Escape Velocity

If we want off of any massive body, we need energy. Force (given a mass) is all about acceleration - so energy is about the net shift in velocity, which shift the nerds call "Delta V". So we need how much V a rocket must Delta. We need to do maths again.

This time, I'm figuring how to get off Venus' flotilla into space. Let's try for direct escape-velocity from 70 km up. I found an equation for escape velocity, and tested it for Earth's in Visual Studio.NET:

?Math.Sqrt(6.673 * 2 * 5.972 * Math.Pow(10,-11) * Math.Pow(10,24) * Math.Pow(10,-3) / 6371)

This got approximately what I wanted. Actually closer to 11185 ms^-1 than the 11184 I found here but we should all agree that 11185 be Good Enough.

Luckily, my flotilla (besides getting us out of the cloudlayer and worse) also gets us a head-start on space. Swapping out the mass for Venus', and the radius for 70 km from said planet's surface:

?Math.Sqrt(6.673 * 4.867 * Math.Pow(10,-11) * Math.Pow(10,24) * Math.Pow(10,-3) * 2 / (70+6052))
?Math.Sqrt(324774910000 * 2 / (70+6052))

So that is 10300 ms^-1. A little less than 10360, which the Internet told me - and a rounder value than what I had for either planet!

Hitting that delta-V remains expensive though. To overcome delta-V 10300 ms^-1, by the 0.5mv² equation, takes 53,045,000 x Mass (in kilogram) of "Joules". Twenty tonnes would put all this in the terajoule range, 10¹², trillions. We were hoping for up to 3000 tonnes.

For a sanity-check on those numbers: Apollo 11 at liftoff bore 29 tonnes; its Saturn V required 75 terajoules to get only as far as Low Earth Orbit. (It did help that most of this mass was chemical fuel, which got burned and expelled.)

For reference 4.184 terajoules represents a kiloton of 'splodey TNT; 4.184 petajoules, a megaton.