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If all the water on Earth’s surface and in the air were put into a ball, how large would the sphere be? Could it exist in space by itself? (continued)
Derek Bolton
Sydney, Australia
The response from Garry Trethewey concludes that a 700 km-radius ball of ice in space would evaporate away. He appears to have assumed the context of Earth’s orbit, but the original question doesn’t mention any nearby star. Iceball comets can last for billions of years, only losing mass on approaching the sun. So the question becomes, at what radius from the sun could such an iceball survive?
There may also be some confusion between evaporation and boiling. Respondents mention air pressure, but that is relevant only to boiling. For evaporation, what matters is saturation vapour pressure (SVP).
Regardless of any other chemical species present, there needs to be enough water in the ball to produce a partial pressure (the component of atmospheric pressure that is due only to its water molecules) that exceeds the SVP at the ambient temperature. At 33 Kelvin on Enceladus, the SVP is a mere 0.00001 pascals.
At our iceball’s radius, that only requires an atmosphere of 10,000 tonnes of water, a tiny fraction of what is available. And that atmosphere can remain because at this temperature, the typical velocity of a water molecule in the atmosphere is around 200 metres per second, while escape velocity from the iceball is 520 m/s.
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