1. **Problem Statement:** I) Choose the correct option: When the distance between a planet and the Sun decreases, what happens to the gravitational pull? II) Calculate the orbital period of Venus using Newton’s version of Kepler’s third law. III) Design a diagram showing a satellite revolving around Earth with forces acting on it. 2. **I) Correct Option:** The gravitational force between two masses is given by Newton's law of gravitation: $$F = \frac{G M m}{r^2}$$ where $r$ is the distance between the planet and the Sun. As $r$ decreases, $F$ increases. An increase in gravitational pull causes the planet to move faster to maintain its orbit. **Answer:** a) increases, causing the planet to move faster. 3. **II) Orbital Period of Venus:** Given: - Mean orbital radius $r = 1.076 \times 10^{11}$ m - Mass of Sun $M = 1.99 \times 10^{30}$ kg - Gravitational constant $G = 6.67 \times 10^{-11}$ m$^3$ kg$^{-1}$ s$^{-2}$ Newton’s form of Kepler’s third law relates orbital period $T$ and radius $r$: $$T^2 = \frac{4 \pi^2 r^3}{G M}$$ Calculate $T$: $$T = \sqrt{\frac{4 \pi^2 r^3}{G M}}$$ Substitute values: $$T = \sqrt{\frac{4 \pi^2 (1.076 \times 10^{11})^3}{6.67 \times 10^{-11} \times 1.99 \times 10^{30}}}$$ Calculate numerator: $$4 \pi^2 (1.076 \times 10^{11})^3 = 4 \times 9.8696 \times (1.246 \times 10^{33}) = 39.4784 \times 1.246 \times 10^{33} = 4.917 \times 10^{34}$$ Calculate denominator: $$6.67 \times 10^{-11} \times 1.99 \times 10^{30} = 1.327 \times 10^{20}$$ Therefore: $$T = \sqrt{\frac{4.917 \times 10^{34}}{1.327 \times 10^{20}}} = \sqrt{3.705 \times 10^{14}} = 1.925 \times 10^{7} \text{ seconds}$$ Convert seconds to days: $$\frac{1.925 \times 10^{7}}{86400} \approx 223 \text{ days}$$ 4. **III) Satellite Diagram Explanation:** - A satellite revolves around Earth in circular orbit. - Forces acting on satellite: - Gravitational force $F_g$ directed towards Earth’s center. - Centripetal force required for circular motion is provided by $F_g$. Diagram would show Earth at center, satellite in orbit, arrow pointing from satellite to Earth labeled $F_g$. 5. **Summary:** - I) Correct option: a) - II) Orbital period of Venus $\approx 1.925 \times 10^{7}$ seconds or 223 days. - III) Satellite diagram with gravitational force acting towards Earth.