A spaceship is stationed on Mars. How much energy must be expended on the spaceship to launch it out of the solar system ? Mass of the space ship = 1000 kg; mass of the sun = 2×1030 kg; mass of mars = 6.4×1023 kg; Radius of mars = 3395 km; Radius of the orbit of mars = 2.28×108 kmG=6.67×10−11 Nm2kg−2.

Question

A spaceship is stationed on Mars. How much energy must be expended on the spaceship to launch it out of the solar system ? Mass of the space ship = 1000 kg; mass of the sun = 2×1030 kg; mass of mars = 6.4×1023 kg;  Radius of mars = 3395 km;  Radius of the orbit of mars = 2.28×108 kmG=6.67×10−11 Nm2kg−2.

Filo · Accepted Answer

Mass of the spaceship, ms​=1000 kgMass of the Sun, M=2×1030 kgMass of Mars, mm​=6.4×1023 kgOrbital radius of Mars, R=2.28×1011 mRadius of Mars, r=3.395×106 mUniversal gravitational constant, G=6.67×10−11 Nm2kg−2The potential energy of the spaceship due to the gravitational attraction of the Sun, Us​=−GMms​/RPotential energy of the spaceship due to the gravitational attraction of Mars, Um​=−Gmm​ms​/rSince the spaceship is stationed on Mars, its velocity and hence, its kinetic energy will be zero.Total energy of the spaceship, E=Um​+Us​=−GMms​/R−Gmm​ms​/r The negative sign indicates that the satellite is bound to the system.Energy required for launching the spaceship out of the solar system =−E −E=RGMms​​+rGmm​ms​​       =Gms​(RM​+rmm​​)       =6.67×10−11×103×(2.28×10112×1030​+3.395×1066.4×1023​)       =5.91×1011 J

Question Text	A spaceship is stationed on Mars. How much energy must be expended on the spaceship to launch it out of the solar system ? Mass of the space ship = 1000 kg; mass of the sun = $2 \times 1 0^{30} k g$ ; mass of mars = $6.4 \times 1 0^{23} k g$ ; Radius of mars = 3395 km; Radius of the orbit of mars = $2.28 \times 1 0^{8} km$ $G = 6.67 \times 1 0^{- 11} N m^{2} k g^{- 2}$ .
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