Find the escape velocity form the earth for a $1000$ kg spacecraft and find the kinetic energy it must have at the surface of the earth in order to escape earth's gravitational field. $M = 6 \times 10^{24} k g$ , $R = 6400$ km, $G = 6.67 \times 10^{- 11}$ .

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Solution

$v_{e} = \sqrt{\frac{2 G M}{R}} = \sqrt{\frac{2 \times 6.67 \times 10^{- 11} \times 6 \times 10^{24}}{6400 \times 10^{3}}} = 11183.13 {m s}^{- 1} K . E = \frac{1}{2} m v_{e}^{2} = \frac{1}{2} (1000) \times (11183.1300) = 5591567.3 J$

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Find the escape velocity form the earth for a 1000kg spacecraft and find the kinetic energy it must have at the surface of the earth in order to escape earth's gravitational field. M=6×1024kg, R=6400km, G=6.67×10−11.

ve=√2GMR=√2×6.67×10−11×6×10246400×103=11183.13ms−1K.E=12mv2e=12(1000)×(11183.1300)=5591567.3J

Find the escape velocity form the earth for a $1000$ kg spacecraft and find the kinetic energy it must have at the surface of the earth in order to escape earth's gravitational field. $M = 6 \times 10^{24} k g$ , $R = 6400$ km, $G = 6.67 \times 10^{- 11}$ .

$v_{e} = \sqrt{\frac{2 G M}{R}} = \sqrt{\frac{2 \times 6.67 \times 10^{- 11} \times 6 \times 10^{24}}{6400 \times 10^{3}}} = 11183.13 {m s}^{- 1} K . E = \frac{1}{2} m v_{e}^{2} = \frac{1}{2} (1000) \times (11183.1300) = 5591567.3 J$