Editing Orbital mechanics (section)

===Escape velocity===
{{Main|Escape velocity}}
The formula for an [[escape velocity]] is derived as follows. The [[specific energy]] (energy per unit [[mass]]) of any space vehicle is composed of two components, the [[specific potential energy]] and the [[specific kinetic energy]]. The specific potential energy associated with a planet of [[mass]] ''M'' is given by
:<math>\epsilon_p = - \frac{G M}{r} \,</math>

where ''G'' is the [[gravitational constant]] and ''r'' is the distance between the two bodies;

while the [[specific kinetic energy]] of an object is given by
:<math>\epsilon_k = \frac{v^2}{2} \,</math>

where ''v'' is its Velocity;

and so the total [[specific orbital energy]] is
:<math> \epsilon = \epsilon_k+\epsilon_p = \frac{v^2}{2} - \frac{G M}{r} \,</math>

Since [[conservation of energy|energy is conserved]], <math> \epsilon</math> cannot depend on the distance, <math>r</math>, from the center of the central body to the space vehicle in question, i.e. ''v'' must vary with ''r'' to keep the specific orbital energy constant. Therefore, the object can reach infinite <math>r</math> only if this quantity is nonnegative, which implies
:<math>v\geq\sqrt{\frac{2 G M}{r}}.</math>

The escape velocity from the Earth's surface is about 11&nbsp;km/s, but that is insufficient to send the body an infinite distance because of the gravitational pull of the Sun. To escape the Solar System from a location at a distance from the Sun equal to the distance Sun–Earth, but not close to the Earth, requires around 42&nbsp;km/s velocity, but there will be "partial credit" for the Earth's orbital velocity for spacecraft launched from Earth, if their further acceleration (due to the propulsion system) carries them in the same direction as Earth travels in its orbit.