The mass of sun is `2xx10^(30)` kg and mass of earth is `6xx10^(24)` kg. if the distance between the centers of sun and earth is `1.5xx10^(8)` km, calculate the force of gravitation between them.

Explanation

To calculate the gravitational force between the Sun and the Earth, we can use Newton's law of universal gravitation, which states:

\[ F = G \frac{m_1 m_2}{r^2} \]

Where:
- \( F \) is the gravitational force,
- \( G \) is the gravitational constant, approximately \( 6.674 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \),
- \( m_1 \) is the mass of the first object (Sun),
- \( m_2 \) is the mass of the second object (Earth),
- \( r \) is the distance between the centers of the two objects.

### Step-by-Step Solution:

1. **Identify the values**:
- Mass of the Sun, \( m_1 = 2 \times 10^{30} \, \text{kg} \)
- Mass of the Earth, \( m_2 = 6 \times 10^{24} \, \text{kg} \)
- Distance between the Sun and Earth, \( r = 1.5 \times 10^{8} \, \text{km} = 1.5 \times 10^{11} \, \text{m} \) (since \( 1 \, \text{km} = 1000 \, \text{m} \))

2. **Substitute the values into the formula**:
\[ F = G \frac{m_1 m_2}{r^2} \]
\[ F = 6.674 \times 10^{-11} \frac{(2 \times 10^{30})(6 \times 10^{24})}{(1.5 \times 10^{11})^2} \]

3. **Calculate \( r^2 \)**:
\[ r^2 = (1.5 \times 10^{11})^2 = 2.25 \times 10^{22} \, \text{m}^2 \]

4. **Calculate the product of the masses**:
\[ m_1 m_2 = (2 \times 10^{30})(6 \times 10^{24}) = 12 \times 10^{54} \, \text{kg}^2 \]

5. **Substitute back into the equation**:
\[ F = 6.674 \times 10^{-11} \frac{12 \times 10^{54}}{2.25 \times 10^{22}} \]

6. **Calculate the fraction**:
\[ \frac{12 \times 10^{54}}{2.25 \times 10^{22}} = \frac{12}{2.25} \times 10^{54 - 22} = 5.3333 \times 10^{32} \]

7. **Final calculation of \( F \)**:
\[ F = 6.674 \times 10^{-11} \times 5.3333 \times 10^{32} \]
\[ F \approx 3.56 \times 10^{22} \, \text{N} \]

### Final Answer:
The gravitational force between the Sun and the Earth is approximately \( 3.56 \times 10^{22} \, \text{N} \).