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Gravitation — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsGravitation3 Marks
Question
A spaceship is launched into a circular orbit close to earth's surface. What additional velocity has to be imparted to the spaceship in the orbit to overcome the gravitational pull? Radius of earth = $6400km$ and $g = 9.8ms^{-2}$.
✓

Answer

Orbital velocity of space ship close to earth, v_0 $=\sqrt{\frac{\text{Gm}}{\text{R}}}=\sqrt{\frac{\text{gR}^2}{\text{R}}}=\sqrt{\text{gR}}$ escape velocity, $\text{v}_{\text{e}}=\sqrt{2\text{gR}}$
$\therefore$ Additional velocity required $\text{v}_{\text{e}}-\text{v}_{\text{o}}=-\sqrt{\text{2gR}}-\sqrt{\text{gR}}$
$=\sqrt{2\times9.8\times6.4\times10^6}$
$-\sqrt{9.8\times6.4\times10^6}$
$=3.2805\times10^3{\text{ms}^{-1}}$

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