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The question Would a human colony on Venus be possible? received an answer showing how inhospitable the surface is. But combined with comments to the answer implies that a station in the upper atmosphere might be a bit more practical.

Of course Around the World in Eighty Days by Jules Verne popped into my mind (thought the balloon is from the 1956 film not the book), on looking into it seems feasible in theory, and with Wikipedia giving wind speeds of 300 km/h (190 mph), it seems like you might be able to circumnavigate Venus in 8 days or less.

Saving the challenges of deploying, arriving and departing for another question...

Would a balloon colony/station in the Atmosphere of Venus be possible? If so what elevations would it be at, and in Earth and/or Venus days how fast would it circumnavigate Venus?

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It would be quite easy. As you mentioned, the wind speed is roughly 300 km/hour, in the clouds, where Venus is the most hospitable. The same article mentions that oscillations of the atmosphere happen every 4.8 Earth days. Hot air balloons move at about the same speed as the wind around them. Thus, a hot air balloon should be able to circumnavigate Venus in 8 Earth days, no problem.

There would be some architectural challenges, but the key question is, what is the turbulence like. In fact, there has been a balloon flight which, according to Wikipedia:

Designed to fly in the trans-oceanic jet streams, the Pacific Flyer recorded the fastest ground speed for a manned balloon at 245 mph (394 km/h).

The atmosphere at that level will have a similar pressure to Earth's, but there will be sulfuric acid all around, and the heat would be too hot for traditional hot air balloons. I would recommend using some sort of a helium type balloon, but it could be possible.

This was done once unmanned, by the Russians. Wikipedia quotes the performance as:

In 1985, the Soviet Union took advantage of the opportunity to combine missions to Venus and Comet Halley, which passed through the inner Solar System that year. En route to Halley, on 11 and 15 June 1985, the two spacecraft of the Vega program each dropped a Venera-style probe (of which Vega 1's partially failed) and released a balloon-supported aerobot into the upper atmosphere. The balloons achieved an equilibrium altitude of around 53 km, where pressure and temperature are comparable to those at Earth's surface. They remained operational for around 46 hours, and discovered the Venusian atmosphere was more turbulent than previously believed, and subject to high winds and powerful convection cells.

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In tradition with the mentioned Jules Verne's Around the World in Eighty Days, this would take a fair deal of imagination to achieve, but yes. Let's see what our cheat sheet could look like:

  • The length of one Venusian solar day is equal to 116 Earth solar days and 18 Earth hours, so 8 Venusian days translate to 22,416 Earth hours.
  • Assuming we travel West to East and in the direction of the planet's rotation, which is the direction its atmosphere would move on average so a better choice for a balloon and also the direction Fogg and Passepartout travelled (London - Suez - Bombay - Calcutta - Hong Kong - Yokohama - San Francisco - New York City - London) for the authenticity factor, and we started and ended our circumnavigating journey like our protagonists did at or near the prime meridian, half way along your path you would cross the 180th meridian as the Venusian date line, gaining a whole Venusian calendar day, or 2,802 Earth hours.
  • If you could assume a Sun-Synchronous Orbit in Venusian upper atmosphere, and it should be perfectly possible given Venusian slow rotation period even though impossible for satellites due to the planet being simply too spherical, in theory and as far as you're concerned, not a single day would have passed (though one rotation of Venus around in axis in hours, or 2,802 Earth hours would) before the planet completes its rotation period, rotating a full 360° around its axis.

So I won't even bother plugging in all the numbers, and as you can see, there are many ways to argue that you've indeed circumnavigated Venus in eight or less days. It could take 25,218 Earth hours, and you could argue you've been counting Venusian days and crossed its date line into the previous calendar day in the process, you could simply assume an orbit that would further decrease or even completely stop the rate of the planet's day cycle from your vantage point, or even try tucking against the upper atmospheric winds to effectively stay geostationary relative to its ground and let the planets rotation do that for you in a mere Venusian day with its own rotation on its axis.

I guess what I'm trying to say is, that you're already cheating with the balloon, since it has so many ways to take advantage of the calendar systems that are usually established for the purpose of on the planet's surface living beings. Jules Verne was a visionary that could see that before most would think it's even possible, and described one way to achieve that in a most fabulous adventure novel from 1873 that is still exciting to read even in this day and age with spaceships and maglev trains and whatnot.

So next time you think you're jet lagged, don't complain before you checked your calendar. You might have a whole day to fight it, all for free and courtesy of conventions. ;)

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