Two stars are 1.3times 10^3 m apart. Each star has a mass of 3.8times 10^15 kg. What is the gravitational attractive force between them? 569times 10^14 8.54times 10^24 9.99times 10^37 1.1times 10^28

To find the gravitational attractive force between the two stars, we can use Newton's law of universal gravitation, which is given by the formula:<br /><br />\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]<br /><br />where:<br />- \( F \) is the gravitational force,<br />- \( G \) is the gravitational constant, approximately \( 6.674 \times 10^{-11} \, \text{N}\cdot\text{m}^2/\text{kg}^2 \),<br />- \( m_1 \) and \( m_2 \) are the masses of the two objects,<br />- \( r \) is the distance between the centers of the two objects.<br /><br />Given:<br />- \( m_1 = m_2 = 3.8 \times 10^{15} \, \text{kg} \),<br />- \( r = 1.3 \times 10^{3} \, \text{m} \).<br /><br />Substitute these values into the formula:<br /><br />\[ F = \frac{(6.674 \times 10^{-11}) \cdot (3.8 \times 10^{15}) \cdot (3.8 \times 10^{15})}{(1.3 \times 10^{3})^2} \]<br /><br />First, calculate the numerator:<br /><br />\[ (6.674 \times 10^{-11}) \cdot (3.8 \times 10^{15}) \cdot (3.8 \times 10^{15}) = 6.674 \times 14.44 \times 10^{19} = 96.32776 \times 10^{19} \]<br /><br />Now, calculate the denominator:<br /><br />\[ (1.3 \times 10^{3})^2 = 1.69 \times 10^{6} \]<br /><br />Now, divide the results:<br /><br />\[ F = \frac{96.32776 \times 10^{19}}{1.69 \times 10^{6}} \approx 5.698 \times 10^{13} \]<br /><br />The closest option to this result is \( 569 \times 10^{14} \), which simplifies to \( 5.69 \times 10^{13} \).<br /><br />Therefore, the gravitational attractive force between the two stars is approximately \( 569 \times 10^{14} \, \text{N} \).