Question 1: Define an orbit in the context of planetary motion within the Solar System.

Answer: An orbit is the curved path of a celestial object around a star, planet, or moon, maintained by gravitational forces.

Question 2: Explain why planets follow elliptical orbits rather than perfect circles.

Answer: Planets follow elliptical orbits because the gravitational force varies with distance, causing orbits to be elongated rather than perfectly circular, as described by Kepler's First Law.

Question 3: What is the significance of the semi-major axis in an orbit?

Answer: The semi-major axis is half the longest diameter of an elliptical orbit and determines the size of the orbit, affecting the orbital period.

Question 4: Calculate the orbital period of a planet orbiting at a distance of 150 million km from the Sun, assuming the Sun's mass is 1.989 × 10^30 kg. Use Kepler's Third Law: T^2 = (4π^2 / GM) * r^3, where G = 6.674 × 10^-11 N·m^2/kg^2.

Answer: Approximately 365 days

Question 5: Identify two variables that affect the stability of a planet's orbit.

Answer: Mass of the central star and the distance of the planet from the star.

Question 6: Which of the following best describes a geostationary orbit? A) An orbit where the satellite remains fixed relative to a point on Earth's surface. B) An orbit with an orbital period of 24 hours. C) An orbit that passes over the equator. D) An orbit with high eccentricity.

Answer: A) An orbit where the satellite remains fixed relative to a point on Earth's surface.

Question 7: Fill in the blank: The shape of a planet's orbit is primarily determined by the balance between its ______ and the gravitational pull from the Sun.

Answer: velocity

Question 8: Describe a practical method scientists could use to determine the orbital period of a newly discovered exoplanet.

Answer: Scientists can observe the exoplanet's transit across its star over time, recording the interval between successive transits to determine the orbital period.

Question 9: In your own words, explain why understanding orbits is important for satellite deployment and space exploration.

Answer: Understanding orbits allows scientists and engineers to accurately position satellites for communication, navigation, and observation, and helps in planning space missions by predicting spacecraft trajectories.

Question 10: Identify a real-world application of orbital mechanics in the technology or industry you are familiar with.

Answer: GPS satellites rely on precise orbital mechanics to provide accurate positioning and navigation services worldwide.