Yes, in 2012 it was talked about quite a lot. But also meaningfully?

For those who don't remember: On October 14, 2012, Felix Baumgartner ascended to a height of 39 kilometers in a helium balloon and then jumped down.

We ask some questions and try to answer them.

Was it a jump from space?

The answer to this question probably depends on how we define "space". I guess the most common definition is "space outside the Earth without an atmosphere". But the atmosphere doesn't just end suddenly, the transition from atmosphere to space is like going up a hill, not like a step.

If we talk about the language of numbers, the International Space Station ISS (which is apparently in space) orbits the earth at an altitude of 300 km. It is internationally agreed that the limit of outer space is at an altitude of 100 km. If so, 39 km doesn't come close. Although it is quite high.

But what about the air density there? The air density on the ground is about 1.2 k g/m ³ . At an altitude of 39 km, the air density is only 7.3 x 10 ^-4 kg/m ³ . Since everyone loves graphs, here we plot the density of air as a function of altitude, as described by this density model .

Therefore, it is not too much wrong to call this height space. Because you definitely need a space suit to be there, right?

How do you get that high?

There are several options. The most obvious of these is, of course, the rocket. Why not a plane? Because an airplane needs air to fly. But, as explained in the answer to the previous question, there is not much air at such a height. So next to a rocket, the best option is a light gas-filled balloon. But, didn't we just say there's no air that high? Yes, we said it. Balloons also need air. But they still work if we make them big enough.

If we imagine a balloon flying at a certain height, such forces act on it.

We have gravity and buoyancy. In essence, the uplift force is caused by the air particles hitting the lower side of the balloon more often than the upper side. The bigger the ball, the more bounces and the more lift. But there is one problem with that. If you take a balloon and simply blow air into it, the force of gravity increases as the ball increases. Therefore, we must use a gas whose density is less than that of air. This gas is usually helium.

However, since the air density is really very low at 39 kilometers, there are also very few collisions between the air molecules and the ball, and we need a pretty big ball ... which is unfortunately also heavier. The calculations show that a ball with a diameter of 80 meters is needed to carry the jumper and his capsule to this height.

How much has gravity decreased at an altitude of 39 kilometers?

The air is pretty thin at that altitude, but what has happened to the force of gravity? Clearly, gravity must exist in space. Because this force keeps the Moon in the Earth's orbit and the Earth in the Sun's orbit. It is worth repeating here, because people often think that there is no gravity in space.

Gravitational force depends on the distance between bodies (at least for spherical objects, this is the case). If you double the distance between the spaceship and the center of the Earth, the gravitational force between them decreases four times. And the key word in that sentence is "Earth's center." So if I'm three meters above the ground and then rise to 6 meters, how far have I moved from the center of the Earth? The answer is that it did not move away (in the first approximation). How so? Because the earth is huge. Its radius is about 6.38 x 10 ⁶ meters.

Let's keep trying. Type 2.09 x 10 ⁷ + 100 into your computer. What is the answer? The answer is 2.09 x 10 ⁷ . Because the computer rounds the actual value.

Okay, the force of gravity doesn't change much near the Earth's surface. But at an altitude of 39 kilometers? By calculating, we get that if a force of about 9.8 N acts on a 1 kg mass on the ground, then at an altitude of 38 kilometers this force is 9.68 N. This is 98.8% of the force of gravity that acts on the ground. So, the force of gravity at an altitude of 39 kilometers is pretty much the same as it is on the ground.

It may also be mentioned that the gravity on the International Space Station is 91% of the gravity on Earth. So why are they floating freely in space. Good of you to ask!

What is the speed of sound?

One of the cool things about the Red Bull Stratos jump is that you can fall there faster than the speed of sound. But what is the speed of sound? You might even ask "what is sound", but we'll leave that question for another time.

Introductory physics courses say that the speed of sound is about 340 m/s. This is the speed of sound at normal temperatures and pressures (near the ground). But sound is the interaction of air particles, so a lot really depends on their behavior (and this whole topic is not easy at all). But there is a model that says the speed of sound is proportional to temperature (it's just a model, but it still works pretty well).

The higher we go, the lower the air temperature becomes (up to a certain limit). Using the same model for air density, we get the temperature and thus the speed of sound. The following figure describes the speed of sound as a function of height.

At an altitude of 39 kilometers, the speed of sound is only about 200 m/s.

Can he fall faster than the speed of sound?

This is the question we've been waiting for. The answer is yes. To understand this, let's examine the forces acting on Felix just after he leaves his capsule.

Since he is not moving (yet) and there is not much air at such a height anyway, only the force of gravity acts on him. As this force acts downward, it causes him to fall faster and faster,

As the speed increases, air resistance begins to act on it. You've probably felt this force when you reached out of a moving car. The faster you go, the greater the air resistance. But it also depends on the air density. So at the beginning of the fall, the forces acting on Felix could be represented something like this:

Since the force from air resistance acts in the opposite direction to the gravitational force, it makes the total force smaller (but still pointing downwards). This means that the speed increases, but the rate of growth (acceleration) decreases. It is important to note that his speed continues to increase. And somewhere here, his speed could be faster than the speed of sound.

But Felix cannot gain speed indefinitely. Finally, the speed becomes very high, and the density of the air also increases as it gets lower. At some point, the force of air resistance becomes greater than the force of gravity:

Because air resistance acts in the opposite direction to the force of gravity, the speed decreases. Eventually, the velocity decreases to a value where the force of air resistance and the force of gravity become equal. From that moment on, his speed will neither decrease nor increase. This speed is called terminal speed or limit speed.

I know I haven't answered the question yet. How about the speed of sound? Calculating terminal speed is not easy at all. The created problem must be divided into several small problems and then given to the computer to be solved as a program.

If we do this, we get Felix's speed as a function of time. I've also included the speed of sound as it falls in this figure.

According to the calculations (which include several simplifications), it travels faster than sound for about one minute. For a while, the speed also becomes greater than the speed of sound on the ground.

Why do parachutists fall at approximately 200 km/h?

Paratroopers? Really. Felix? He doesn't. Why? Because the air density (and therefore also the air resistance) changes during his jump. He will not be at any height long enough for his velocity to equal the terminal velocity for that height. This happens only at the very end of the fall. This is his speed compared to the final speed of the corresponding height:

You may notice that I have cut the first end off the graph. This is because the terminal velocity is ridiculously high at these altitudes and it looked weird on the graph.

What actually happened? The speed of Felix Baumgartner's jump was:

Sources:

https://www.wired.com/2012/02/stratos-space-jump-can-you-fall-faster-than-the-speed-of-sound/

http://www.redbullstratos.com/science/scientific-data-review/index.html