# Under what practical conditions would Earth's atmosphere be a dilatant?

I have read and heard in many places that when the astronauts of Apollo were coming back to Earth, they had to determine the best angle of attack to re-enter the atmosphere. This is usually indicated with an angular window.

I understand that if they approached the atmosphere head-on, their ship would have probably overheat due to the friction and burn up in the atmosphere. I am also aware of a "skip re-entry" method where the pilot actively controls the ship during re-entry to bleed off momentum, exit the atmosphere, and then begin the final entry.

My question is regarding the "skipping" effect that this site mentions:

Like a fast stone skimming across a pond, Apollo spacecraft would have simply bounced off the earths surface if the angle of attack was too shallow.

My (minimal) understanding of fluidics intuits me to believe that given the sparse density, the exosphere would not act as a non-newtonian fluid, that the friction would not "bounce" the craft. Keep in mind, I'm asking specifically about the unpowered, uncontrolled ships in relation to atmospheric effects, not angular momentum effects like (powered and controlled) Hohhman Transfers, gravity assists, or planned skip-re-entries. Essentially my question is this:

Is there a known effect wherein given a specific angle and velocity for a ship the size of the Apollo capsule, in unpowered, and uncontrolled flight, that Earth's atmosphere would become a dilatant to the point that the capsule would be deflected, overcoming the effects of gravity and friction, ejecting the craft back into orbit?

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## migrated from skeptics.stackexchange.comApr 5 '13 at 16:13

This question came from our site for scientific skepticism.

Moving this to the appropriate site, Physics – Sklivvz Apr 5 '13 at 16:12

## 1 Answer

No, the "skipping" effect does not work like this. It is not like a stone skipping on water.

The problem is that before re-entry the capsule is travelling at a high velocity relative to the Earth and this means it is in a highly elliptical orbit. Actually it's in something approximating a Hohmann transfer orbit. If you did nothing to change this velocity the casule would just orbit the Earth forever and the astronauts would all die of asphyxiation, starvation or old age - whichever came first.

If the capsule carried lots of fuel it could simply fire it's rockets to slow itself, but by the time the capsule returned from the Moon it had nothing like enough fuel left to do this. So the capsule is slowed by allowing it to hit the atmosphere so the drag from the atmosphere can slow it.

The problem is that the density of the Earth's atmosphere varies with altitude. Have a look at this image that I cribbed from this site:

If the angle is too shallow you hit a part of the atmosphere that is too thin to slow you enough. You don't bounce in any sense. It's just that you're orbit isn't changed enough and you just carry on orbitting the Earth. This isn't necessarily a problem, because as you go round the orbit you'll come back to the same place and have another go. The trouble is that the Apollo capsule didn't have enough air to keep the astronauts alive for a second go. If they missed the corridor they would have suffocated before they completed the orbit and approached the Earth again. That's why they had to get it right first time.

If the angle is too steep you also don't get a second chance, but for rather different reasons :-)

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