Question

A planet has a mass of 5*10 24 kg and a radius of 6.1*10 6 m. Find the energy needed to lift a mass of 2.0 kg from its surface into outer space

Answer 1

Solution. Consider the case where an object is launched from the surface of a planet with an initial velocity directed away from the planet.  The object gives up the last of its kinetic energy just as it reaches infinity, where the force of gravity becomes zero. Therefore, according to the law of conservation of energy, the required energy is

$$E=\frac{mv^2}{2}=\frac{GMm}{R}$$

where m=2.0 kg is the body mass; M=5*10 24 kg is the planet mass; R=6.1*10 6 m is the planet radius;

G=6.67*10^-11 N*m^2/kg^2 is gravitational constant. Hence

$$E=\frac{6.67\times 10^{-11}\times 5\times 10^{24} \times 2}{6.1 \times 10^6}\approx 1.1\times 10^8J$$

Answer.

$$E=1.1\times 10^8J$$