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Is it possible, for the sake of argument, to launch a payload into an orbit around the earth by putting almost all the energy going at a 90 degree angle? What velocity would it take, and what horizontal orbital burns would you need?

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Leaving the atmosphere headed straight up with escape velocity would do it, it just wouldn't be very useful. And the "useful" thing is the catch, once you say what you need to accomplish then you can figure what your orbit needs to look like. –  dmckee Apr 1 '13 at 21:01
    
For example, if one were trying to build and resupply a space station orbiting anywhere from LEO to L2, what would be the best way using the method above? –  Jaren Fleischman Apr 1 '13 at 21:13
    
Then you need to match orbits. Unless you want the lunch and air and other stuff coming in at orbital velocity. L2 is a cute idea but it is still going fast enough to go around in one lunar month. You're probably not going to stick a butterfly net out the airlock to catch that, but I don't have the figures in front of me. –  dmckee Apr 1 '13 at 21:32
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As an orbit goes around the Earth, your challenge if you launch vertically is that once you reach the desired height you will then need to accelerate sideways to orbital velocity. For an L2 orbit, this is around 1km/s with respect to the Earth.

So you need to carry all that fuel up with you, to then burn it. That's a vast amount of mass wasted in the initial launch, so realistically it isn't going to happen.

In reality, the launch profiles used give you orbital velocity and height as efficiently as possible, to maximise payload.

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That's pretty much what I figured, but I thought I might as well ask.. It seems that it would be far easier to reach escape velocity using some form of vertical mass driver, than to try to achieve a stable earth orbit. –  Jaren Fleischman Apr 1 '13 at 22:14
    
See the space elevator if you want a possible (nearly) solution to get to geostationary orbit (or twice that far-using matching earth to hub and hub to outer orbit cables) –  Rory Alsop Apr 1 '13 at 22:18
    
Let's be honest, there's very little chance of a carbon nanotube line 60,000 miles long happening within the next 20 years.. I'm wondering if a shorter cable's bugs could be worked out, gaining the velocity required to either reach escape velocity, or giving it a little upward push on it's way to orbit. –  Jaren Fleischman Apr 1 '13 at 22:23
    
Have a look at physics.stackexchange.com/questions/26739/… for some useful information. –  Rory Alsop Apr 1 '13 at 22:25
    
Thanks, but by "Shorter Cable", I was thinking something more along the lines of 100 miles (161 km). –  Jaren Fleischman Apr 1 '13 at 22:36
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