Are there any studies on the ideal form for a spacecraft at large velocity in vacuum?

Question

Spacecraft meant to operate in both, an atmosphere & space, are typically

• Stream-lined (as in the case of the Space Shuttle, and Buran), or
• Spherical (Vostok comes to mind).

In contrast spacecraft meant to work in a vacuum may dispense with the niceties of aerodynamics. Wikipedia displays the Apollo Lunar Module in all it's functional glory.

The Voyager craft are designed to work in a vacuum, and have the appropriate shape for it.

• Are there any studies on the ideal form for a spacecraft at large velocity in vacuum?
• Would velocity be relevant to the shape?
• What velocity must technology achieve for the shape of the craft to be relevant?

Alternately the last may be rephrased to read -

Assuming the technology to achieve it becomes available (whenever that happens (+:) What kind of shape might contribute most to the craft approaching even a minimal 0.1c?

Answer 1

The optimal form is the same as in atmosphere: long and slender, and pointed at the end, for the acceleration phase, and wide, flat and perpendicular to the path for the decelleration phase.

This is because space is not a true absolute vacuum, but has at least a few atoms per cubic meter. This induces a small, but measurable, drag. The closer one is to a body, the thicker the "interplanetary medium"; the closer to a star system, the thicker the interstellar medium.

Densities¹

• Atmosphere at 1 Bar is roughly 3e19 molecules per cc.² Slightly more than double that to get density in atoms, and note that free subatomic particles are rare. further, in terms of mass, these roughy 6.1e19 atmos per cc are heavier, nearly 10 times more mass per atom on average.⁴
• The interplanetary medium is estimated to be about 5 particles per cc, but can hit peaks of 100 particles per cc.³ Those particles are mostly atomic nuclei, but some are subatomic particles. Note that Protium (¹H) is both an atomic nucleus and also a free proton, and Deuterium (²H) is a proton neutron pair; Hydrogen is the bulk (75%) of the IPM, mixed between Protium, and Deuterium nuclei, in various ionization states.
• The interstellar medium is about 1 atom per cc², again mostly hydrogen

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¹: cc = cubic centimeter
²: http://www-ssg.sr.unh.edu/ism/what1.html
³: http://nineplanets.org/medium.html
⁴: Air atomic mass per atom (0.78 * 14)+ (0.21 * 16) = 14.3 is a good approximation
ISM atomic mass per particle (0.75 * 1) + (0.25 * 4) = 1.5 is a workable approximation, and accounts for some heavier atoms scattered about.