Example 1: Calculate the gravitational force if the mass of the sun is \( 1.99 \times 10^{\wedge} 30 \mathrm{~kg} \) and earth is \( 5.97 \times 10^{\wedge} 24 \mathrm{~kg} \) separated by the distance \( 1.5 \times 10^{\wedge} 11 \mathrm{~m} \) ?(Gravitational constant \( \mathrm{G}=6.673 \times 10^{\wedge}-11 \mathrm{Nm} 2 / \) Kg 2 ) \( \quad \) Edited 19:23

To calculate the gravitational force between the sun and the earth, we can use the formula for gravitational force: \[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \] where: - \( F \) is the gravitational force - \( G \) is the gravitational constant - \( m_1 \) is the mass of the sun - \( m_2 \) is the mass of the earth - \( r \) is the distance between the sun and the earth Given: - Mass of the sun, \( m_1 = 1.99 \times 10^{30} \, \text{kg} \) - Mass of the earth, \( m_2 = 5.97 \times 10^{24} \, \text{kg} \) - Distance between the sun and the earth, \( r = 1.5 \times 10^{11} \, \text{m} \) - Gravitational constant, \( G = 6.673 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2 \) Substitute the given values into the formula to calculate the gravitational force. Calculate the value by following steps: - step0: Calculate: \(\frac{\left(6.673\times 10-11\right)\times 1.99\times 10^{30}\times 5.97\times 10^{24}}{\left(1.5\times 10^{11}\right)^{2}}\) - step1: Multiply the numbers: \(\frac{\left(66.73-11\right)\times 1.99\times 10^{30}\times 5.97\times 10^{24}}{\left(1.5\times 10^{11}\right)^{2}}\) - step2: Subtract the numbers: \(\frac{55.73\times 1.99\times 10^{30}\times 5.97\times 10^{24}}{\left(1.5\times 10^{11}\right)^{2}}\) - step3: Multiply: \(\frac{662089119\times 10^{48}}{\left(1.5\times 10^{11}\right)^{2}}\) - step4: Evaluate the power: \(\frac{662089119\times 10^{48}}{2.25\times 10^{22}}\) - step5: Reduce the fraction: \(\frac{220696373\times 10^{48}}{75\times 10^{20}}\) The gravitational force between the sun and the earth is approximately \( 2.94 \times 10^{34} \, \text{N} \).