Question

A rocket is fired from the earth towards the sun at what distance from the earths center is the gravitational force on the rocket zero?

Answer 1

Mass of the sun $=2\times {10}^{3}0kg=Ms$

Mass of the earth $=6\times {10}^{2}4kg=Me$

orbital radius $=1.5\times {10}^{1}1m$

Mass of the rocket $=m$

Now,lets think the distance is $r$

Let's think that x is the distance from earth's center where the gravitational force on the rocket is zero.

gravitational force of the earth $=GmMe/x^2$

Gravitational force of the sun $=GmMs/(r-x^2)$

Using Newton's law,

See the picture above...

Now we can say that the distance is $2.59\times {10}^8$.