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 will use Newton's law of universal gravitation, which states that the gravitational force \( F \) between two masses \( M_1 \) and \( M_2 \) separated by a distance \( R \) is given by the formula:

\[ F = \frac{G M_1 M_2}{R^2} \]

Where \( G \) is the gravitational constant.

### Step-by-Step Solution:

1. **Identify Initial Conditions**:
- Let the initial distance between the Sun and the Earth be \( R \).
- The initial gravitational force \( F \) can be expressed as:
\[ F = \frac{G M_1 M_2}{R^2} \]

2. **Change in Distance**:
- According to the problem, the distance is increased by three times. Therefore, the new distance \( R' \) is:
\[ R' = 3R \]

3. **Calculate New Gravitational Force**:
- The new gravitational force \( F' \) when the distance is increased to \( 3R \) is:
\[ F' = \frac{G M_1 M_2}{(3R)^2} \]
- Simplifying this gives:
\[ F' = \frac{G M_1 M_2}{9R^2} = \frac{F}{9} \]

4. **Determine the Change in Force**:
- The attraction between the two bodies has decreased from \( F \) to \( F' \). The change in force can be calculated as:
\[ \text{Change in Force} = F - F' = F - \frac{F}{9} = \frac{8F}{9} \]

5. **Calculate Percentage Decrease**:
- The percentage decrease in the gravitational force is given by:
\[ \text{Percentage Decrease} = \left(\frac{\text{Change in Force}}{F}\right) \times 100 = \left(\frac{\frac{8F}{9}}{F}\right) \times 100 \]
- This simplifies to:
\[ \text{Percentage Decrease} = \frac{8}{9} \times 100 \approx 88.89\% \]

### Conclusion:
The attraction between the Sun and the Earth will decrease by approximately 89%.