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Often people will use "aerobraking" in the context of landing a space ship or probe on a planet with atmosphere. This appears to be a casual and technically incorrect usage, for example from https://en.wiktionary.org/wiki/Appendix:Glossary_of_atmospheric_reentry:

aerobraking

when the free molecular gas of a planet's upper atmosphere is used to reshape the orbit of a spacecraft. Heating due to aerobraking is normally insignificant thus requiring no special thermal protection. The term aerobraking is often used incorrectly by people outside the aerospace industry.

And also of relevance:

aerocapture

when the continuum gas of a planet's atmosphere is used to dissipate the kinetic energy of a spacecraft entering from a heliocentric hyperbolic trajectory and which then skips out of the atmosphere into an elliptical orbit centered around the capturing planet.

I haven't found any contradiction to aerobraking referring specifically to gentle orbital reshaping. But what then is the correct way to refer to using a planet's atmosphere as a brake during entry and descent?

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I can't say that the terminology is consistent across all users, but where I work (at JPL) we use aerobraking to refer to many light dips to lower an orbit, aerocapture to refer to a single deep dip to bring a hyperbolic approach to an elliptical orbit, aeroentry or simply entry to refer to an entry into an atmosphere with no exit, and aeroassist as a general term for the use of an atmosphere to effect a change in trajectory. Aerocapture has also been used to describe going from high-elliptical to nearly circular in a single pass, e.g. a lunar return to LEO. There are other kinds of aeroassists, such as a hyperbolic to hyperbolic aerogravity assist (usually making use of a lifting body flying upside down). There is also skip entry, which is a hyperbolic or high-elliptical (a la lunar return) approach with an entry and an exit, followed by a final entry. Both Apollo and Shuttle were qualified for skip entry, in order to increase cross range, but neither used it.

Entry is sometimes called reentry, humorously even when that is incorrect, such as for a vehicle entering at a planet it hasn't been to before. (I suppose a Mars ascent could appropriately be called a re-exit.)

I have seen aerobraking used elsewhere as the generic term, instead of aeroassist. I would not call that use incorrect.

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