Worked example 12.6: Launch energy

Question: What is the minimum energy required to launch a probe of mass $m=120 {\rm kg}$ into outer space? The Earth's mass and radius are $M_\oplus =5.97\times 10^{24} {\rm kg}$ and $R_\oplus = 6.378\times 10^6 {\rm m}$, respectively.

Answer: The energy which must be given to the probe should just match the probe's gain in potential energy as it travels from the Earth's surface to outer space. By definition, the probe's potential energy in outer space is zero. The potential energy of the probe at the Earth's surface is

$$U = - \frac{G M_\oplus m}{R_\oplus} = \frac{(6.673\times 1... ...times 120} {( 6.378\times 10^6)} = -7.495\times 10^9 {\rm J}.$$

Thus, the gain in potential energy, which is the same as the minimum launch energy, is $7.495\times 10^9 {\rm J}$.