A rocket is fired from the earth towards the sun. At what point on its path is the gravitational force on the rocket zero? Mass of the sun is `2 xx 10^(30)kg`, mass of the earth is `6 xx 10^(24) kg`. Neglect the effect of other planets etc. ( orbital radius `= 1.5 xx 10^(11) m )`.

Explanation

To find the point on the path of a rocket fired from the Earth towards the Sun where the gravitational force on the rocket is zero, we can follow these steps:

### Step 1: Understand the Forces Acting on the Rocket
The rocket experiences gravitational forces from both the Earth and the Sun. The gravitational force exerted by the Sun (F_sun) and the gravitational force exerted by the Earth (F_earth) can be expressed using Newton's law of gravitation.

### Step 2: Write the Gravitational Force Equations
The gravitational force exerted by the Sun on the rocket is given by:
\[ F_{sun} = \frac{G \cdot M_s \cdot M_r}{(R_0 - r)^2} \]
...