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?"

Comments

Extemely Complex Calculations

[Shadow Wrought]

What with all the epicycles and all;-)

Re:Extemely Complex Calculations

[squidfood]

What with all the epicycles and all;-)

You'd think it was rocket science.

Re:Extemely Complex Calculations

[Keebler71]

Well, since we are starting off with a joke...

How do you know if an astrodynamicist is an extrovert?

He looks at your feet when he talks to you!

Re:Extemely Complex Calculations

[tbischel]

Whats so hard about rocket science?
Pointy end goes up

Why would you expect us to?

[aklix]

I see more budget cuts have caused NASA to outsource to the open-source

Hmmm.

[Anonymous Coward]

Try Google maps.

Numerical integration

[mattjb0010]

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...

Re:Numerical integration

[ichin4]

I asked a rocket scientist what he said to indicate that something isn't so difficult. He said: I say, "this isn't nuclear physics."

I asked a nuclear physicist what he said to incicate that something isn't so difficult. He said: I say, "this isn't brain surgery."

I asked a brain surgeon what he said to indicate that something isn't so difficult. He said: I say, "this isn't rocket science."

What about

[SamAdam3d]

having the entire Earth jump at the same time?

I am sure that can get you to Mars. ;)

The Slashdot "common"

[MosesJones]

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.

easy

[colton cummings]

Point it in the general direction, and launch.

It's like a message in a bottle, but so much cooler.

Simplifying interplanetary control software

[Debian Troll's Best]

While the actually hardware behind a successful Mars shot is undeniably critical, a similar amount of attention should be paid to human interface factors back at mission control. Mission controllers work long shifts, often without adequate sleep or food, and small mistakes on the ground can be fatal to the brave astronauts travelling through space, or walking on the surface of the Mars. The computer science community has conducted considerable work on human interfaces, but in my mind there is one which stands out above all others as an intuitive, easily understood and easy to use mission control interface: Debian's apt-get.

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!

Mathematics is for Mathematicians

[Anonymous Coward]

Tired of calculating so many epicycles? That's why we've introduced the Ronco Equant Point!

The Ronco Equant Point is a pointless mathematical abstraction that gives you that perfect Renaissance instrumentalist astronomical result! Up to 200% more accurate than the other leading brand of Ptolemaic system, the Ronco Equant point will actually reduce the number of epicycles within 20 minutes - or your money back!

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Re:Simple Newtonian

[aidan folkes]

But.. three is not analytically solvable. From there, numerics takes over and this is still a very active field of research, still far from perfect. But they're surely good enough :-)

As long as you don't get your units mixed up. :-)

Re:method...

[FLAGGR]

You want a formula? A formula for the optimal flight path to Mars? Here's one:

y = (o*u) / (ar^e + an - (i*(d-i)+(o-t)))

Keep dreaming. It's a complicated thing. You have to factor in the gravity of all the planets, moons, other large bodies and the ship itself. You have to make sure the thing doesn't crash into any asteriods, and it's going to have to make course corrections en route, to avoid things and to stay on track. Maybe the best route is to loop around a planet, and get a speed boost from its gravity. Maybe there isn't enough fuel to do it the fastest way, maybe the timeframe for one route is too small, etc etc etc.

Sorry to break it to you, but there isn't an equation that spits on a directional vector for you to shoot your rocket at. If you want to play pretend, download some solar system simulator, I'd assume at least one of them has some dinky flight planner thingy.

Re:method...

[superpulpsicle]

That's the problem. There is no formula that calculates where the foam comes off by itself. Oh that X factor.

Re:Trip to mars dont seem that "simple"

[squidfood]

Nasa has probably built a nifty model...

<cheap shot>
Here's a line of the code: // TODO: INSERT ENGLISH-METRIC CONVERSION
</cheap shot>

Re:easy: 4 step program

[DaveCar]

how to calculate a trip to Mars?

1) Leave Earth
2) ???
3) Arrive Mars
4) PROFIT!!!