The balloon antenna idea came to me while working as a mission controller on the Magellan spacecraft orbiting Venus.
The idea, as it turns out has been thought of several (probably independently) times. I did it independently and will keep it here because of that and the additions and enhancements I have made that I have not seen anywhere else. I found out shortly after my initial work that there was an engineer at JPL working on a similar project but when I tried to contact him he was rather negative to my ideas. Perhaps it is harder than it looks and he was a bit frustrated.
My idea is on a much greater scale than his, which was only feet in diameter. He was trying to solve the problem of rigidity with a non-expendable solution (a hardening of the balloon into a rigid structure). I chose an expendable gas at light pressure with sealant and mobile repair robots. I think that will work because my design will be in very deep space where there are few forces of distortion.
What I propose is a large sphere or lens shape (TBD) with a reflective metal coating on one surface. larger than 1 kilometer and hopefully much larger than that. It was to be primarily orbiting quite distant from earth, not LEO. I was considering behind the moon or earth in opposition to the Sun to use the Earth or Moon as a shield for the solar wind that would be a strong distorting force and would also tend to move the balloon out of position.
Now, I also propose a larger mission with 4 separate balloons launched out of the solar system in 4 equidistant directions (forming a pyramid shape).
Doing this allows the system to be used as a large array (approximately 1000 AU distance each makes it a 2000 AU aperture antenna, I.E. 2KAU project). This also allows for a certain redundancy built in with graceful degradation due to failure. The look angle is spherical with 4 balloons. With 3 it is limited to only 2 directions looking out of the plane formed by the 3 points in space. with 2 balloons the picture is still scientifically useful but can not create undistorted images. With one left, the balloon is reduced to a large telescope far away (also useful). By using the earth based instruments, some lost utility can be made up with a smaller base line 1000 AU and thus offers a considerable backup ability. By having an identical near Earth based balloon considerable backup is obtained and much improved sensitivity is gained.
The advantage of this array is the very fine resolution and detail (due to the 2KAU) as well as quite good sensitivity (due to the Kilometer size). Some immediate results to be expected would be direct visualization of planets about other solar systems. Also, direct measurements of distances to stars, and possibly direct visualization of nearby stars. Also, detailed imaging and data of the beginning of the universe can be expected.
Some unusual features of this project would be using the balloon as a sail to get there, thus reducing the requirements for fuel. Also, use the antenna as both optical and radio telescope(depending on how accurate the shape can be maintained). The antenna can be used in multiple directions at the same time depending on the number of free floating receivers (which again offers useful redundancy with graceful degradation).
The antenna could also be used as its own comm ant to earth with both radio and laser receive and radio transmit at little added cost but some loss of utility (time out for the comm).
A different idea for funding might be to try to use direct public funding as well as national contributions. Suppose the system had a small staff of controller engineers but the mission control function could be done over the internet by multiple volunteers. With many volunteers checking each other and computer checking, a nearly free control function might be obtained, perhaps even charging for the chance to be on the team (a small amount from many volunteers might be substantial). With a group like the Space society overseeing it, much funding could be obtained. Selling shares in the venture and selling the data are other concurrent possibilities. Selling name-space and even picture space for those who support the project is another. A Special DVD ROM with many names and pictures on it could be made and included at little extra cost if done carefully. For instance, the Space born DVD need not be as thick as the ones sold on earth and could be more heavily compressed data, perhaps even printed/etched on the side of a bulkhead costing no weight at all!
Some other ideas in the earlier one balloon project is the use of a spherical shape and then using a multiple element receiver. In near earth use, solar power could be use by the same means as the mail ant. but the requirement for fine accurate focusing is negated and much cheaper ant can be used.
Note that these ideas can be used for other projects as well. A free standing solar collector made from a balloon can acquire enough solar energy it use in much farther locations than solar cells since the size to weight ratio can be so great. Possibly a solar powered astroied mission could be done, perhaps even Jupiter mission. The quality of the balloon is much reduced and it may be possible to use it for radio comm too.