Key Ideas

Apparent Motions of the Planets: Like the Sun and the Moon, the planets move on the celestial sphere with respect to the background of stars. Most of the time a planet moves eastward in direct motion, in the same direction as the Sun and the Moon, but from time to time it moves westward in retrograde motion.

The Ancient Geocentric Model: Ancient astronomers believed Earth to be at the center of the universe. They invented a complex system of epicycles and deferents to explain the direct and retrograde motions of the planets on the celestial sphere.

Copernicus’s Heliocentric Model: Copernicus’s heliocentric (Sun-centered) theory simplified the general explanation of planetary motions.

• In a heliocentric system, Earth is one of the planets orbiting the Sun.
• A planet undergoes retrograde motion as seen from Earth when Earth and the planet pass each other.
• The sidereal period of a planet, its true orbital period, is measured with respect to the stars. Its synodic period is measured with respect to Earth and the Sun (for example, from one opposition to the next).

Kepler’s Improved Heliocentric Model and Elliptical Orbits: Copernicus thought that the orbits of the planets were combinations of circles. Using data collected by Tycho Brahe, Kepler deduced three laws of planetary motion: (1) the orbits are in fact ellipses; (2) a planet’s speed varies as it moves around its elliptical orbit; and (3) the orbital period of a planet is related to the size of its orbit.

Evidence for the Heliocentric Model: The invention of the telescope led Galileo to new discoveries that supported a heliocentric model. These included his observations of the phases of Venus and of the motions of four moons around Jupiter.

Newton’s Laws of Motion: Isaac Newton developed three principles, called the laws of motion, that apply to the motions of objects on Earth as well as in space. These are (1) the tendency of an object to maintain a constant velocity, (2) the relationship between the net outside force on an object and the object’s acceleration, and (3) the principle of action and reaction. These laws and Newton’s law of universal gravitation can be used to deduce Kepler’s laws. They lead to extremely accurate descriptions of planetary motions.

• The mass of an object is a measure of the amount of matter in the object. Its weight is a measure of the force with which the gravity of some other object pulls on it.
• In general, the path of one object about another, such as that of a planet or comet about the Sun, is one of the curves called conic sections: circle, ellipse, parabola, or hyperbola.

Energy: There are different forms of energy an object can have. Kinetic and gravitational potential energy are the most important for orbiting objects.

• Kinetic energy: The greater an object’s speed, the larger its kinetic energy. For two objects with equal speed, the more massive object has a larger kinetic energy.
• Gravitational potential energy: The farther an object is located from the surface of a planet, the greater its gravitational energy.
• Conservation of energy: Energy can change forms, and be transferred from one object to another, but energy cannot be created or destroyed.

Escape Speed: The escape speed of a planet is the ejection speed an object would need to have near the surface of the planet so that the object can “break free” from the planet and never return.

• The escape speed does not depend on the mass of the object, but it does depend on both the size and mass of the planet.

Tidal Forces: Tidal forces are caused by differences in the gravitational pull that one object exerts on different parts of a second object.

• The tidal forces of the Moon and the Sun produce tides in Earth’s oceans.
• The tidal forces of Earth have locked the Moon into synchronous rotation.