By now everyone’s heard of Felix Baumgartner and his record-breaking leap out of a balloon some 24 miles over the New Mexico desert. While the “official” definition of outer space is generally considered to start at either 60 miles or 100 kilometers, Felix’s leap of some 39,045 meters is in many respect a drop from outer space. He was above essentially all of the atmosphere, the daylight sky above him was a black starry void, and he had to wear a spacesuit to breathe.
So why didn’t he burn up on re-entry? The physics-savvy among you may scoff at such a question, but it’s one that a lot of people had and it deserves a serious answer. It’s also a great chance to clarify the difference between “in space” and “in orbit”, which are two related but very different concepts.
So, what’s an orbit? The best explanation probably involves Newton’s cannon. If you fire a cannonball, it will sail through the air until eventually gravity brings it crashing to the ground. If you load in even more powder, it will sail farther still. The farther it goes, the more the horizon will curve away under it.
Fire the canon hard enough, and the fall of the cannonball due to gravity will be exactly counterbalanced by the fact that the horizon is dropping away from under it.
This is an orbit. You can reach very high altitudes – even into space – without going into orbit. Orbit is fundamentally about sideways motion, and while it’s a nice way to stay in space around a massive planet, you don’t have to be in orbit to be in space. You can just hitch a balloon ride or whatever other method you prefer to take you straight up.
To get into orbit you need to be going sideways pretty fast. As it happens, the velocity for a circular orbit is
Where G is the gravitational constant, M is the mass of the earth, and r is the radius of the orbit. For Baumgartner’s jump, r is essentially equal to the radius of the earth. (The earth is about 6400 kilometers in radius, so the extra 40 make little difference.) Plug in, and you find that orbital velocity near the earth is some 7900 m/s.
Kinetic energy is
Plugging in orbital velocity, that’s a solid 31 million joules per kilogram. The potential energy due to gravity is just*
This is about 380,000 joules per kilogram, a much smaller number.
And fundamentally this is the reason why you can jump from a balloon without burning up. Coming from orbit, you have to dissipate both your kinetic and potential energy, and your kinetic energy is greater by a factor of 100. Coming from a balloon, you only have to dissipate potential energy because you’re not moving at orbital speeds.
Of course there were a million other ways for the jump to have gone horribly wrong, and the Red Bull team deserves great congratulations for pulling it off. I’m don’t usually pay a lot of attention to commercial stunts, but I tip my hat to this one.
*(g is effectively the same in low orbit as it is on the ground. If the earth were the size of a basketball, the space station would orbit perhaps a centimeter above it)