Given;
Radius of earth (R) = 6400 km = 6400000 m
Mass of satellite (m) = 2000 kg
Height of satellite (h) = 800 km = 800000 m
Total Energy needed (E) = ?
We have,
Energy needed = Increase in Potential Energy + Kinetic Energy at Orbit
$\left [ -\;\frac{G\;M\;m}{r}\;-\;\left (\frac{-\;G\;M\;m}{R}\right )\; \right ]$
= $-$$\frac{G\;M\;m}{r}$$\;-\;$$\frac{-\;G\;M\;m}{R}$$\;+\;$$\frac{1}{2}$$mv^2$
= $-$$\frac{G\;M\;m}{r}$$\;-\;$$\frac{-\;G\;M\;m}{R}$$\;+\;$$\frac{1}{2}$$m$$ \frac{G\;M}{r}$ [∵ r = R+h]
= $g\;R^2\;m[$$\frac{1}{R}$$\;-\;$$ \frac{1}{2(R+h)}$$]$ = $g\;m[R\;-\;$$\frac{R^2}{2(R+h)}$$]$
= $2000\;*\;10\;[6400000 \;-\; $$\frac{(6400000)^2}{2(6400000 \;+\; 800000)}]$
= $7.12\;*\;10^{10}\;J$
∴ The total Energy needed (E) = $7.12\;*\;10^{10}\;J$
Return To Main Menu
No comments:
Post a Comment