The distance between earth and moon is about `3.8xx10^(5) km`. At what point or points will the gravitational field strength of earth-moon system be zero? Given mass of earth is `81` times the moon's mass.

Explanation

To find the point or points where the gravitational field strength of the Earth-Moon system is zero, we can follow these steps:

### Step 1: Understand the System
We know that the distance between the Earth and the Moon is approximately \( r = 3.8 \times 10^5 \) km. The mass of the Earth \( M \) is 81 times the mass of the Moon \( m \), i.e., \( M = 81m \).

### Step 2: Set Up the Gravitational Field Equations
The gravitational field \( E \) due to a mass \( M \) at a distance \( d \) is given by the formula:
\[
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