Astronomy Astronomy Celestial Mechanics and Orbits 1 — Questions and Answers
Question 1: Which of Kepler's Laws states that planets sweep out equal areas in equal times?
- Second Law (Law of Equal Areas) (Correct answer)
- First Law (Law of Ellipses)
- Third Law (Law of Periods)
- Newton's extension of Kepler's laws
Correct answer: Second Law (Law of Equal Areas)
Kepler's Second Law states that a line segment joining a planet and the Sun sweeps out equal areas during equal time intervals, meaning planets move faster when closer to the Sun.
Question 2: What is the eccentricity of a perfectly circular orbit?
- 0 (Correct answer)
- 1
- 0.5
- 2
Correct answer: 0
A perfectly circular orbit has an eccentricity of 0, while values between 0 and 1 represent elliptical orbits, and values of 1 or greater represent parabolic or hyperbolic trajectories.
Question 3: What is the point in a planet's orbit where it is closest to the Sun called?
- Perihelion (Correct answer)
- Aphelion
- Perigee
- Apogee
Correct answer: Perihelion
Perihelion is the point in a planet's orbit closest to the Sun; Earth reaches perihelion in early January each year at about 147 million km from the Sun.
Question 4: What is a Lagrange point?
- A position where gravitational forces allow a small object to maintain a stable orbit (Correct answer)
- The point where a planet's gravity equals the Sun's gravity
- A location where two planets have the same orbital speed
- A fixed point in space relative to the galactic center
Correct answer: A position where gravitational forces allow a small object to maintain a stable orbit
Lagrange points are five specific positions in a two-body orbital system where a smaller object can maintain a stable position due to the balance of gravitational forces.
Question 5: According to Kepler's Third Law, how does a planet's orbital period relate to its distance from the Sun?
- The square of the period is proportional to the cube of the semi-major axis (Correct answer)
- The period is proportional to the square of the distance
- The period equals the distance divided by orbital speed
- The period is inversely proportional to the planet's mass
Correct answer: The square of the period is proportional to the cube of the semi-major axis
Kepler's Third Law states that P² ∝ a³, meaning the square of a planet's orbital period is proportional to the cube of the semi-major axis of its orbit.
Question 6: What is orbital resonance?
- A ratio relationship between orbital periods of two objects that gravitationally affects each other (Correct answer)
- The vibration of a satellite due to tidal forces
- The synchronization of a moon's spin with its orbital period
- The alignment of planets in the same orbital plane
Correct answer: A ratio relationship between orbital periods of two objects that gravitationally affects each other
Orbital resonance occurs when two orbiting bodies exert regular gravitational influences on each other due to their orbital periods forming a simple integer ratio.
Astronomy Astronomy Celestial Mechanics and Orbits 1
Which of Kepler's Laws states that planets sweep out equal areas in equal times?