That's the orbital velocity.

He also calculated how much more energy would be

required to liberate the object entirely from the gravity of the earth.

Essentially send it to an infinite distance from the earth.

And for any object, the escape velocity is the square root of 2 or about 40%

more than the circular velocity or the velocity required to put it in orbit.

These are the fundamental relationships that underlie the entire space

telecommunications and space travel business.

The energy requirement to create orbital, or

escape velocities, are the basis of almost everything that NASA does.

In terms of exploring the solar system, or other gravity situations, we can think of

terms of the gravity as a potential well, where a certain amount of energy or

velocity or kinetic energy is required to be liberated from that potential well.

Being liberated from the earth's gravity, of course does not imply being

liberated from the solar system because the earth is in orbit around the sun.

So a separate calculation is involved, in understanding how much velocity or

kinetic energy,

is required to liberate an object, like a satellite, from the solar system itself.

Quite important in space travel, and in sending satellites around

the solar system, are particular situations where gravity balances.

These are called the Lagrange Points.

They were first theorized by a mathematical physicist in

France 200 years ago.

The Lagrange Points are valuable in space exploration.

They're places where gravity balances so

very little energy is required to keep a spacecraft or a probe in these situations.

Some of the Lagrange Points are unstable, in which case small retro-rockets, or

ballistics, are required to keep a satellite in its position.

Only one of them is stable.

These are valuable locations and many large space missions of the recent past or

future, are destined for the Lagrange Points.

In particular, the second Lagrange Point, L2, is a favored location for

many NASA and ESA missions, such as the Wilkinson Microwave Anisotropy Probe,

WMAP, and Herschel and Planck, two current satellites.

The James Webb space telescope is also destined to be launched there in 2016.

Space travel also uses other tricks of gravity, such as gravitational assist.

Gravitational assist is a nice idea.

If you bring a fast-moving object up behind a larger,

more massive object, then even without them colliding, their

gravitational interaction can transfer kinetic energy to the smaller object.

A space probe.

It's a gravity assist.