A lot about how things work in space is counter-intuitive, as all of our intuition is gained from daily experiences where the air is thick, gravity doesnt seem to change and movement is relatively slow. We do see lots of movies about space, but, unless youre watching an IMAX documentary, they vary from slightly wrong, like The Martian (good movie!), to mostly absurdly wrong, like Red Planet (dont watch this, it will hurt your brain), which also doesnt help intuition.
Gravity Never Stops
The most important concept to appreciate is that the range of gravity is infinite. This sometimes comes across as mind-blowing, but is pretty easy to understand once you know how to imagine it. Think of space like a very slippery (no friction), stretched sheet with objects of various sizes dropped on it. Each of those objects creates a funnel shape in the sheet, with the size of the funnel proportionate to its mass, so a tiny object makes a tiny funnel and a giant object creates a giant funnel.
Now imagine placing a marble somewhere on that slippery sheet -- it is guaranteed to fall into one of the funnels. The shallow part of any given funnel gets really, really shallow, but it has no limit, so anything with mass has a gravity field that extends to the far reaches of the Universe, including you! Heres the weird thing: if you and your pet were the only objects in space and you had no relative motion, you would eventually collide even if you started off millions of light-years apart. This why it is velocity that matters, not distance. There is no such thing as escape distance, only escape velocity.
The only way that the marble is not going to fall into one of the funnels is if you spin it around a funnel, like the ball on a roulette wheel, so that it orbits around the center.
Getting back to everyday reality, the impression that most people have is that gravity stops once you reach a certain altitude above Earth, at which point you start floating around in zero g, but, as we just talked about, this is obviously not true. The force of gravity drops proportionate to the square of the distance between the centers of two objects. This makes total sense when thinking about gravity wells like funnels -- if you moved the marble 2% further away from the center of the funnel, it would still fall in, just very slightly slower.
Earth is a slightly squashed sphere with an average distance from surface to center of 6,371 km (3,959 miles). That means if you were in a spacecraft hovering 100 km above the surface, the force of gravity would only drop by the ratio of the squares of the distance or about 3%! This is why you dont experience any weight loss flying in a plane at 10 to 15 km altitude or climbing a mountain -- you are technically slightly lighter, but not enough to notice.
Velocity (how to make what goes up, stay up)
So why are the astronauts in the Space Station, which is at just under 400 km altitude ( 90% of surface gravity), floating around in what looks like zero g? This is because they are actually moving around Earths gravity funnel at the blistering speed of 27,000 km/h (17,000 mph), completing a round-the-world trip every 90 minutes!
The reason they are floating around is that they have no net acceleration. The outward acceleration of (apparent) circular motion, which wants to sling them out into deep space, exactly balances the inward acceleration of gravity that wants to pull them down to Earth.
Kinetic Energy
Almost all two stage rocket systems have a staging altitude of around 100 km, plus minus 20 km. Therefore, the critical figure of merit for a rocket booster is how fast it can throw a payload of what mass at roughly 100 km. It is important to note that the amount of energy needed to achieve a given velocity increases with the square, so going from 1000 km/h to 2000 km/h takes four times as much energy as going from 0 km/h to 1000 km/h, not twice as much.
In the case of the Falcon 9 rocket, the boost stage is able to accelerate a payload mass of 125 metric tons to 8000 km/h and land on an ocean platform or to 5000 km/h and land back at the launch site. The second one is lower because the rocket is moving super fast away from the launch site, so it has to do a screetching U-turn with nitrogen attitude thrusters, then fire the engines to create a reversed ballistic arc, then reorient again for atmospheric entry and have the engines pointed in the right direction for the landing burn. Since the propellant is liquid, it wants to centrifuge out during these maneuvers, so there has to be a system of baffles and internal holding tanks to keep it in place. It also needs three axis control surfaces that dont melt easily and work well from hypersonic through subsonic speeds.
For a sea platform landing, the Falcon 9 figure of merit is therefore roughly 300 gigajoules (GJ) of kinetic energy and for a return to launch site landing, the number is about 120 GJ. These are fairly sizable by terrestrial standards. To put it into perspective, the city of San Francisco uses about 1 GJ per second of electricity, so the Falcon 9 booster transfers enough energy to power a city of almost a million people for five minutes.
When trying to understand the value of a reusable rocket booster, the kinetic energy transfer at a 100 km reference altitude is what matters. That altitude is the equivalent of the starting line of a race. The race itself is the kinetic energy.
SpaceX Reusability Progress to Date
Weve done several vertical take-off and landing flights with the same Falcon 9 first stage test rig, called Grasshopper. These were important to ensure that the final velocity attenuation algorithms worked properly. In particular, we needed to prove out a hard slew maneuver and a high acceleration landing. The first is important because the rocket is still moving sideways before landing, so we need to zero
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A lot about how things work in space is counter-intuitive, as all of our intuition is gained from daily experiences where the air is thick, gravity doesnt seem to change and movement is relatively slow. We do see lots of movies about space, but, unless youre watching an IMAX documentary, they vary from slightly wrong, like The Martian (good movie!), to mostly absurdly wrong, like Red Planet (dont watch this, it will hurt your brain), which also doesnt help intuition.
