The distance between the Sun and the Earth is 1.5 × 10^{11} m - AQA - A-Level Physics - Question 13 - 2018 - Paper 2

To calculate the gravitational force exerted between two bodies, we use Newton's law of universal gravitation, which is given by the formula:

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

Where:

• $F$ is the gravitational force between the objects,
• $G$ is the gravitational constant, approximately $6.674 \times 10^{-11} \text{ N m}^2/\text{kg}^2$,
• $m_1$ is the mass of the Earth ($5.972 \times 10^{24} \text{ kg}$),
• $m_2$ is the mass of the Sun ($1.989 \times 10^{30} \text{ kg}$),
• $r$ is the distance between the centers of the two bodies ($1.5 \times 10^{11} ext{ m}$).

Substituting the values:

$F = 6.674 \times 10^{-11} \frac{(5.972 \times 10^{24})(1.989 \times 10^{30})}{(1.5 \times 10^{11})^2}$

Calculating this gives: $F \approx 3.542 \times 10^{22} \text{ N}$

Thus, the most appropriate answer from the options provided is A) $3.5 \times 10^{22} \text{ N}$.