Is it possible to use a balloon to float so high in the atmosphere that you can be gravitationally pulled towards a satellite? A recent joke on the comedy panel show 8 out of 10 cats prompted this question.  I'm pretty sure the answer's no, but hopefully someone can surprise me.
If you put a person in a balloon, such that the balloon ascended to the upper levels of the atmosphere, is it theoretically possible that an orbiting satellite's (i.e. a moon's) gravity would become strong enough to start pulling you towards it, taking over as the lifting force from your buoyancy?
Clearly this wouldn't work on Earth, as there's no atmosphere between the Earth and the moon, but would it be possible to have a satellite share an atmosphere with its planet such that this would be a possibility, or would any shared atmosphere cause too much drag to allow for the existence of any satellite?
If it were possible, would it also be possible to take a balloon up to the satellite's surface, or would the moon's gravity ensure that its atmosphere was too dense near the surface for a landing to be possible thus leaving the balloonist suspended in equilibrium?
Could you jump up from the balloon towards the moon (i.e. jumping away from the balloon in order to loose the buoyancy it provided).
http://www.channel4.com/programmes/8-out-of-10-cats/4od#3430968
 A: No, a shared atmosphere between body and moon is not possible.
For a natural satellite to remain, the orbit must be very stable, because those satellites exist for billions of years. Even the tiniest bit of atmosphere (a few molecules) would cause a tiny drag. However, drag adds up, so over a long time period, even a heavy object (such as the moon) would be dragged down due to drag and ultimately collide with the body it is rotating around.
A balloon needs a quite significant atmosphere to be used. Present balloons can reach up to 30–35 km altitude. Since atmospheric density (in the heterosphere) drops off exponentially with elevation, balloons would get gigantic even to reach a little bit higher. Reaching an elevation where the atmosphere has negligible density is, in a balloon, impossible.
One can however, in theory, try to go as high as possible with a balloon, and then use other methods (such as rockets) from there, thus bypassing the densest part of the atmosphere and save a lot of fuel.
Edit: one more way to look at it: if a satellite would have enough gravitational pull to pull up an observer in a balloon, it would certainly pull up the atmosphere; therefore the satellite would be in the atmosphere, which is impossible. Therefore, a a satellite can never have enough gravitational pull to pull up an observer inside the atmosphere.
A: When the balloon is rising, it's doing so because it is less dense than the surrounding air and there is a net gravitational pull "down." The air is pulled more than the balloon - hence the buoyant force. If the balloon is to be found falling "up" toward the satellite, then surely the air around it would be falling even faster in that direction, since it is by hypothesis more dense.
The best you could hope for is for the two transitions
\begin{align}
\text{balloon less dense than air} & \to \text{balloon more dense than air} \\
\text{gravity dominated by planet} & \to \text{gravity dominated by satellite}
\end{align}
to occur at the same altitude, and for your inertia to carry you from one to the other. However, this kind of precarious situation wouldn't last very long.
