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I've been to Kennedy Space Center in Florida, where I saw the huge Saturn V rocket...

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This was used to get to people to the moon. It had a Lunar Module to propel itself on and off the moon's surface once the rest of the rocket had been ejected and dropped to Earth.

So as far as the moon goes, the Saturn V was an ideal machine because the Moon has a relatively small acceleration due to gravity on its surface. $g = 1.624 m/s^2$, so the Lunar Module doesn't have to be too big or powerful.

But how can NASA apply the same technology to getting people to Mars? Not only is Mars a lot farther, needing more fuel, and an even bigger rocket, but Mars also a higher acceleration due to gravity amounting to $g = 3.741 m/s^2$. This would not only need a huge rocket, but also a pretty big (and I dare say unfeasible) Martian Module. So, even if we could make the journey to Mars, how would we get back to Earth?

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    $\begingroup$ "Not only is Mars a lot farther, needing more fuel". Uhm. No? Just that it is farther away does not mean more fuel. It means either more fuel/speed or more travel time. $\endgroup$ – Hennes Oct 4 '13 at 22:38
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    $\begingroup$ True, I guess the same amount of fuel to get to the Moon would suffice though you would need more fuel to get there faster. $\endgroup$ – shortstheory Oct 5 '13 at 4:04
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    $\begingroup$ delta v to leave earth - moon system (to travel to mars) is higher than for earth to moon, so more fuel to mars. $\endgroup$ – mart Oct 23 '13 at 9:30
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    $\begingroup$ ...significantly more. Earth escape velocity is 11.2km/s while Moon's orbital velocity is just above 1km/s. Luckily, we can use Moon for gravitational slingshot, meaning you don't need ten times as much fuel. $\endgroup$ – SF. Oct 23 '14 at 8:39
  • $\begingroup$ @SF.: In theory, you can get anywhere in the Solar system, or even outside of it, if you have enough fuel to get you to the Moon, by using one or more gravity assists off the Moon to enter solar orbit and then raising and/or lowering your orbit using one or more gravity assists off Earth, possibly followed (depending on the destination) by gravity assist(s) off one or more of the other planets. $\endgroup$ – Sean Oct 27 '18 at 20:15
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If the US Government ever gets back in gear, you can read NASA's Design Reference Architecture 5.0 (DRA 5) for human missions to Mars. (I have a copy, but I don't see a way to upload it here.) Here is a summary.

The basic idea is to use several Saturn V's or equivalent, and put up pieces of the mission. Some parts are assembled in Earth orbit, some meet up on the surface of Mars or in Mars orbit. The document shows variations that require seven to twelve Ares V launch vehicles, where each Ares V is about equal to 1.5 Saturn V's. In the chemical propulsion variant, about 2/3 of the launches are rocket stages with propellant.

As for how to make getting back appear somewhat feasible, a few tricks are applied. First, Mars orbit rendezvous is used, just as we used Lunar orbit rendezvous for Apollo. Then the humans only need a rocket on Mars big enough to get them into Mars orbit, and a capsule that they only need to survive in for hours or days. Their return vehicle in orbit around Mars, with the propellant to leave Mars and the supplies to survive the trip, didn't have to land, vastly reducing the mass required. Second, the rocket on Mars is mostly fueled there using carbon and oxygen extracted from the CO2 atmosphere. (They bring hydrogen to make methane with.) Third, the orbiting return vehicle got into orbit around Mars by using aerocapture, replacing a lot of propellant with an aeroshell, saving some mass.

Though I would ask: why do we need to provide a way to get back? The ability to get back is something like 2/3 of the mission cost. It would be far cheaper to send them on a one-way trip, and follow that with much smaller and inexpensive resupply missions to keep them alive and productive indefinitely. There would be no shortage of highly-qualified volunteers.

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    $\begingroup$ Unfortunatly as the US government has gone down, so has the link above? Is there anything else on this? The though of people round trippng Mars still fills me with wonder and excitement. I found Cassini Huygens pictures I hadn't seen before and they genuinely brought tears to my eyes. There is so much 'magic' out there it just blows me away, and greatly saddens me that money, funding and all this is taking away from some absolute marvels of our universe. You are an absolute hero to me, and I admore and the work you have done, it has brought tears of amazement and joy many times! $\endgroup$ – RossC Oct 4 '13 at 15:15
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    $\begingroup$ @RossC: Click on the second link in the first paragraph to see a paper written as a summary of that document. $\endgroup$ – Mark Adler Oct 4 '13 at 16:10
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    $\begingroup$ Wow, that's a neat idea from NASA. Thanks for the answer! $\endgroup$ – shortstheory Oct 5 '13 at 4:47
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    $\begingroup$ @MarkAdler To follow up that last paragraph, supply missions could send along tools to aid the building of rockets on Mars. Meaning that you don't have to send a rocket along with the first misison. $\endgroup$ – called2voyage Oct 21 '13 at 14:10
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    $\begingroup$ Yes. Also having people on Mars without a ride back might help a little with getting funding for the ride back. $\endgroup$ – Mark Adler Oct 21 '13 at 17:36
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Instead of NASA approach, which without a change in funding isn't going to happen within any foreseeable perspective, let me look at the SpaceX approach.

Combining ISRU (In-situ resource utilization, essentially off-Earth production of fuel) technologies and airbraking one can make huge savings in fuel.

Let me describe the missions in a similar way as one goes with Kerbal Space Program, starting from the end and adding more stages, more boosters, heavier rockets as one gets towards the launch.

Apollo was all-in-one:

  1. Earth reentry and landing: airbraking; a robust capsule with a heavy heatshield, no fuel.
  2. Earth return from lunar orbit: ~1km/s with the above, plus an engine and a tank for that. (also, propelling the ascent vehicle, point 3., even though it was unnecessary)
  3. Lunar ascent - Lunar Ascent Module. A small lightweight, paper-thin-walled 2-person craft with ~1km/s of delta-V, enough RCS fuel and capability to meet the capsule in lunar orbit.
  4. Lunar descent and landing - a Lunar descent stage of ~1km/s carrying the above with all its fuel to a soft surface touchdown. Also landing legs and a bunch of equipment not needed on ascent.
  5. Lunar insertion - Propelling everything so far by about 1km/s into low Moon orbit, using the tank and engine from (2.)
  6. Lunar transfer - propelling same as above from LEO, again same engine. About 4km/s. This was done by last stage of the launcher, with the above payload in a massive fairing ("stage IV/B").
    1. and 9. Finishing orbital ascent with same as 6 + acceleration to near orbital speed with stage II (alongside with a launch escape system) and lifting it all up and giving initial kick with stage 1. For nearly 10km/s total.

Every time you reach next point multiply the mass so far, including fuel so far, by delta-V needed and you're getting the scale, size and mass of the next (actually previous) stage. As you can see this grows into the enormous Saturn V with a tiny capsule in the end. Nothing reused. All the fuel including last return burn carried and propelled all the way. Lots and lots of fully disposable stages.

Now let's try the same for BFR mission to Mars and back.

  1. Earth landing. Powered, using small pressure tanks with cryofuels carried in BFS inside its large tanks. Only several hundred m/s. although the vehicle is large, and includes heavy heat shielding.
  2. Earth reentry. Using airbraking, so free (using heat shielding on one side of the rocket)
  3. Earth capture. Airbraking, free, same as above.
  4. Mars orbit departure and Mars-Earth transfer. About 2.5km/s out of the BFS main tanks.
  5. Mars orbital refueling. A launch of 1-2 BFSs from the surface to bring fuel to the return vehicle, followed by their return to Mars surface. While free for the return vehicle, double or triple the cost of everything from now on; you need to get them to Mars!
  6. Mars ascent. Main tanks, using fuel made from Mars in-situ resources. About 4km/s but essentially free other than initial cost of the equipment. Before that step, the tanks in all the vehicles can be empty, the only mass so far brought to the surface is 3 or so BFSs, not a drop of Earth-made fuel.
  7. Mars landing - powered, small pressurized tanks, several hundred m/s.
  8. Mars reentry - free, aerobraking.
  9. Mars capture - free, aerobraking.
  10. Earth-Mars transfer - about 4.5km/s out of BFS main tanks. (x3 rockets)
  11. Earth orbit refueling. Now the numbers really grow, because we need about 6 BFR launches to bring all the fuel for point 10. And they can't be too far apart in time, due to boil-off, so you need a fleet of at least 9 of these (3 to Mars, 6 for fueling them up). Maybe slightly less (you may relaunch the first ones by the time the 4th or so finishes fueling up the ones in orbit.) So, this step is not adding anything, just multiplying the subsequent steps by 7.
  12. and 13 About 9-10km/s - Earth ascent and orbital insertion, either with payload for travel (food, life support, science, crew) or just payload of fuel, split between the BFS and the BFR booster (reusable).

And that's it. One Mars landing means about 9 BFRs, each of which is about the size of Saturn V, and likely costs similarly. The difference being that everything either is recovered, or remains at the destination as permanent infrastructure for further reuse. After building these 9 BFRs, if nothing crashes, you can send as many missions to Mars as you like and they will cost about 18 tanks of methane and oxygen worth each, in exhaustible resources. Meanwhile, all that's left from Apollo is some museum pieces and you're not going to reuse them.

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