Answer:
5. 9GmM/(10R)
Explanation:
m is the mass of the satellite
M is the mass of the earth
W is the energy required to launch the satellite
Energy at earth surface = Potential energy (PE) + W
W = Energy at earth surface - Potential energy (PE)
But PE = [tex]-\frac{GMm}{R}[/tex]
Therefore: W = Energy at earth surface - [tex]\frac{GMm}{R}[/tex]
Energy at earth surface (E) at an altitude of 5R = [tex]-\frac{GMm}{5r} +\frac{1}{2}mV^2[/tex]
But [tex]V=\sqrt{\frac{GM}{5R} }[/tex]
Therefore: [tex]E=-\frac{GMm}{5R}+\frac{1}{2}m(\sqrt{\frac{GM}{5R} } )^2= -\frac{GMm}{5R}+\frac{GMm}{10R} = -\frac{GMm}{10R}[/tex]
W = E - PE
[tex]W=-\frac{GMm}{10R}-(-\frac{GMm}{R})=-\frac{GMm}{10R}+\frac{GMm}{R}=\frac{9GMm}{10R} \\W=\frac{9GMm}{10R}[/tex]
