I always thought the N-Prize was a good challenge and I want to put out my idea on it and see if there is something to work with .  Please see http://n-prize.com/ if you are not familiar with the challenge.

Here is the idea dump:
Internet sources
https://en.wikipedia.org/wiki/Space_tether https://en.wikipedia.org/wiki/Project_Echo https://www.sciencedaily.com/releases/2016/02/160226133603.htm https://en.wikipedia.org/wiki/Momentum_exchange_tether http://science.nasa.gov/missions/tss/
If you have the time, watch the Youtube videos by Robert Murray-Smith. He goes through the development of graphene for the home experimenter.

 The thought is this: A balloon lifts an uninflated graphene coated (puffed laser-scribed graphene) balloon with gear to ~110,000 feet. The coated balloon will inflate as the attitude increases due to the pressure change. The graphene increases the electrostatic charge based on the surface area being increased 1000s of times with the coating, so the charge become huge. The balloon has a tail of graphene to act as a tether and a discharge conduit to form a circuit from a high density charge to a corona discharge point. The tail will generate electricity as it passes through the Earth's magnetic field. The balloon will also be covered with the new perovskite solar film. The film charge will push against the Earth's magnetic field and increase its velocity and/or altitude (There are issues with the angle of the Earth's magnetic field at the poles). The balloon will be launch from the South Pole a week before the summer solstice (December - it's a different hemisphere). The date of launch date will allow for two weeks of maximum solar exposure and time to reach orbital velocity.  The South Pole during this time will have 24 hour sunlight and because of overflight issues, there are less political country issues. The thrust will be slow at first, because the angle of the tail to the Earth's magnetic field is bad, but it will get better as it spirals north away from the poles. The thrust would be best at the equator and get the boost from Earth's rotation, but too many countries to fly over and only 12 hours of daylight.  An extra tail could be used as an rectenna to charge from a ground based radio transmission, but I am thinking it would not be efficient enough, I might be wrong. The circuit flow might be able to power an ion craft drive, but I do not know, plus air resistance at mach speeds may be too much (At very high altitude, say 300000 ft, the air speed mach numbers may not be an issue. The best source of a big boost in thrust would be to use the hydrogen gas from the balloon as propellant for a microscale ion drive. The balloon should be made to become a vacuum balloon (Halfbakery) like ECHO 2, but instead of aluminum, use a UV cured plastic to harden by unfiltered UV space radiation. A vacuum balloon will not have the thermal issues of a lifting gas expanding and contracting during day and night. Multiple tails with different current might be the way to steer it or a just a big thin graphene sheet that turns (probably too clumsy) and uses the very thin air to change its inclination.

Please let me know if this is interesting and if it has potential.

Basic Math
1209600 is roughly the number of seconds in two weeks.
7900 meters per second to reach orbit
7900/1209600=0.0065 meters per sec
A little faster than a quarter of an inch per second.

Working against gravity (9.8 m/s) is the major challenge.