If the distance between the sun and the earth is increased by three times, then attraction between two will

Options

A. remains constant
B. decrease by 63 %
C. increase by 63 %
D. decrease by 89 %

Explanation

To solve the problem, we need to understand how gravitational attraction changes with distance according to Newton's law of universal gravitation. The formula for gravitational force (F) between two masses (M1 and M2) separated by a distance (R) is given by:

\[ F = \frac{G \cdot M1 \cdot M2}{R^2} \]

where:
- \( F \) is the gravitational force,
- \( G \) is the gravitational constant,
- \( M1 \) and \( M2 \) are the masses of the two objects,
- \( R \) is the distance between the centers of the two masses.

### Step-by-Step Solution:

1. **Identify the initial distance**: Let the initial distance between the Sun and the Earth be \( R \).

2. **Determine the new distance**: If the distance is increased by three times, the new distance \( R' \) will be:
\[ R' = 3R \]

3. **Write the initial gravitational force**: The initial gravitational force \( F \) can be expressed as:
\[ F = \frac{G \cdot M1 \cdot M2}{R^2} \]

4. **Write the new gravitational force**: The new gravitational force \( F' \) when the distance is increased to \( 3R \) will be:
\[ F' = \frac{G \cdot M1 \cdot M2}{(3R)^2} \]

5. **Simplify the new gravitational force**:
\[ F' = \frac{G \cdot M1 \cdot M2}{9R^2} \]

6. **Compare the new force with the initial force**:
\[ F' = \frac{1}{9} \cdot \frac{G \cdot M1 \cdot M2}{R^2} = \frac{1}{9} F \]

### Conclusion:
Thus, if the distance between the Sun and the Earth is increased by three times, the gravitational attraction between them will decrease to one-ninth of the original force.