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I searched the web and found a couple entries on Wikipedia (Skip reentry & Atmospheric entry) that kind brush at the topic. The article on Stone skipping has some science and physics involved (speed, etc) but I don't find any about skipping off the atmosphere.

I recall seriously worded concerns during the Apollo Program of the returning ships skipping off the atmosphere with dire results.

It is fairly easy to image the stone skipping scenario, when the stone brushes across the surface of the water as it moves at an angle. But the atmosphere does not have a "surface" it is more of a continual thinning as you get farther from the planet.

How do you skip off of a boundary that does not have a solid scientific existance?

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First off, a stone does not skip off the surface of the water. It skips off the water. The stone has to bite into the water to use its lift to come back out. A skipping stone can, and sometimes does, go completely under the surface in the process of skipping.

The air is a fluid as well, and a lifting body can in fact skip in the same way as a stone does in water. Air has a very substantial "existence", especially as you move faster.

However lift is not required for "skipping" out of the atmosphere, since unlike the apparent surface of a pond, the atmosphere is curved. All that is really meant in the case of a skip entry is that the entry flight path angle was not steep enough to prevent the object from leaving the atmosphere again. The trajectory of the ballistic skip flight does not curve up like that of a skipping stone. It still curves down. However the radius of curvature is greater than that of the radius of curvature of the atmosphere, so it departs back into space.

We get back to needing a lifting body if you want the skip to have a predictable set of exit conditions. While you can skip ballistically with no lift, the uncertainty in the entry angle gets amplified to large uncertainty on the exit conditions, which is not good if you plan to reenter or insert into an orbit. Lift and/or drag on the entry vehicle is modulated through the atmospheric flight of the skip in order to control the exit conditions. That is what Apollo was qualified to do, in order to control the conditions of the second reentry and allow a safe landing at a predictable site.

Skip entries can also be used to spread out the total heat load of an entry over multiple passes, allowing cooling between passes. The aerobraking approach used by several Mars orbiters is an extreme example of many high-altitude skip entries.

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  • $\begingroup$ The challenge of braking from interplanetary speed (i.e. hyperbolic w.r.t. the target planet) to the orbital speed (albeit with a LARGE apoapsis) for further orbit shaping is quite severe: you have to do it in one go. $\endgroup$
    – Deer Hunter
    Dec 7, 2013 at 21:33
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    $\begingroup$ That's called aerocapture. We have yet to try it, but all of the necessary tools were demonstrated both by Apollo and MSL (Curiosity). In particular they both did guided entry of a low L/D lifting body, which is needed to control the exit conditions for aerocapture. $\endgroup$
    – Mark Adler
    Dec 8, 2013 at 7:24
  • $\begingroup$ What makes the skip exit so unpredictable? Is it atmosphere, are high-alt drag effects too variable? I'm thinking of 'skips' more in terms of aerobraking or aerocapture, useful for slowing a craft on hyperbolic trajectory down from exit velocity into an elliptical orbit. From there small amounts of thrust could be used at Apoapsis to fine-tune next reentry pass (if reentry is desired). Or, do you mean if reentry is planned on the first pass and craft still has too much velocity that it exits atmo, is what makes it unpredictable? I think this is what you mean, Wikipedia pic is confusing me $\endgroup$
    – IT Bear
    Feb 20, 2015 at 19:11
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    $\begingroup$ It is mostly uncertainty in the atmosphere density along the path. Uncertainty in the drag of the vehicle is also a contributor, though a small one. $\endgroup$
    – Mark Adler
    Feb 20, 2015 at 20:42
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    $\begingroup$ @ITBear - the exit conditions can be difficult to control during a skip entry or aerocapture maneuver because as the vehicle is climbing back out of the atmosphere, its control authority (proportional to dynamic pressure) decreases to zero. This means that the ability of the vehicle to correct errors in its predicted exit conditions diminishes to zero by the time the vehicle actually achieves them. To make sure the vehicle is on the correct trajectory, it has to try to predict its future trajectory, and those predictions contain assumptions (atmospheric density, etc) which may be wrong. $\endgroup$
    – zigzag
    Nov 5, 2017 at 20:20
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Skipping is actually a bad word choice, since it would indicate that the skip would be a change in your trajectory and the reentry would be your "non-interrupted" trajectory.

Gravity can be considered a conservative force (for non-relativistic speeds) so your energy would be conserved while in orbit. This means that once in orbit, you will stay in orbit (assuming only one gravity well will dominate in exerting a force on you).

However once you get into the atmosphere you will experience drag, which is a non-conservative force, so your orbital energy will decrease. But if your energy is not decreased enough, you can leave the atmosphere again. This is what they call a skip. This can be due to a not deep enough trajectory into the atmosphere, since the density and therefore the drag decreases approximately exponentially with height.

But if reentry is too deep you will experience too much drag, which will cause a lot of heat from shock layer gas, and you might burn up.

So if you have a too-high orbital energy, you might have to do a skip reentry, since otherwise you will burn up. But if you come in from an hyperbolic trajectory you do want to decrease your orbital energy enough such that you will get at least in an orbit around the celestial body. Otherwise I think you will have to get captured with the help or rockets (or plan another intercept trajectory).

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One can see this for one's self playing Kerbal Space Program. They don't talk about angle of attack so much in KSP, but they do talk about the perigee of re-entry.

If you have a perigee of re-entry at, say, 40km in game, you will enter the atmosphere (At about 70km), start to slow down, and in the end, you will leave the atmosphere, going slower than you were to begin with, but will continue to do another orbit.

If your perigee is something like 30km, then you will most likely enter the atmosphere at a reasonable speed, keeping your spacecraft together and overall working quite well.

If you enter at a lower perigee, then you run the risk of hitting the air too fast, which could potentially damage your spacecraft. Note that KSP spacecraft are generally speaking more resistant to re-entry than corresponding real spacecraft, but the principal still exists.

The bottom line is, for real spacecraft, you want to enter the atmosphere in such a way that you will stay in the high atmosphere for a while, and slow down your spacecraft more gradually. If you try and do this too conservatively, however, you will end up continuing in orbit, having not slowed down enough.

This shows a KSP too fast reentry. I can't find a good too slow one, but take a look a this mission to Eve, the Venus equivalent KSP planet.

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    $\begingroup$ Kerbal Space Program? Seriously? $\endgroup$
    – Philipp
    May 5, 2015 at 20:24
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    $\begingroup$ You'd be surprised, the physics is pretty good $\endgroup$
    – PearsonArtPhoto ♦
    May 6, 2015 at 2:58
  • $\begingroup$ Maybe if you install FAR... I've skipped off the atmosphere many times playing Realism Overhaul, but that implies you aren't using the bizarre stock aerodynamic model. $\endgroup$
    – Anton Hengst
    May 17, 2020 at 22:15

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