Question

The $105,000kg$ space shuttle is doing a training exercise in outer space.
How much energy would it take to bump up the space shuttle from an altitude of $500km$ to $1000km$ above the surface of the earth?
Assume the radius of the Earth is $6.37\times {10}^{6}m$ and the mass of the Earth is $5.98\times {10}^{24}kg$

• A. $2.07\times {10}^{11}J$
• B. $2.10\times {10}^{13}J$
• C. $4.15\times {10}^{11}J$
• D. $-4.19\times {10}^{13}J$
• E. $-2.09\times {10}^{13}J$

Answer 1

The correct option is A $2.07\times {10}^{11}J$

Given : $G=6.67\times {10}^{-11}$ $N{m}^2/(kg{)}^2$ $M_e=5.98\times {10}^{24}$ kg $R_e=6.37\times {10}^6$ m

$M_s=105000$ kg

Radius of initial orbit $r_1=(6.37+0.5)\times {10}^6=6.87\times {10}^6$ m

Radius of final orbit $r_2=(6.37+1.0)\times {10}^6=7.37\times {10}^6$ m

Energy required $E=\frac{G{M}_e{M}_s}{2}[\frac{1}{r_1}-\frac{1}{r_2}]$

$\therefore$ $E=\frac{6.67\times {10}^{-11}\times 5.98\times {10}^{24}\times 105000}{2}[\frac{1}{6.87\times {10}^6}-\frac{1}{7.37\times {10}^6}]=2.07\times {10}^{11}$ J