Derive an expression for escape velocity.
Answers
Explanation:
Suppose that the planet be a perfect sphere of radius R having mass M. ... So, escape velocity is defined as the minimum initial velocity that will take a body away above the surface of a planet when it's projected vertically upwards. On throwing the object upwards, work has to be done against the gravity.
The formula for escape velocity can be derived from the law of conservation of energy
Let’s consider that an object with mass m is near to a planet with mass M with a radius r. Neglecting the frictional forces, the final velocity of the planet will be infinitely small , and assumed to be 0 and the final distance from the planet would be infinitely large and assumed to be 0. The initial velocity is the required escape velocity and symbolized as ve
So the equation would look like,
((1 )/2×m×ve2) + ((-G×M×)/r^2 ) = 0 + 0
ve2 = (G×M×2)/r^2
ve = √((2*G*M)/r) m/s
Where ve is the escape velocity
M is the mass of the planet
G is the gravitational constant = 6.67 ×〖10〗^(-11) m3⋅kg−1⋅s−2
R is the radius of the planet.
SI unit is m/s