The pork chop plot shows contours of delta-V (in blue) vs. launch and arrival date. The red lines are lines of constant flight time. These type of plots are typicaly constructed using a tool like MIDAS or Lambert's problem, and are publically available. Here's one example http://trs.nis.nasa.gov/archive/00000438/
I typically don't do navigation-level detail work, but I do performance level work used to size spacecraft, determine mass/power/thrust/specific impulse levels, etc.
Generally there are two types of missions, high thrust (chemical) and low-thrust (ion engine, solar sail, etc).
For a chemical mission you need to know where and when you leave (your initial state vector), where and when you are going (your final state vector). One can solve Lambert's problem to determine the performance and trajectory. There are also software programs such as MIDAS but unfortunately I don't believe they are publicly available.
For chemical missions, you can take the delta-V result, and since the chemical system applies the delta-V nearly instantaneously, you can simply use the rocket equation to calculate your mass fraction:
delta-V = g * Isp * ln(m0/mf)
Where g is sea-level gravity, Isp is the specific impulse, m0 is your initial mass, and mf is your final mass.
What else is there to consider? Well, you want to launch at the date when the trajectory will require the least propellant, but you want a wide enough window such that if you launch a week, or two, late due to mechanical problems, your spacecraft will still have enough propellant to do the job.
Aside from programs, you can also find useful data in a 'pork chop plot,' such as this: http://marsprogram.jpl.nasa.gov/spotlight/porkcho
As someone who is interested in performance, rather than navigation, I can generally assume that the planets are massless (unless I'm doing a gravity assist). The amount that Jupiter perturbs your when youre going to Mars CAN make the difference between capturing into the correct orbit and slamming into the ground, but it has a very small affect on the amount of propellant needed.
We also often assume that the spacecraft leaves from the center of mass of Earth, and goes to the center of mass of the target body. Again, this doesnt affect performance much but the additional complexity for the optimizers usually isnt worth it.
For low-thrust missions, things are generally much more complicated mathematically. With chemical missions, you can assume instantaneous changes in velocity. But for low-thrust missions, the thrust is being applied continuously for long time durations. The number of degrees of freedom in the optimization grows substantially.
For Earth-orbiting low-thrust vehicles, simple-control laws can perform the desired maneuver (orbit raising, station keeping, etc) while minimizing propellant mass. I recommend searching NASA's techinical databases for "control laws" if youre interested.
For interplanetary low-thrust spacecraft, there are several codes used to solve the problem ranging from "performance level" accuracy to "navigation level" accuracy. One that is publically available to US citizens is OTIS. http://otis.grc.nasa.gov/ OTIS can be used to compute high-fidelity interplanetary high-thrust, low-thrust, lauhch vehicle, aircraft, and many other types of trajectories. Its very general, very powerful, but has a very steep learning curve. The developers are always looking to widen the user base, so feel free to try it out.
"Open the pod by doors, Hal" > "I'm afraid I can't do that, Dave" sudo "Open the pod bay doors, Hal" > alright
Your source at NASA Johnson Space Center may use "simple" Newtonian physics, but please remember, NASA JSC has not ever planned and executed a trajectory to Mars or any other planet. The NASA focus of expertise in interplanetary navigation is NASA Jet Propulsion Lab (JPL), affiliated with Caltech. Here is a useful link: A chapter on spacecraft navigation from JPL's "Basics of Spaceflight" http://www.jpl.nasa.gov/basics/bsf13-1.html A search on JPL's home page will yield numerous references to navigation and trajectory information: http://www.jpl.nasa.gov/ Also, remember that navigation generally involves several course corrections along the way. There are early burns to correct the trajectory after launch, another possibly at the midpoint, and one or more final burns for orbital insertion or landing ellipse targeting.
Your source at NASA Johnson Space Center may use "simple" Newtonian physics, but please remember, NASA JSC has not executed a trajectory to Mars or any other planet. The NASA focus of expertise in interplanetary navigation is NASA Jet Propulsion Lab (JPL), affiliated with Caltech. Here is a useful link: A chapter on spacecraft navigation from JPL's "Basics of Spaceflight" http://www.jpl.nasa.gov/basics/bsf13-1.html A search on JPL's home page will yield numerous references to navigation and trajectory information: http://www.jpl.nasa.gov/ Navigation generally involves several course corrections along the way. There are early burns to correct the trajectory after launch, another possibly at the midpoint, and one or more final burns for orbital insertion or landing ellipse targeting.
Google around for information on the Mars Direct Mission plan. Very interesting stuff. Of course, with peak oil and the crashing world economy it's obvious there will never be a manned mission to Mars.
Lots of good resources there. See the Atomic Rockets section. http://www.projectrho.com/> Atomic Rockets: http://www.projectrho.com/rocketstub.html>
"Ah Mr. Gibbon, another damned, fat, square book. Always, scribble, scribble, scribble, eh?" (The Duke of Gloucester, o
Can someone please take the actual live data from MRO and calculate it to verify that these guys got it right this time.
Two heads are better than one.
Thanks.
This is why you were taught Physics, after all.
The Space Race increased attention on math and science in primary schools.
If you did your homework, made it through calculus by Senior Year, and had a Physics class, you could do this easy.
Meaning, there are probably a quarter billion people on this planet with the mathematical acumen to figure out any trajectory from a thrown baseball to a Mars shot.
The thing about terrestrial ballistics is that it isn't "ballistic". The wind gets in the way and is a random input. So the important feature of a weapons system isn't the ballistic estimate of the trajectory, it's the control system that negates perturbative inputs. That is what's classified.