Anyone announcing the successful sale of tourist trips around the moon would attract ridicule and laughter. Unless your name is Elon Musk. In that case the announcement amounts to nothing more than a logical and rather modest step towards Musk's promise of getting a million people to live on Mars. 

One might question why humanity would be interested to colonize an inhospitable planet. Sure, rising CO2 levels in Earth's atmosphere do pose a challenge, and this issue might make few of us long for a second planet. But when given a choice between a planet with a CO2 level a notch above 0.04% and and a planet with an atmosphere consisting 96% of CO2, the choice seems pretty clear to me. Risks other than rising CO2 levels are no different: trading Earth for Mars means going from bad to worse. 

But let's set aside the question for the need to migrate humans to Mars. I want to focus instead on the plausibility that Elon's company, SpaceX, can indeed pull off its promise of human emigration to Mars. I am going to cut Elon some slack: I will not insist on the aggressive timeline he put forward (Mars colonization starting in 2024). So the question is: can the rocket technology utilized by SpaceX ultimately be expected to deliver Mars colonization? 

Have a look at above diagram. It shows historical records for the distance humans have moved away from Earth's surface. This distance, the altitude, is measured in Earth diameters. Note that the vertical axis covers a huge range in altitudes with each tick mark representing a factor 1000 increase. On the right hand side it is indicated which altitudes correspond to LEO (Low Earth Orbits), to Moon travel, to Interplanetary Travel, and to Interstellar Travel. 

Two technologies are shown: 1) lighter-than-air balloon technology, and 2) chemical propulsion rocket technology. You don't need to be a rocket scientist to spot that both technologies are characterized by a short initial period of rapid progress, followed by a long period of painstakingly slow progress. The transition between both regimes occurs when engineers hit upon fundamental limitations to the technology. When past the transition, progress is still feasible but this progress is logarithmically slow and typically realized by brute-force attacks. 

The human altitude records for balloon technology starts in 1783, when the Montgolfier brothers launch a balloon on a tether. In it is Jean-François Pilâtre de Rozier, a chemistry and physics teacher. De Rozier stays aloft for almost four minutes at a height of 24 m, and makes it safely back to Earth. The altitude reached is modest, but the first airborne human is a fact. From that point on record after record gets broken. In less than a year the Montgolfier brothers 10-fold and again 10-fold the altitudes reached by humans. In the process De Rozier, the first airborne human, also becomes the first fatality in an air crash. But this doesn't stop progress, and altitudes of a few kilometers are reached. But then, just two years after the first airborne human, progress slows down considerably. It takes more than two centuries for the next 10-folding of altitudes to take place. 

From a physics perspective it is clear that once higher altitudes get reached, balloon builders start combating thinner and thinner atmospheres. Every next step in increasing altitude requires an exponential increase in volume-to-mass ratio of the manned balloon. It is this challenge that causes progress to slow down.

The human altitude records established with rockets follows a similar curve. This curve starts off with Yuri Gagarin's 1961 space flight reaching a record altitude of 325 km. This makes Gagarin the first human officially leaving Earth's atmosphere and reaching empty space. A few years later, also Gagarin, the first man in space, dies in a test flight. But progress in reaching higher altitudes is fast, and less than a year after Gagarin's death the first humans orbit the Moon thereby establishing an altitude record exceeding that of Gagarin by as much as three orders of magnitude. 

But then progress in reaching farther from Earth stalls. Two years later, in 1970 the human altitude record gets improved, but only marginally. The record of 401,056 km still holds today, almost half a century later. If we are optimistic and assume SpaceX is successful next year (!) in improving upon this altitude record, we get the rocket altitude curve as shown above. 

Also here, from a physics perspective it is clear what is happening. With chemical propulsion technology the exhaust velocity for rockets is limited to 4.4 km/s. Given this limitation, reaching farther and attaining higher speeds (in rocket scientist speak: obtaining a higher delta-v) requires an exponential increase in the fueled-to-empty mass ratio of rockets. It is this challenge that makes progress stall.

Setting aside technical details, just eyeballing the rocket technology progress curve, drives down the conclusion that deep space exploration by humans is well past the era of rapid progress. This immediately raises the question "what technical miracle is SpaceX counting on?" It is clear that what SpaceX needs is a novel propulsion technology generating exhaust velocities well above the 4.4 km/h mark. This would create a novel curve in above plot that would flatten out at much higher altitude values. Yet, the sobering news is that SpaceX's ITS (Interplanetary Transport System) is not based on any novel propulsion technology. ITS is based on the same chemical rocket propulsion technology that is responsible for the absence of progress in the above plot. It is the propulsion technology that proved extremely useful in bringing humans and payload into LEO. The technology can even be stretched to bring humans to the moon and back. But counting on it to colonize Mars carries the flavor of counting on balloons to bring humans into space. Won't happen. 

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