A probe to sun - 4

Work done, dW= F.dr

Integrating gives , $\Rightarrow \Delta w=\int { F.dr }$

$\Rightarrow \Delta w=\int _{ { r }_{ 1 } }^{ { r }_{ 2 } }{ \frac { -GMm }{ { r }^{ 2 } } } \quad \quad where,\\ M\longrightarrow mass\quad of\quad earth\\ m\longrightarrow mass\quad of\quad object\\ { r }_{ 1 }\longrightarrow initial\quad separation\quad from\quad center\quad of\quad earth\\ { r }_{ 2 }\longrightarrow final\quad separation\quad from\quad center\quad of\quad earth$

$\Rightarrow \Delta w=-GMm\int _{ { r }_{ 1 } }^{ { r }_{ 2 } }{ { r }^{ -2 } }$

$\Rightarrow \Delta w=-GMm{ { \left[ \frac { { r }^{ -1 } }{ -1 } \right] } }_{ { r }_{ 1 } }^{ { r }_{ 2 } }\quad$

$\Delta w=GMm{ { \left[ \frac { 1 }{ { r }_{ 2 } } -\frac { 1 }{ { r }_{ 1 } } \right] } }$

On substituting values we get $\Delta w=\boxed{8.48\times { 10 }^{ 8 }J}$