What's the record for the fastest orbit around Earth? [closed]

I am just curious what record is fastest orbit around the Earth. Although I suppose there are three different metrics one could use to measure what does one mean by fast so here are the three I thought of.

1. Shortest Orbital Period
2. Fastest Ground Speed
3. Fastest Orbital Velocity

If someone could give me a quick answer to any or all three of those categories that would be great. Would also be awesome to see the fastest orbit for manned and unmanned spacecraft (separately). If anyone could point me to the information that would be awesome!

• Minimum of how many orbits achieved would you accept? Fast orbits are low ($v_o \approx \sqrt{\frac{GM}{r}}$), and low orbits decay fast due to atmospheric drag. There are however some highly eccentric orbits in use with extremely low perigee, e.g. Molniya orbits. May 14 '14 at 1:40
• Sqrt(GM/r) is velocity of a circular orbit. For an elliptical orbit v is sqrt(Gm(2/r-1/a). Astronauts returning from the moon were moving just under escape when they reached the earth, a little under 11 km/s. May 14 '14 at 1:52
• @HopDavid Yes, I realize that, that's why I asked for clarification what minimum number of orbits would be acceptable. Apollo "free-return" trajectories were technically not orbits around the Earth. May 14 '14 at 1:54
• "around the earth" needs to be better defined. If earth's focus lies at an orbit's center, I would call it an orbit about the earth. This would include parabolic and hyperbolic orbits. After Apollo was well clear of the moon's sphere of influence, it's orbit could be closely modeled as an ellipse with a focus lieing at earth's center. May 14 '14 at 2:02
• Lowest orbit was GOCE, the European gravity probe with the fins and the ion drive keeping it aloft. I think that's the simple answer to this question. May 15 '14 at 5:40