Why is it so hard to build crewed rockets/spacecraft able to reach escape velocity?

Why are we still not going farther than to Low Earth Orbit? Orbital velocity is about 4.8 mi/s (7.7 km/s) and escape velocity is about 7 mi/s (11.2 km/s), about 45% faster. Why is it so hard to reach these additional 45%, even almost 60 years after Gagarin's flight? Or at least translunar velocity, because to go to the Moon you don't have to reach full escape velocity? If we can put people into LEO, and space probes at escape velocity, why do crewed spacecraft still circulate in LEO, what are the main obstacles to build a craft reaching 145% of orbital velocity?

• Why? Because One Little Mistake, and BOOM!!!! Jan 17, 2021 at 7:00
• What would people (I presume you're talking about crewed flight?) do beyond LEO that space probes can't? Jan 17, 2021 at 14:00
• Does this answer your question? Why not build Saturn V's again? Jan 17, 2021 at 14:10
• "Still not going farther than to Low Earth Orbit"? We've been to the Moon. And back. And that was very expensive. But now that we have been there, there's little incentive to go back, given the cost. So the next step is Mars, but that's a whole different ballgame, for many reasons going beyond just the basic technology to get there and back, including the duration of the trip. Jan 17, 2021 at 15:20
• @jcaron Before we go to Mars we should learn how the human body evolves in low gravity over the course of several months in the vicinity of Earth, on the Moon. A Mars mission (with conventional propulsion) would last about two years, one year of it in weightlessness and one year on Mars. The longest ISS stay was a bit over a year, but we anyway ought to test how to work in partial gravity, not no gravity. Unless one aims for nuclear pulse propulsion, but that's unrealistic to be realized any time soon. Jan 17, 2021 at 18:07

Delta-V to LEO is about 10 km/s. From there to C3 (Earth escape) is another 3.2 km/s. It's just another 30% delta-V.

The problem is the Tyranny of the Rocket Equation. More delta-V means more fuel. More fuel means more mass. More mass means more fuel.

How much more? Fuel costs scale according to $$e^{\frac{\Delta V}{v_e}}$$, that is e to the power of the ratio between delta-V and exhaust velocity. A typical chemical rocket has an exhaust velocity of 3 km/s.

• To LEO that's $$e^{\frac{10 km/s}{3 km/s}}$$ or 28.
• To C3 that's $$e^{\frac{13.2 km/s}{3 km/s}}$$ or 81!

30% more delta-V costs almost 3 times more fuel.

That's just to reach escape velocity. You'd need more to go somewhere, and more to come back.

Or at least translunar velocity, because to go to the Moon you don't have to reach full escape velocity?

It's more expensive to get to the Moon than it is to get to C3. LEO to low lunar orbit is about 4.8 km/s.

• To low lunar orbit that's $$e^{\frac{14.8 km/s}{3 km/s}}$$ or 139.

Low lunar orbit requires 5 times the fuel as LEO.

Landing is another 1.6 km/s. 1.6 km/s to leave. 0.7 km/s to go from Lunar to Earth's gravity. Then you can aerobrake. Add that to 14.8 km/s to get to low lunar orbit gives 18.7 km/s to play golf on the Moon.

• To the Moon and back $$e^{\frac{18.7 km/s}{3 km/s}}$$ or 509.

Oh dear, a round trip to the Moon costs 18 times more fuel than LEO.

These are all very rough delta-V numbers and simplistic single stage calculations, but it should give you some idea how fast the size of a spacecraft balloons as delta-V increases.

• Comments are not for extended discussion; this conversation has been moved to chat. Jan 18, 2021 at 14:56
• Why the small delta in the exponent? Shouldn't it be capital? Jan 18, 2021 at 19:22
• @JanDorniak That's how MathJax renders \delta. Ahh, I didn't realize capitalization mattered in MathJax. Jan 18, 2021 at 19:27
• "Three times as much" not "three times more". - If you do something once more than once, you do it twice. Jan 19, 2021 at 9:46
• @Peter-ReinstateMonica. All answers are "because that's how the universe works". But that's not really helpful. Jan 19, 2021 at 14:33

It's not hard, it's just expensive. We know exactly how to do it. Compare this to building computer processors with 1nm transistors, or making reliable self-driving cars. Those are both things that we currently don't know how to do, and we don't even know exactly how to get better at doing them.

Even going past low Earth orbit to another planet, like Mars, is something we know how to do and have the technology to do--in terms of getting humans to the right velocities and on the right trajectories. What starts to become the hard part is a little different--how to minimize human exposure to radiation, and bring all the supplies necessary to avoid having to make dozens of trips to refuel any humans you would bring that far.

What's currently holding us back from sending humans beyond low-earth orbit isn't technological, it's economical. Why should governments or private companies spend the money to do it? NASA is working on doing it because it's part of their directive, but because again of budget restrictions it's slow going. Private companies like Blue Origin and SpaceX are working on it both because they're owned by people worth hundreds of billions of dollars (Bezos and Musk respectively), and are driven in combination by hubris of their owners, the desire to cement their legacies, the sense of human exploration, and the expectation that eventually they'll be able to make a business out of the tools and capabilities they're creating.

• Indeed. The very first circumnavigation of the planet involved a 90% casualty rate, and the loss of 80% of the vehicles. But 500 years ago such odds were deemed acceptable. We could go to Mars right now (aka very soon), with similar or slightly better odds. We just choose not to.
– vsz
Jan 17, 2021 at 13:05
• +1 The last paragraph is particularly pertinent; we need a reason to spend so much money. Last time it was a race between the USA and the USSR, what is the reason this time? Jan 17, 2021 at 13:58
• @vsz 500 years ago -> The first man to circumnavigate the globe died on the way! (Should have had leg armour :-( ). Jan 18, 2021 at 10:28
• Excellent point. Perhaps though one could reframe the question: Why were we willing to spend that money in the 1960s? Jan 19, 2021 at 13:46
• @Peter-ReinstateMonica Indeed. Almost immediately after Apollo 11 had left their footprints the endless money rain turned into a trickle, because the political reason to get over the humiliation of Soviets having beat you to orbit was fulfilled. Jan 19, 2021 at 16:59

Return trips are harder

The main "problem" with crewed trips is that we generally want those people to return back. This means that we don't just need to accelerate the manned part to the required velocity, but we also need to accelerate a sufficient amount of fuel and engines for the return trip, which is a significant increase - as the other answer states, 30% increase in delta-v requires a threefold increase in fuel. Disposable one-way probes are much more efficient.

Efficient routes are slow

Another problem with crewed trips is that we generally need them to be over quickly, because every extra day en route requires extra supplies and thus weight. Most of the current probe missions are planned to use routes that are efficient fuel-wise (both from orbit perspective, and also including gravity assists) but take a long time to arrive. Taking a more direct route requires more delta-v for the same trip, and again, that can easily incur an order of magnitude increase in the size of rocket required for the same payload.

Moon

• It is clearly within our general technological ability to reach the Moon. It's not that we have technologically regressed since the successful missions in the 1960s; but like with automobiles and bicycles we haven't made much progress either in the core technology in the past 80 years or so. We are still using the same propulsion (chemically driven rocket motors, no nuclear or antimatter drives). We are still using steel, aluminum and titanium (no neutronium, no magic diamond fiber — perhaps a little carbon fiber here or there). Hell, we are literally using 20 year old rocket motors whose first designs were drawn 45 years ago. That's the glacial pace of change in this field.

Most progress was in the computing and manufacturing sector. Better manufacturing means that we can probably, with a little luck and good management, manufacture rockets at lesser expense and in larger numbers, but it is still hard.

Mars

• Because rocket technology has not advanced a lot, it is still only borderline possible to put humans on Mars. A lot can go wrong, and humans don't thrive in low gravity, high radiation environments for extended periods of time.

• In spite of better manufacturing space flight is still crazy expensive. "Because rocket equation" (to put it succinctly) going farther out is exponentially more expensive.

Why haven't we?

First of all, it has not become much easier than 50 years ago. The cold equations are still the same, as is our principle tool, the chemically propelled rocket. It is still hard.

As with all hard but possible things it's a question of money. Nobody has been willing or able to spend the crazy billions. The money could be private or public:

• There seems no profit to be made on the Moon or Mars. No investor except the one multi-billionaire with non-economic goals will shell out the billions to finance a mission.

• Public money can only be allocated when doing so is "politically profitable" for the politicians. Some of the profit can be "pork" (investments in their state or district); but for such a sustained, massive siphoning-off of tax dollars significant public enthusiasm is needed.

In retrospect the intense competition during the Cold War of the 20th century provided a unique window of opportunity (which, hopefully, in this shape never occurs again) in the public opinion.

Of course many of us today, and many enthusiasts back then, also support(ed) space flight for idealistic reasons: Explore the unknown, push the frontier, fulfill dreams. But I'd be surprised (and delighted, of course) if such enthusiasm could be fomented again.

If we ever go to Mars it'll involve beaucoup money from some crazy billionaire.