Back in the secondary school I worked on a physics project about the escape velocities. Really interesting stuff – it was the first time when school intersected space – but looking back 20 years I can’t help but notice that I was missing the big picture. Here’s why.
The escape velocity is the minimum speed need for an object in order to escape from the gravitational influence of a celestial body. For the Moon, it’s 2.38km/s at its surface. For Jupiter, it’s 60km/s. For a black hole, it’s infinity.
There are 3 important things to remember when talking about the escape velocity:
it is independent of the mass of the object. It doesn’t matter if you’re shooting a small bullet or a big spaceship. However, the escape velocity depends on the mass of the celestial body
it assumes that the object travels in vacuum, not in an atmosphere. So no friction
it assumes that the object is no longer subject to thrust after reaching the escape velocity
With these 3 things in mind, a good example to illustrate the escape velocity would be an imaginary cannon launching a projectile on the Moon. Launch it with an initial speed inferior to 2.38km/s and it will come back; anything above that will cause the projectile to leave the gravitation influence of the Moon (well, until it reaches the gravitational sphere of another massive body). On the other hand, using the Earth as the celestial body is a terrible example. Not only Earth has an atmosphere (until an altitude of about 100km) which introduces friction and makes the object mass and shape important, but in a subliminal way, everybody would imagine that the object reaching the escape velocity is a rocket. But at the Earth surface, the escape velocity is 11.2km/s, and no material known to man would resist the combined effect of the brutal acceleration and aerodynamic forces or heating.
So how did Apollo missions did reach the Earth’s escape velocity? Well, in short, they didn’t.
So, I’ve been locked out of my PayPal account because I was using Multi-Factor Authentication (MFA) with Google Authenticator codes. After I changed my phone I noticed that (1) on the new phone, Google Authenticator was empty and (2) there was no way to log in to PayPal without the Google Authenticator codes:
The PayPal call center is unable to help me for the moment. There are multiple take-aways from this, and probably the most important is to use an authenticator app that backs up the accounts in the cloud. Google Authenticator doesn’t do this. Authy does.
A few notes after reading ‘One giant leap‘ – an excellent book by Charles Fishman about the Apollo space program.
1. The unsung hero of the Apollo program
In the Smithsonian Air and Space Museum in Washington DC there is a section dedicated to the Moon race. There are some Russian artifacts on display, one of them being the Soviet Moon Suit. It looked like this:
The caption added by the museum read ‘All dressed up but nowhere to go‘, along with the following explanation: “Soviet cosmonauts had a lunar orbiter, a lunar lander and a space suit for the Moon. Why didn’t they go? The crucial missing piece was a rocket powerful and reliable enough to send a manned spacecraft to the Moon” (inclusion note: ‘manned’ should really read ‘crewed’).
But after reading ‘One giant leap’, I think that we could safely argue that even if the Russian had a powerful enough rocket, they would still come second. Why? Because they didn’t have a computer to take them to the Moon.
Some background: even in the Apollo program, the computer came more like an afterthought. First, it was imagined like a nice-to-have guidance tool. More or less like the first generation GPS kits installed on the cars: used for guidance only, but never for control (forget about Tesla Auto Pilot for a second :D). “The astronauts wanted to fly the damn ship themselves; the computer was to play an advisory role“. But time proved that rocket science is… well, rocket science:
“During the final descent to the Moon, the lunar module burned off 17400 pounds of fuel – 9 tons of fuel gone in 12 minutes. Eagle weighted only 9500 pounds without fuel. The math was hard, and the mission was to get the hard math into the computer”
So welcome AGC – the Apollo Guidance Computer, along with it’s nice little diskee (DSKY), which had to fit exactly in one cubic foot. The UI was primitive (remember, it was the sixties), but the NASA and the MIT guys managed to find a common language for the AGC and the astronauts:
“Commands were entered numerically, as two-digit numbers: Verb, and Noun. Verb described the type of action to be performed and Noun specified which data were affected by the action specified by the Verb command”
Just a few seconds before the famous ‘The EAGLE has landed‘ , Buzz Aldrin said ‘413 is in‘. 413 was one of the nouns, indicating the AGC the next flight sequence.
It was not the first time NASA used computers for the space flight. And expensive errors have been made before. But the Apollo computer was there to stay, and for the first time in the human history, it had direct responsibility for human lives.
“The computer is, in fact, the largely unsung hero of the thrust into space”
2. Apollo’s costs
One of the constraints of the Apollo program was the deliverable: it was all or nothing. NASA could not deliver only half of the trip to the moon. Or get to the Moon, but leave the astronauts there. Lyndon Johnson, who had “much more authentic passion for the race to the Moon that JFK“, explained it in layman’s terms: ‘there is no second-class ticket to space‘.
So how much did the space ticket cost in the end?
In 1969 money, between $19 and $24 bn. Too expensive? It depends on the perspective. JFK said that it’s ‘somewhat less‘ than the price spent by all the Americans on cigarettes in one year. Here’s another perspective: the Vietnam war costs were over $110 bn. Not including the human cost, with millions of lives being lost.
Some of the opponents of the Apollo program were urging the US to invest the Apollo money into education, or to help fight poverty.
“The problems that NASA and the 400,000 people overcame to get to the Moon were daunting, but they were all solvable. That’s, in part, because non of them involved human behavior or the social systems in which humans live. Once you solve the problems of flying to the Moon, you don’t wake up next morning and find those solutions have unraveled overnight. The problems of poverty and education don’t get solved the same way”
Moreover, the Apollo program had an enormous economic impact:
“None of the $24bn it cost to go to the Moon actually got spent in space; it was spent right here on Earth. The economic impact is magnified many times when you account for the power the moon race had in accelerating the digital revolution”
3. Apollo’s impact
Did Apollo kill the space exploration? Some people think so, since no man has left the Earth orbit since 1972. “A remarkable achievement, yes, but it distorted the entire space program and it left US space exploration adrift“. Might be true. The fast-forward program compressed 50 years of technological development in 8 frantic and exciting years. But this was another constraint: “Apollo didn’t exist in a world where we could lay out a thoughtful, methodical, half-century-long plan for space exploration“ On the other hand, “we haven’t spent 50 years neglecting space, we’ve spent 50 years catching up“. And that’s because Apollo was dramatically ahead of its time.
The Apollo’s value wasn’t only in the space travel. The race to the Moon kick-started the technological development that we currently enjoy:
“Apollo launched rockets to the Moon. But it also launched us into the Digital Age. NASA didn’t invent the integrated circuit. But NASA’s needs forced the semiconductor companies to create the perfect chip, and the continuously improved chip, on which the modern digital economy is built”
So indeed, Apollo didn’t sent us in the Space Age, but at least it sent us in the Digital Age.
4. A few more interesting things
How the nuclear submarines made the world safer:
During the Cold War, the US had a fleet of nuclear submarines. They had a number of interesting properties. First, they were really powerful war machines since they carried nuclear weapons. Second, they were also powered by nuclear energy, which meant that they had a ridiculous long range and were roaming in oceans all over the world. Lastly, their position was never known by the others. Thanks to these properties, they made the idea of a first nuclear strike much less likely:
“They provided certainty for the strategy of ‘mutually assured destruction’: no matter what damage was done to the US by the USSR, the nuclear submarines would survive to counter-attack”
How do you actually fly in space?
There’s no GPS with turn by turn directions. Soon after you leave the Earth, you only have the stars to guide you. Just like the first sailors a few thousands years ago, with the important difference that space navigation is in 3D, not 2D. So how did the astronauts do it?
The answer was the inertial navigation system, originally developed for rockets. The first application was guiding the missiles (making them immune to radio interference), then space flight and commercial airliners.
“It proved to be the only way to fly from earth into space. […] In other words, the inertial navigation system is a super-sophisticated version of the human inner ear: it perceives every motion, every shift, every acceleration and deceleration”
However, inertial guidance is difficult without computers. The desire to use inertial guidance in the Project Apollo drove early attempts to miniaturize computers.
How many lunar moduleswere built?
There is a bit of confusion related to the number of lunar modules built during the Apollo program (interesting note – it took a decade to build them all). We know for sure that 10 LMs flew into space, 6 of them landing on the Moon. 3 never left the Earth and are still on display in US space museums (Washington DC – pictured below, Florida and Long Island). Here‘s more about the fate of the few others.