Escape Velocity & Survival of Life

I was thinking the other day about the applicability of maths to real world problems, and it occurred to me that the formula for Escape Velocity is arguably one of the most important mathematical discoveries in humankind. Without it, we would not be able to launch ourselves from the prison of gravity and enter space and discover new worlds. And if you believe some of the science journals and sci-fi novel plots, eventually our Sun will die (many millions of years hence), and Man may settle somewhere else in the galaxy. Our future literally depends on this formula.

Technical description can be found on Wikipedia:
http://en.wikipedia.org/wiki/Escape_velocity

In physics, for a given gravitational field and a given position, the escape velocity is the minimum speed an object without propulsion, at that position, needs to have to move away indefinitely from the source of the field, as opposed to falling back or staying in an orbit within a bounded distance from the source. The object is assumed to be influenced by no forces except the gravitational field; in particular there is no propulsion, as by a rocket, there is no friction, as between the object and the Earth's atmosphere (these conditions correspond to freefall) and there is no gravitational radiation. This definition may need modification for the practical problem of two or more sources in some cases. In any case, the object is assumed to be a point with a mass that is negligible compared with that of the source of the field, usually an excellent approximation. It is commonly described as the speed needed to "break free" from a gravitational field.

In the simple case of the escape velocity from a single body, it can be calculated by setting the kinetic energy equal to minus the gravitational potential energy. This is because the positive kinetic energy is needed to increase the negative gravitational potential energy to zero, which applies when the object is at an infinite distance.



where ve is the escape velocity, G is the gravitational constant, M is the mass of the body being escaped from, m is the mass of the escaping body (factors out), and r is the distance between the centre of the body and the point at which escape velocity is being calculated, and μ is the standard gravitational parameter.