Question

If due to any reason, the orbital speed of a satellite increases $41.4\%$. Then in this situation would the satellite escape? Explain.

Answer 1

Orbital velocity of the satellite $=v_0$

When any hour , its orbital velocity is increased by $41.4$ % then the new value of orbital velocity

$v_0^{\prime }=v_0+\frac{41.4}{100}{v}_0=v_0[1+\frac{41.4}{100}]$

$=v_0[1+0.414]$

$=v_0\times 1.414=v_0\sqrt{2}$

or $v_0^{\prime }=v_e$ (escape velocity)

Therefore, the satellite will escape.