Earth re-entry from orbit by a sequence of upper-atmosphere dips to reduce kinetic energy?

Question

There are quite a few questions on this sort of theme here, and I've also read one or two other things, like non-ballistic re-entry. So this might be a duplicate, but I don't think so.

To clarify: I'm not talking about using aerodynamic characteristics of the returning craft, at least not until the atmospheric speed has really been brought down to very low, mach 3 or so maybe.

I'm simply wondering: suppose you do a burn which slows you down from LEO, causing your craft to travel through the mesopause (coldest part of the atmosphere), just slowing you down (and heating you up) a tiny bit... your craft would then carry on beyond the confines of the circular LEO orbit effectively in a more elliptical orbit. At apogee of that orbit you then do a new minor burn to ensure that as you fall to Earth again you are once again on a trajectory through the mesopause, which skims off a bit more kinetic energy, and gives you a bit more heat. This trajectory again sends you off away from Earth to a slightly slower apogee. Your effective orbits would become more and more elliptical. But you'd be losing kinetic energy on each dip.

The idea would of course be to try and cool the craft between each dip. Just off the top of my head you might want to make use of the shadow of the Earth as much as possible (difficult because you are spinning round it, but some timings might be better than others), but also perhaps of the Moon sometimes. Also you might conceivably have a shield, large enough to cover the narrowest profile of the craft, which could be manoeuvred into place between the craft and the Sun, so that it would stop any solar thermal radiation falling on the craft. I read the idea somewhere that cooling takes longer than heating, but on the other hand maybe that depends on the relative time spent between dipping and cooling?

Doing a minor burn at apogee would mean that a small thrust would go a long way because at that point you would be going slowest.

The aim being essentially to kill the "orbiting" and at the end find yourself in a craft which was simply falling, probably from a very great height. But mightn't it be possible to reduce significantly the super-high speeds and temperatures of re-entry from orbit by such an approach? Maybe something like the Space Shuttle could be feasible using this approach, as it was killed off by extreme heat (or an inability to design for it).

NB some of the the heat might be used, fairly obviously, for keeping the inner temperature comfortable.
NB2 you might also scoop up some atmosphere on each dip: oxygen could be used for oxidiser and nitrogen for propellant, perhaps, to contribute something when tweaking your trajectory with the burn at each apogee...

Answer 1

Unpowered re-entry into an atmosphere is about trading orbital energy for heat. If the planet being orbited has radius $R$, then the additional specific energy of an elliptic orbit compared to being stationary at the surface is $$- { \mu \over 2a } + { \mu \over R }$$ where $\mu$ is the standard gravitational parameter, (which you can approximate as $G$, the gravitational constant, * the mass of earth, given that the mass of the orbiter is likely to be negligible in comparison) and $a$ is the semi-major axis of the orbit involved.

To park your spaceship, you need to lose that additional energy. In order for that additional energy to go down, the semi-major axis of your orbit has to go down (as there are no other parameters you can reasonably change!), but you can only squeeze down that $a$ parameter so far before your apogee hits the atmosphere, or the perigee hits the surface, and in either case you will not being staying in space for long.

Your plan is to somehow bleed off a big chunk of that energy and yet remain in an orbit, but the problem is that any trajectory that is still an actual orbit (and not merely a suborbital trajectory) has an enormous amount of energy, and you haven't escaped all of the heating you'll experience when you finally commit to re-entry. You've still got to shift a good 30 megajoules per kilo of your re-entry vehicle.

To clarify: I'm not talking about using aerodynamic characteristics of the returning craft, at least not until the atmospheric speed has really been brought down to very low, mach 3 or so maybe.

You can't remove a significant proportion of the energy of your spacecraft without entering into a sub-orbital trajectory, and once you're in one of those the only way you're getting back out of the atmosphere for any length of time is to engage in a pull-up or skip manoever, and that means you need to make use of of the aerodynamic characteristics of your re-entry vehicle and you'll have to deal with it travelling at high hypersonic speeds because you won't be doing much skipping if you're going any slower.

The Apollo spacecraft could have made a skip re-entry, and here's a nice diagram from a relevant answer by Organic Marble: Did the Apollo Command module really "skip" within, or off of the atmosphere as a part of its reentry program?

Apollo never made a crewed skip re-entry in the end, but it could have done, even without fancy Space Shuttle wings. This was intended to reduce heating loads by extending re-entry times, a little bit like you would like to do in your plan. edit: as pointed out by Steve Pemberton, the skipping probably wasn't intended to reduce heating, and the wikipedia text I (and the author of the linked question) took this claim from didn't cite a source. My bad.

The aim being essentially to kill the "orbiting" and at the end find yourself in a craft which was simply falling, probably from a very great height

There's a tradeoff to be made with the number of skips. With each skip, you can bleed off more lateral velocity, but that means you mostly end up going downwards and free falling from the edge of space will end up with you going pretty fast when you hit the thicker atmosphere below which means big g-forces which are bad for delicate payloads, like people. Apollo considered one skip to be enough, but it might have been unsafe to do more.

A winged re-entry vehicle may help here. The Space Shuttle's mission planners already had to take into account the tendency of the Shuttle to produce lift and potentially skip during re-entry because such a thing made determining the final landing position quite challenging. So, from ~75km altitude, it had to engage in a couple of long banking turns to keep its lift vector from pointing too high up causing a skip (this sometimes gets erroneously reported as S-turns to reduce speed, rather than roll-reversals to prevent skip and flying off course).

Now, you've got a re-entry vehicle, doing skip entries, in a way that the Shuttle and Apollo could have done if anyone wanted it to, but didn't actually have to. So you have to wonder whether your more complicated scheme is actually worth the extra hassle, compared to just making a better thermal protection system.

NB2 you might also scoop up some atmosphere on each dip: oxygen could be used for oxidiser and nitrogen for propellant

This seems somewhat impractical... the amount of energy required to accelerate the scooped gas to up the velocity of your vehicle is going to be punishing, so you'll have a job getting enough oomph back from your engines to make it worthwhile. Maybe some futuristic scramjet would work here, but I suspect even that would be tenuously effective at these high hypersonic speeds. You can do skip-gliding without the need for extra thrust, however.

Answer 2

When Does an Orbit Stop Being an Orbit

Low Earth Orbit is (rough) 7.8 km/s. This is the lowest amount of energy you can have in an orbit of the Earth. If you try to create a lower energy orbit, you will simply return to Earth.

So if you start at 8km/s, and skip off the atmosphere two or three times to end up at 7.7 km/s, then you would need to add energy back into the system (ie, fire a rocket) to stay in any kind of orbit.

This hard lower bound on the energy in orbit makes "skipping" unlikely to be worthwhile.

The difference in heat shielding required to shed 8km/s worth of energy and 7.7 km/s is not worth the added complexity of figuring out how to skip off the atmosphere in a controlled fashion.

Note:

The Apollo skip that @StarfishPrime references does not complete a full orbit; in the linked answer you can see that the time from the skip to landing was less than 10 minutes, which is significantly less than the shortest possible orbit. So you can do a one-shot: burn off some orbital energy, then delay descent for a minute or two too radiate heat, then plunge into atmosphere. But a multi-orbit strategy is a not realistic.

Answer 3

"Earth re-entry from orbit by a sequence of upper-atmosphere dips to reduce kinetic energy?"

A satellite in a long very eccentric elliptical orbit will have a greater energy than one in a low circular orbit. In such a case it is possible to do something similar to what you suggest by dipping into Earth's atmosphere at perigee each pass. This is known as aerobraking https://en.wikipedia.org/wiki/Aerobraking

However there are two catches:

Firstly the lower the degree of heating at each pass the more orbital passes will be required to slow down so for a very high orbit and a very modest amount of heating it could take many months, years even to achieve a circular Low Earth Orbit.

Secondly once LEO is achieved options are limited. Once orbital decay reaches a certain point the satellite will re-enter and there is no going back. With the correct shape of vehicle skipping is possible as others have mentioned but this only gives a modest change to the trajectory and the heating time.

I suspect (but don't know for sure) that theoretically with a large enough surface area a craft probably could make more use of an extended form of skipping, but the aerodynamics and mass that would be required mean that it is not a remotely practical solution.

Answer 4

There is a fundamental limit to skipping for entry from low orbit: The Karman line.

That's the point where the atmosphere is so thin that flight becomes impossible--your stall speed becomes equal to orbital velocity. That is far below the altitude where you can actually stay in orbit, though.

Skipping is only feasible if you're coming in way above orbital velocity--Apollo and a few sample return missions. And when you don't have a delicate payload such as a human you come in steeper anyway--you take less total heat if you slow down faster. And if you do have a human on board you fare better putting an extra pound into the heat shield than an extra pound into consumables for said human to wait out the skip. Hence in the real world we only see very minor skipping.

Answer 5

In outer space, vehicles are vacuum-insulated. The only way to cool down is by radiation.

Assuming that the vehicle is adequately shaded, either by the earth of by a parasol, the energy loss will be proportional to T^4, temperature to the fourth power. At 300K, with a perfect emitter surface, say 40W per square meter

Assuming a kinetic energy of around 30MJ/kg, a 1000kg object at orbital speed will need to blead off 30GJ. If you have a surface area around 300m², radiating at 12KW, you'll need 30G/12K seconds: 4*10⁶ seconds.

46 days

If you come down into the atmosphere, you're going so fast that the atmosphere is like jelly. You warm up a little bit, but most of the energy is expended stirring the jelly around. The jelly gets hot, but you leave it behind as you plunge on and down. You do get a little convective heat flow (that's why you have a heat shield), but it doesn't take a month to blead off the heat, because you've left most of the energy above and behind you.

You can skip in and out of the upper atmosphere, but your skips won't help you cool down unless you stay out there for a while. When you actually want to come down, it's quicker to loose energy in fluid dynamics rather than in radiation.