Which of the following Kepler's laws comes from the observations that planets appear to move slower when they are farther from the sun than when they are nearer?

The correct answer is Law of areas.

Key Points

• The Law of Areas, also known as Kepler's Second Law, states that a line segment joining a planet and the sun sweeps out equal areas during equal intervals of time.
• This law implies that planets move faster when they are closer to the sun and slower when they are farther from the sun.
• Kepler formulated this law based on the precise observations of planetary motions made by Tycho Brahe.
• It is fundamental in understanding the elliptical orbits of planets and their varying velocities at different points in the orbit.

Additional Information

• Kepler's Laws of Planetary Motion
  • Law of Orbits: Planets move in elliptical orbits with the Sun at one of the foci.
  • Law of Areas: A line joining a planet and the Sun sweeps out equal areas during equal intervals of time.
  • Law of Periods: The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.
• Elliptical Orbits
  • Planets do not move in perfect circles but in ellipses, with the sun at one focus.
  • The shape of the elliptical orbit is defined by its eccentricity.
• Velocity of Planets
  • Planets move faster when they are closer to the sun (perihelion) and slower when they are farther from the sun (aphelion).
  • This variation in velocity is a direct consequence of the Law of Areas.
• Historical Context
  • Kepler's laws were derived from the meticulous observations of Tycho Brahe.
  • These laws significantly advanced the heliocentric model of the solar system proposed by Copernicus.