Respuesta :
Answer:[tex]19.80\times 10^{10} J[/tex]
Explanation:
Given
mass of satellite [tex]m=7.45 \times 10^3 kg[/tex]
orbital radius [tex]R=7.50\times 10^6 m[/tex]
mass of Earth [tex]M=5.97\times 10^{24} kg[/tex]
Minimum amount of Energy to move Satellite from its orbit to an infinite distance is sum of Potential Energy + Kinetic Energy of Satellite
[tex]W=U+K.E.[/tex]
[tex]U=-G\frac{Mm}{R}[/tex]
[tex]U=-6.67\times 10^{-11}\times \frac{5.97\times 10^{24}\times 7.45 \times 10^3}{7.50\times 10^6}[/tex]
[tex]U=-\frac{296.658\times 10^{16}}{7.5\times 10^6}[/tex]
[tex]U=-39.55\times 10^{10} J[/tex]
[tex]K.E.=\frac{1}{2}\times mv^2[/tex]
Where [tex]v=orbital\ velocity [/tex]
[tex]v=\sqrt{\frac{GM}{r}}=\sqrt{\frac{6.67\times 10^{-11}\times 5.97\times 10^{24}}{7.50\times 10^6}}[/tex]
[tex]v^2=5.30\times 10^7 m/s[/tex]
[tex]K.E.=\frac{1}{2}\times mv^2[/tex]
[tex]K.E.=\frac{1}{2}\times 7.45\times 10^3\times (5.30\times 10^7)=19.74\times 10^{10} J[/tex]
[tex]W=-39.55\times 10^{10}+19.74\times 10^{10}[/tex]
[tex]W=-19.80\times 10^{10} J[/tex]
i.e. [tex]19.80\times 10^{10} J[/tex] Energy is required to provide to move Satellite out of its orbit
