QUESTION 14 What is the escape velocity from Earth\'s gravity for a spacecraft l

Question

QUESTION 14 What is the escape velocity from Earth's gravity for a spacecraft launched from the orbit at an altitude of 18,669 kilometers above the Earth surface? Earth's mean radius is RE 6.37 x106 m: Earth's mass is ME 5.97x1024kg. Express your answer in km/s and round it to two decimals. QUESTION 15 What is the escape velocity from Sun's gravity for a spacecraft with mass 10,731 kilograms launched from a distance equal to the Jupiter's average orbital distance from the Sun i.e. 5.2 AU (1AU 1.5x 108 km)? MSun 1.99 x 1030 kg. Express your answer in km/s and round it to two decimals

Explanation / Answer

14. In an orbit,

total energy = PE + KE = - G M m / r + G M m / 2 r

=- G M m / 2 r

so Ke needed to escape = G M m / 2 r

m v^2 /2 = G M m / 2 r  

v = sqrt[ G M / r ]

v = sqrt[ (6.67 x 10^-11 x 5.97 x 10^24) / (6.37 x 10^6 + 18.669 x 10^6 )]

v = 3990 m/s

v = 4 km/s .....Ans

15. v = sqrt[ (6.67 x 10^-11 x 1.99 x 10^30) / (5.2 x 1.5 x 10^11)]

v =13044 m/s

v = 13 km/s

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