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Right now, space travel is all about carefully moving between orbits. If you want to go from Earth to Mars, you wait until the two planets are correctly aligned, and then place yourself into an elliptical orbit around the sun so that the apoasis of the orbit hits Mars. You only have to make a single, long burn at the start of the orbital change, and if you do it right you'll fall into a neat Martian orbit.

Using this method, it takes quite a long time to get to Mars! It seems that most of the work getting there is done by gravity - the craft's engines only do a little.

It's as if the craft is a transistor - its engines provide a little seed current so that gravity can do the rest.

I suppose we do it like this because fuel is hard to get into space, and our engines are not very good. 100 years from now, when these are no longer issues, how will spacecraft move from one planet to another? Will they still think about orbital changes, or will they just point towards the target and hit the accelerator?

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That will depend on the speed. Gravity and inertial will always be taken into account. It's crucial today, as you say, because the natural speed we can achieve by jets is smaller than the typical speeds of orbiting planets etc. Once people have motors that naturally achieve higher speeds than the orbital speeds of planet, the orbital influences will become irrelevant. No one will tell you when it will occur if it will occur ever at all. –  Luboš Motl Sep 24 '12 at 7:16
    
This is rather specilative, closing as not constructive. Please see the faq next time :) –  Manishearth Dec 28 '12 at 12:45
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closed as not constructive by Qmechanic, Manishearth, Sklivvz Dec 28 '12 at 12:45

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A quick Google will find lots of analyses of interplanetary travel under constant acceleration. The best one I found is here, and gives results for travel between Earth and Mars. It even provides MatLab code to do the calculation, and you could easily modify this to calculate travel between different planets.

We're not supposed to just give links without discussion, but I'm not sure how much there is to say. Unsurprisingly there's no simple analytical solution to the problem so a numerical solution is necessary. The trajectory ends up looking like an S. I've nicked one of the pictures from the site to show this:

Earth to Mars

Green shows the Earth's orbit, Cyan shows the orbit or Mars, the red line is the constant outward acceleration and the blue line is the constant deceleration. The journey takes around 6 days.

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Thanks, this is really interesting. I guess that the faster you can accelerate, the more flat the path taken is. The positions that the Earth and Mars are in on this website are quite close - I wonder what would happen if they were opposite each other around the sun? I may try writing a program to calculate this. –  Oliver Sep 24 '12 at 10:58
    
@JohnRennie: Hello John, I've a single question to ask... Curiosity took about 9 months 'cause it took some different path by wandering around for sometime... Why is that so? –  Waffle's Crazy Peanut Sep 24 '12 at 13:26
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The trajectory discussed in this question is only possible if you accelerate continuously, and this means burning fuel continuously. No current rocket can carry anything like enough fuel to do this. The closest would be the Dawn probe to Ceres and Vesta that uses an ion drive, but ion drives generate only a small thrust. Curiousity used a conventional Hohmann transfer orbit. This takes a long time but uses the minimum amount of fuel. –  John Rennie Sep 24 '12 at 13:42
    
@JohnRennie: Hi John: As you didn't insert my name, I didn't get the message. OK, I haven't seen anything that advanced..! All guys are nowadays taking fuel conservation into account..! Thanks for that :) –  Waffle's Crazy Peanut Sep 29 '12 at 1:43
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