what is escape speed?
Answers
escape velocity is the minimum speed needed for a free object to escape from the gravitational influence of a massive body.
In physics, escape velocity is the minimum speed needed for a free object to escape from the gravitational influence of a massive body. It is slower the further away from the body an object is, and slower for less massive bodies. The escape velocity from Earth is about 11.186 km/s at the surface.
The Law of Conservation of Energy states that the total energy of a closed system remains constant. In this case, the closed system consists of the two objects with the gravitational force between them and no outside energy or force affecting either object.
Thus the total final energy—potential energy plus kinetic energy—must equal the total initial energy:
TEi = TE∞
KEi + PEi = 0
Substitute values:
mve2/2 − GMm/Ri = 0
Add GMm/Ri to both sides of equation:
mve2/2 = GMm/Ri
Solve for ve2:
ve2 = 2GM/Ri
Take the square root of each expression to get:
ve = ± √(2GM/Ri)
Considering our gravitational convention for direction, ve is upward or away from the other object and is thus negative:
ve = − √(2GM/Ri)