Please explain the physics of a spacecraft launching from the Moon or from Mars

Thanks Babale, that’s a good explanation even I as a layman could follow.

This explanation was brought to you by Kerbal Space Program.

Kerbal Space Program: it’s not rocket science! Well, technically it is, but it’s not that complicated. Except for docking. That’s a trip.

Beat me, I was just about to suggest playing around with Kerbal Space Program to get a handle on it. Seriously, they should use it to teach orbital physics in school.

Escape velocity for Mars is 11,250 mph (5.03 km/s), as opposed to 25,000 mph (11.19 km/s) for Earth. Atmospheric pressure is 0.088 psi, so less than 1% of Earth. The surface pressure is about the same as 22 miles up on Earth. Not sure of drag numbers, as I’m tired and it’s a little out of my wheelhouse.

Aerodynamic drag is proportional to atmospheric density. At Earth’s surface, this is typically around 1.23 kg per cubic meter; for Mars, 0.02. So a factor of approximately 60:1.

How is this calculated so as not to require infinite fuel? I know it doesn’t need infinite fuel but your recursive framing up there broke my tiny brain.

There is a freeware game the point of which is entirely to simulate space missions involving real or fictional spacecraft. I do not know how physically accurate its atmospheric flight model is, but you can definitely experience launching from Earth versus the Moon or Mars…

You don’t need “infinite fuel”, but the change in velocity will be proportional to something like the logarithm of the total mass.

It’s an infinite series that converges on a finite value. A space-age version of Zeno’s paradox.

In a way, you could say it DOES require infinite fuel – under our current understanding, there is no practical way to build a single stage rocket that can carry any any significant payload into orbit using current chemical rockets, because the rocket equation means we get more and more diminishing returns for larger and larger amounts of fuel. It is easy to imagine humanity evolving on a planet with slightly higher gravity and a slightly thicker atmosphere and never achieving orbit with chemical rockets. The same way that we will never build an ion engine that can reach orbit.

You can get around this to an extent by staging. By dropping spent pieces of your rocket – fuel tanks, engines that have used all their fuel – you can greatly reduce the weight that the next stage has to lug up, saving incredible dV. It’s the only reason we can make it into space.

knew it.

Also called gravity drag. For large rockets, most of the ~2 km/s difference that you note is because of gravity drag. The Saturn V only had ~40 m/s aero losses! Because it was such a tall rocket, it had a relatively small cross-section relative to its mass. Smaller rockets have higher drag values but I think most are in the couple hundred m/s range.

There’s a tradeoff between gravity and aero drag in that if you move through the atmosphere slowly, atmo drag is lowered, but you spend more time fighting gravity. There are some additional constraints as well, such as “max Q” (maximum aerodynamic pressure), which could exceed the structural limits of a craft if they didn’t throttle down the engines.

The Moon has a couple of other advantages compared to Earth. In addition to what you mentioned, the low gravity means the engines can have a high thrust-to-weight ratio. And that means less gravity drag, even beyond the proportional difference, because you can accelerate to orbital speed more quickly and again spend less time fighting gravity. The Lunar Ascent stage for Apollo had a TWR of over 2:1, whereas typical Earth rockets are typically <1.5:1.

The vacuum conditions also make rocket engines more efficient. Rocket engines get their thrust through the expansion of gas, and the more you can expand it the more impulse you can extract. Expansion to a vacuum is better than expansion to 1 atm. This doesn’t affect the deltaV requirement but it does mean you get more oomph from the engines. One of the biggest difficulties with single-stage-to-orbit rockets is the inefficiency of engines at sea level and the difficulties in building ones that work well all the way from sea level to vacuum.

The fuel you need is given by the Tsiolkovsky Rocket Equation. For our purposes, we can re-arrange it to m_total = m_payload*exp(V/v_exhaust) . A Saturn V has an exhaust velocity of 2.76 km/s; let’s take that as typical for rockets in general. The escape speed of the Earth is 11.2 km/s. That means that, even if we don’t have to worry about the atmosphere or gravity drag or other inefficiencies, we need a total mass (payload plus fuel) of 57.8 times the mass of the payload.

For Luna, meanwhile, escape speed is 2.38 km/s. That means that we only need a total mass of 2.37 times the payload mass, or 1.37 times as much fuel as payload. That’s not nearly so bad.

Mars is in between: With an escape speed of 5.03 km/s, we need a total mass of 6.19 times our payload, or fuel 5.19 times our payload.

Now, a factor of 6 for Mars doesn’t seem like so much, especially compared with a factor of nearly 60 for Earth. But remember, one rocket’s total mass is another’s payload. If we wanted to send something to Mars and bring it back, all with just what we can bring along ourselves, that means that the Mars return vehicle, including all of its fuel, would have to be part of our initial payload. So we take our payload (say, a couple of humans and what they need for life support), multiply that by 6.19 to get what we need to have delivered to the surface in the Mars lander, and then multiply that by 57.8 to get what we need to launch from Earth. Suddenly, what was already a large enough number to be a serious problem, is now a HUGE number.

This is why all plans for returning something from Mars involve making fuel for the return on the surface. Instead of landing full fuel tanks on the surface, you land some sort of small (and therefore slow) energy source like solar panels or an RTG, and use that energy source to turn local water (you’d better find a spot with local water) into hydrogen and oxygen. Because this process is slow, you’re going to launch the fuel-maker a long time before you launch the humans, and probably wait to launch the humans until you’re certain that the fuel-maker has finished its job successfully.

Returning anything massive, you mean. It’s possible to return small amounts of material without anything too crazy.

One of the Red Dragon variants (a proposal to use a SpaceX Dragon capsule to land on Mars) proposed to pack a small rocket in the vehicle, like an ICBM silo. This would have been feasible–a small rocket like that is far easier on Mars than on Earth due to the aforementioned exponential nature of the rocket equation. I’m not sure how much material they planned on returning but something on the order of 1 kg would probably have been possible.

Once you start trying to return people, ISRU (In-situ Resource Utilization–the local fuel production process you mentioned) makes a lot more sense. Though even then, it could make more sense initially to leave a large transfer craft in Mars orbit, and use small pre-fuelled ascent vehicles to carry the people up.

True; I oversimplified by using Mars’ escape speed. You’ll need to get escape speed eventually to get back to Earth, but you don’t need all of that fuel on the surface: From the surface, you only need enough to get to orbit, where you can rendezvous with your interplanetary vehicle.

And yeah, you could feasibly return a kilogram or two from Mars with fuel you brought with you, but there’d be little reason to: You can do more science in an Earthly lab than you can do on a probe on Mars, but you don’t get much science from just a couple of kilograms of samples.

Well, NASA seems to disagree. The Perseverance rover already has the facilities for collecting core samples for a sample return mission (up to 31 cores, 1 cm diam by 6 cm len, which is ~500 g).

Of note though is that they don’t seem to have an actual design for a return system. The napkin plan is to have a rover collect the samples, return them to an ascent vehicle, which reaches Mars orbit and releases the sample capsule, and then another orbiting craft picks up the capsule and returns to Earth. As best I can tell this complicated system is to reduce the chance of Earth contamination. It seems like an extremely dubious goal though. There’s no reason to believe that anything from Mars could disrupt Earth’s ecosystem. And if there were, we shouldn’t be looking at any sample return no matter how well protected.

A direct return sounds far more sensible to me. The return vehicle would have to be a tad larger but it would reduce the number of failure points.

And some reason to believe the question has been tested - in the form of numerous Mars-origin meteorites.

I almost brought that up, but thought someone would dismiss it due to the hot ejection/reentry or the long time between the two events, and didn’t feel like arguing the point. Still–it’s absolutely true that there’s a ton of Martian rock already on Earth due to something hitting Mars, ejecting some material, and it finding its way to Earth. So contamination has already happened to a huge extent, and so anyone worried about sample return has to argue that there’s something special about a purposeful mission. Which there probably isn’t. Some kind of hardy life that manages to stick to the outside of a spacecraft and survive reentry can probably survive living a few millimeters down in a rock for hundreds or thousands of years.

Chronos already knows this but it’s worth elaborating on a certain point here. Running the rocket equation on just the payload is usually not the way things are done. It does give you a correct upper bound assuming that the mass of the vehicle is zero. But of course rockets are not zero mass.

The very best rockets have a mass ratio of about 30:1–that is, they can carry 30 units of fuel for every unit of empty weight. Which means the ~60:1 ratio Chronos mentioned leaves no room for payload; in fact such a vehicle couldn’t make orbit at all.

It’s for this reason that all rockets use staging. Babale mentioned the basic idea: it’s dropping off pieces of your rocket that you no longer need (tanks, engines). The net effect is to get a bit closer to the ideal of zero vehicle mass.

Smaller ratios like 6:1 are achievable, as per above. The actual requirement depends on the propellant you use (hydrogen being the best, with a long way down to the worst). But it does mean that a single-stage rocket on the Moon or Mars is viable, even easy.

Another point to mention is that examination of the rocket equation will reveal that exhaust velocity is very important. Get the exhaust velocity up close to the velocity you’re trying to reach (in this case, escape speed), and your mass ratio shrinks to a much more manageable number. And in fact there are some kinds of rockets with much higher exhaust velocities, which are in fact much more efficient.

The problem is that there’s often a tradeoff between exhaust velocity and thrust. An ion engine, for instance, can have a thrust of mere millinewtons or micronewtons. And that makes that “gravity drag” mentioned above a huge problem: You can’t even take off from the surface of a planet at all, unless your thrust is greater than your weight, and you want it to be many times your weight in order to minimize that gravity drag.

Once you’re in orbit, though (and also incidentally free from the atmosphere), ion engines work great.