A space probe is fired from the Earth towards the Sun. At what approximate distance from the Earth's

Question

A space probe is fired from the Earth towards the Sun. At what approximate distance from the Earth's centre is the net gravitational force on the probe zero? (Given: Mass of Sun = $2 	imes 10^{30}	ext{ kg}$, Mass of Earth = $6 	imes 10^{24}	ext{ kg}$, Earth-Sun distance = $1.5 	imes 10^{11}	ext{ m}$)

Professor PC Thomas Classes · Answer

Let $x$ be the distance from Earth. Equating the forces: $\frac{GM_E m}{x^2} = \frac{GM_S m}{(r-x)^2}$. Solving this gives $\frac{r-x}{x} = \sqrt{\frac{M_S}{M_E}} = \sqrt{\frac{2 	imes 10^{30}}{6 	imes 10^{24}}} \approx 577$. Thus, $r/x = 578$, which gives $x = \frac{1.5 	imes 10^{11}}{578} \approx 2.59 	imes 10^8	ext{ m}$.