1 Neptune has a mass that is about 17 times the mass of Earth. The distance between the Sun and Neptune is about 30.1 times the distance between the Sun and Earth. If the gravitational force between the Sun and Earth is \( 3.5 \times 10^{28} \mathrm{~N} \), which is closest to the force between Neptune and the Sun? \( 6 \times 10^{26} \mathrm{~N} \) \( 6 \times 10^{27} \mathrm{~N} \) \( 6 \times 10^{28} \mathrm{~N} \) \( 6 \times 10^{29} \mathrm{~N} \)

To find the gravitational force between Neptune and the Sun, we can use Newton's law of universal gravitation, which is directly proportional to the masses of the two objects and inversely proportional to the square of the distance between them. Since the mass of Neptune is about 17 times that of Earth, and the distance from the Sun to Neptune is approximately 30.1 times that of the Sun to Earth, we can determine the force. The formula for gravitational force is: \[ F = G \frac{m_1 m_2}{r^2} \] Given that the force between the Sun and Earth is \( 3.5 \times 10^{28} \text{ N} \), we can express the force between Neptune and the Sun as: \[ F_{Neptune} = 3.5 \times 10^{28} \text{ N} \times \frac{17}{(30.1)^2} \] Calculating the factor: \[ \frac{17}{(30.1)^2} \approx \frac{17}{906.01} \approx 0.01877 \] Now calculating \( F_{Neptune} \): \[ F_{Neptune} \approx 3.5 \times 10^{28} \text{ N} \times 0.01877 \approx 6.57 \times 10^{26} \text{ N} \] Thus, the closest answer is \( 6 \times 10^{26} \text{ N} \). \( 6 \times 10^{26} \mathrm{~N} \)