Nasa is relying on the existence of Lagrangian points between every set of planetary bodies it intends to explore in order to implement its plan of successful interplanetary space exploration. Although this at first may seem to be a vague and mystical concept, foreign to all but trained astrophysicists, in fact it is really quite simple to understand.

The Lagrangian in physics is merely nothing more than a set of two simpler equations that can be used as an alternative for Newtons second law; force equals mass times acceleration. A Lagrangian point between two bodies exerting competing forces on a body is therefore a point at which the forces are equal and opposite. According to Newtons third law, if the net force on a body is zero, it will stay at rest if at rest and if in motion it will stay in motion.

In mathematical terms, visualize a graph of a big bowl. The Lagrangian point is the point at the very bottom of the bowl. This point represents the point at which the maximum energy, the energy from the bottom of the bowl to the top, must be supplied to kick the body out of the bowl in order to prevent the body from rolling back down to the bottom of the bowl and returning to its energy minimum. Therefore, the point at the minimum of the bowl represents the point of maximum stability in terms of preventing the influence of a net imbalance in the forces of the two gravitational forces on it from disturbing it. This point in question is the orbit which has the most stable velocity and angular momentum. The body acted on could be a space station between two large masses such as the earth and the moon or any two interplanetary bodies of significantly greater mass than the spacecraft.

How this relates to Nasa and its plans for future space travel is that they have the ability to use the Lagrangian formulas to calculate the Lagrangian points between different planetary bodies and therefore to determine the location of these orbits. Therefore, it is possible to build space stations as stepping stones between the earth and the moon, the moon and Mars, and on and on as far as you want to go. As it would be unrealistic to expect any spacecraft to be able to return to earth from far out in space in the case of an emergency or the need to make repairs, this makes the possibility of extending space travel outwards into the solar system and theoretically beyond feasible within the constraints of our technology and budgetary considerations.

Sources:

1) NASA Reveals New Plan for the Moon, Mars & Outward By Leonard David; Senior Space Writer Space.com