A rocket is fired from the earth towards the sun. At what distance from the earth's centre is the gravbitaional force on the rocket zero? Mass of the sun`=2xx10^(30)kg`, mass of the earth`=6xx10^(24)kg`. Neglect the effect of other planets etc. (orbital radius=`1.5xx10^(11)m`).

Explanation

To find the distance from the Earth's center at which the gravitational force on the rocket is zero, we can set up the problem using Newton's law of gravitation. Here’s a step-by-step solution:

### Step 1: Define the Variables
Let:
- \( M_s = 2 \times 10^{30} \, \text{kg} \) (mass of the Sun)
- \( M_e = 6 \times 10^{24} \, \text{kg} \) (mass of the Earth)
- \( R = 1.5 \times 10^{11} \, \text{m} \) (distance from the Earth to the Sun)
- \( x \) = distance from the Earth's center to the rocket
...