|Io with a volcano on the left side of the picture.|
Io (pronounced eye-oh) is the inner-most Galilean moon, that is, one of the four moons discovered by Galileo in 1610. Due to its proximity with Jupiter, tidal forces keep the moon's core molten and there are numerous volcanoes on the moon spewing molten sulfur. Some of the volcanoes shoot the sulfur 200 miles above the surface.
So I decided I wanted to say in my WIP how fast that sulfur was moving. This is an easy calculations and according to my college physics book (yes, I still have it), the formula is:
Where v0 is the initial velocity as it leaves the surface, h = the height it reaches, and g is the acceleration of gravity. In computerese we write that: v0=sqrt(2hg)
For example, if you throw a ball straight up (ignoring air resistance) and it went up 5 meters (about 17 feet) you would have to throw it with an initial velocity of 10 meters per second (about 22 mph). That's because the acceleration of gravity on Earth's surface is about 9.8 meters per second per second so plugging those number is v0=sqrt(2*5*9.8) = 9.9 meters per second.
So let's do this math for the molten sulfur on Io. Again, ignoring air resistance (because there is no air). In this calculation h = 200 miles = 322,000 meters and the acceleration of gravity at Io's surface is (at the equator) is 1.796 meters per second per second. Now, everything is in the units of meters and seconds (don't try to multiply miles by meters, it doesn't work) so you plug those numbers in and v0=sqrt(2*322,000*1.796) = 1,075 meters per second. Which is 2,405 mph. Wow! That just doesn't seem possible. The speed of sound is 767 mph. So that molten sulfur is going three times the speed of sound or Mach 3. (Yes, I know there's no air on Io and thus on sound.)
Anyone out there see a math error, let me know!