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How deep have spacecrafts gone into an atmosphere for doing aerobraking for orbital insertion (or as tech demos)? I suppose it is the braking force of the atmosphere that counts, is that closely correlated with atmospheric density or pressure and does elemental composition matter much?

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No spacecraft has yet used aerobraking for orbital insertion. That's called aerocapture. Aerobraking has been used by orbiters only after a propulsive orbital insertion.

What matters for the drag of aerobraking passes is the atmospheric density profile during the pass, the velocity relative to the atmosphere during the pass, and the presented cross-sectional area of the vehicle during the pass. Corrosion of the vehicle could possibly depend on the composition, e.g. the atomic oxygen found in low-Earth orbit. But it doesn't matter for the drag.

Typical densities are around ${10}^{-8}\,\mathrm{kg/m^3}$. A desired dynamic pressure, $q={1\over 2}\rho v^2$ is targeted, with the periapsis raised and lowered as needed to get to that $q$, where too low of a $q$ makes the process take too long, and too high of a $q$ can damage the spacecraft due to forces from the drag.

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  • $\begingroup$ The pressure at the surface of Pluto is 10^-5 that of Earth at sea level (find no good source for its density, but 4x10^-4 that of Earth's is mentioned). Does this mean that aerobraking like those done at the inner planets, would be possible in Pluto's exosphere? $\endgroup$ – LocalFluff Oct 16 '16 at 21:00
  • $\begingroup$ Yes. The density at the surface is about $7\times 10^{-5}\,\mathrm{kg/m^3}$. Assuming it stays that way. Pluto's atmosphere varies quite a bit over time. It was once thought it could freeze out completely. $\endgroup$ – Mark Adler Oct 16 '16 at 21:21

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