How high must an object be to not be pulled back to Earth?

Gravity falls off at as distance from earth increases, but it never actually fully disappears. So even if you're on the other side of the galaxy, eventually your camera will fall back down (assuming nothing else pulls it first).

However, if your camera is moving fast enough, it will get slowed down by earth's gravity, but it will also keep getting further away from the earth (where gravity is weaker). Effectively, it can "outrun" the earth's gravity, and so gravity will never actually manage to stop it and pull it back down. This is escape velocity.

Unfortunately, as russ waters pointed out, for objects within hundreds of miles from earth, this velocity is about 25,000 mph.

 

I am curious, if you thought that there is no atmosphere past 13km, on what principle did you imagine your baloons were able to raise twice higher?

 

DLHill, you might find this bried discussion of interest:


http://en.wikipedia.org/wiki/Weather_balloon

As a balloon rises, lowering temperatures that would cause contraction of the gas and loss of lift is more than offset by reduced atmospheric pressure wihich causes balloons to expand,is also offset by reduced gravitational attraction.

13km might have been someone's estimate for the altitude where typically 'normal' breathing is significantly diminished. In Denver, for example, the 'mile high city', MMA fighter commentaries often refer to who has trained at altitude and for how long.....and who hasn't....apparently even at that very modest altitude, it can make a difference in performance of highly conditioned athletes. In the Himilayas, at close to 9km altitude, climbers routinely use breathing apparatus for the strenuous effort required

 

I hope you have the necessary background education. It's not that easy to get something into orbit. It is rocket science, after all.

 

Unfortunately, as russ waters pointed out, for objects within hundreds of miles from earth, this velocity is about 25,000 mph.

Not on ring world it ain't

Also for objects between Earth and the Moon at a point where the gravity is equal on an object, the escape velocity could be 1mph which is considerably greater distance than hundreds of miles and a lot less than 25,000 mph.