A spacecraft of mass leaves the Earth’s surface (radius ) with an initial speed of…

PHYSICS · Multi-part · CBSE · Physics · Gravitation · Gravitation

Problem

A spacecraft of mass

m

leaves the Earth’s surface (radius

R_E = 6.4\times10^{6}\,\text{m}

) with an initial speed of

9.0\,\text{km s}^{-1}

along the radial direction away from the centre of Earth. (i) Obtain an expression for the speed

v

of the spacecraft when it is at a distance

r

from the centre of Earth, in terms of the quantities

m,\,G,\,M_E,\,R_E,\,r

and the initial speed

u = 9.0\,\text{km s}^{-1}

. (ii) Using your expression, calculate the speed of the spacecraft when it has reached an altitude of

1.0\times10^{6}\,\text{m}

above Earth’s surface. (iii) State, with reason, whether the spacecraft remains gravitationally bound to Earth on the basis of your calculation.