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Reminders Answering cell phones during class shaves a little off your grade each time. You will be dropped after six hours of absence. The attendance requirement applies not only to students who can attend class, but also to students who cannot attend class. CHAPTER 2: Gravitation and the Waltz of the Planets For the Quiz Know the basics of the Geocentric and Heliocentric theories, and be able to explain planetary motion in terms of each. Be able to state Kepler’s laws and understand their meaning. Be able to define “aphelion” and “perihelion.” Be able to state Newton’s laws of motion, and understand their meaning. Be able to state Newton’s law of gravitation and understand its meaning. Define synodic and siderial period of a planet. Know the important observations Galileo made with his telescope, and why those observations were important. WHAT DO YOU THINK? What makes a theory scientific? What is the shape of the Earth’s orbit around the Sun? Do the planets orbit the Sun at constant speeds? Do all the planets orbit the Sun at the same speed? How much force does it take to keep an object moving in a straight line at a constant speed? How does an object’s mass differ when measured on the Earth and on the Moon? The scientific method is used to develop new scientific theories. Scientific theories are accepted when they make testable predictions that can be verified using new observations and experiments. Early models of the universe attempted to explain the motion of the five visible planets against the background of “fixed” stars. The main problem was that the planets do not move uniformly against the background of stars, but instead appear to stop, move backward, then move forward again. This backward motion is referred to as retrograde motion. Ptolemy explained this motion using a geocentric (Earthcentered) model of the solar system in which the planets orbited the Earth indirectly, by moving on epicycles which in turn orbited the Earth. In the geocentric model of the solar system developed by Ptolemy, A) the planets move with varying speeds in elliptical orbits around the Earth. B) the planets move at constant speeds in circular orbits around the Earth. C) the planets move in circular epicycles around the Sun while the Sun moves in a circular orbit around the Earth. D) the planets move in circular epicycles while the centers of the epicycles move in circular orbits around the Earth. When observing planetary motions from the Earth, the phrase “retrograde motion” refers to A) the apparent westward motion of the planet (and the Sun, the Moon, and stars) across the sky due to the rotation of the Earth. B) motion of the planet away from the Earth during part of its orbit. C) a slow eastward motion of the planet from night to night compared to the background stars. D) a slow westward motion of the planet from night to night compared to the background stars. Nicolaus Copernicus developed the first heliocentric (sun-centered) model of the solar system. In this model, the retrograde motion of Mars is seen when the Earth passes Mars in its orbit around the Sun. 1473-1543 We define special positions of the planets in their orbits depending where they appear in our sky. For example, while at a conjunction, a planet will appear in the same part of the sky as the Sun, while at opposition, a planet will appear opposite the Sun in our sky. However, the cycle of these positions (a synodic period) is different from the actual orbital period of the planet around the Sun (a sidereal period) because both the Earth and the planet orbit around the Sun. The Copernican system for planetary motions is A) Earth-centered, with the planets, the Sun, and the stars mounted on crystal spheres, pivoted to allow the correct motions around the Earth. B) Earth-centered, with the planets moving in epicycles around the Earth. C) Sun-centered, with the planets moving in elliptical orbits, the Sun being at one focus of the ellipse. D) Sun-centered, with the planets moving in perfect circles around the Sun. When Venus is at superior conjunction, A) it is at its smallest distance from the Earth. B) it is at its greatest angle from the Sun as seen from the Earth. C) its speed in its orbit has its greatest value. D) it is at its greatest distance from the Earth. When Mars is at opposition, it is A) high in the sky at midnight. B) high in the sky at sunset. C) high in the sky at noon. D) rising at about midnight. When a planet is seen at opposition, it is always A) at its most distant point from the Sun. B) at its closest point to the Sun. C) at its most distant point from the Earth. D) at its closest point to the Earth. When a new “star” appeared in the sky during the 16th century, a Danish astronomer named Tycho Brahe (1546-1601) reasoned that the distance of the object may be determined by measuring the amount of parallax. The apparent change in the location of an object due to the difference in location of the observer is called parallax. Because the parallax of the “star” was too small to measure, Tycho knew that it had to be among the other stars, thus disproving the ancient belief that the “heavens” were fixed and unchangeable. The phenomenon of parallax is A) the change in the apparent position of a nearby object compared to background objects as a result of the motion of the object. B) the change in direction of motion of a planet from retrograde to direct motion. C) the apparent change in angular size of an object as it moves toward or away from an observer. D) the change in apparent position of a nearby object compared to background objects as a result of the motion of the observer. After Tycho Brahe’s death, Johannes Kepler (pictured here with Tycho in the background) used Tycho’s observations to deduce the three laws of planetary motion. 1571-1630 KEPLER’S THREE LAWS OF PLANETARY MOTION LAW #1. The orbit of a planet around the Sun is an ellipse with the Sun at one focus. Kepler's first law states that a planet moves around the Sun A) in a circle, with the Sun at the center. B) in an elliptical orbit, with the Sun at one focus. C) in an elliptical orbit, with the Sun on the minor axis of the ellipse. D) in an elliptical orbit, with the Sun at the center of the ellipse. The semimajor axis of an ellipse is A) the distance from the center of the ellipse to one end, along the largest diameter of the ellipse. B) the distance from the center to one side of the ellipse, along the shortest diameter of the ellipse. C) the distance from one focus to any point on the circumference of the ellipse. D) half the distance between the foci of the ellipse. The amount of elongation in a planet’s orbit is defined as its orbital eccentricity. An orbital eccentricity of 0 is a perfect circle while an eccentricity close to 1.0 is nearly a straight line. In an elliptical orbit, the distance from a planet to the Sun varies. The point in a planet’s orbit closest to the Sun is called perihelion, and the point farthest from the Sun is called aphelion. KEPLER’S THREE LAWS OF PLANETARY MOTION LAW #2: A line joining the planet and the Sun sweeps out equal areas in equal intervals of time. Planet moves slower in its orbit when farther away from the Sun. Planet moves faster in its orbit when closer to the Sun. Kepler's second law states: A) A line joining a planet to the Sun moves equal distances along the planet's orbit in equal times. B) A line joining a planet to the Sun sweeps through equal angles in equal times. C) A line joining a planet to the Sun points in the same direction at all times. D) A line joining a planet to the Sun sweeps out equal areas in equal times. Kepler's second law states that a planet moves fastest when it A) passes through the minor axis. B) is closest to the Sun. C) is farthest from the Sun. D) is at conjunction. KEPLER’S THREE LAWS OF PLANETARY MOTION LAW #3: The square of a planet’s sidereal period around the Sun is directly proportional to the cube of its semi-major axis. This law relates the amount of time for the planet to complete one orbit around the Sun to the planet’s average distance from the Sun. If we measure the orbital periods (P) in years and distances (a) in astronomical units, then the law mathematically can be written as P2 = a3. Kepler's third law tells us that A) the period of a planet in years is the same number as its semimajor axis in AU. B) the square of a planet's period in years is the same number as the cube of its semimajor axis in AU. C) the square of a planet's period in years is the same number as the fourth power of its semimajor axis in AU. D) the cube of a planet's period in years is the same number as the square of its semimajor axis in AU. Kepler's third law can be described in which of the following ways? A) The time to complete one revolution of its orbit is dependent upon the size or radius of the planet. B) The smaller the radius of a planet, the more rapidly it rotates on its axis. C) The smaller the orbit, the longer it takes for the planet to complete one revolution. D) The larger the orbit, the longer it takes for the planet to complete one revolution. Galileo was the first to use a telescope to examine celestial objects. His discoveries supported a heliocentric model of the solar system. 1564-1642 Galileo discovered that Venus, like the Moon, undergoes a series of phases as seen from Earth. In the Ptolemaic (geocentric) model, Venus would be seen in only new or crescent phases. However, as Galileo observed, Venus is seen in all phases, which agrees with the Copernican model as shown. Galileo also discovered moons in orbit around the planet Jupiter. This was further evidence that the Earth was not the center of the universe. Galileo's early observations of the sky with his newly made telescope included A) the discovery of Pluto. B) the discovery of the phases of Venus. C) the discovery of of Jupiter's magnetosphere. D) the discovery of retrograde motion in planets. Which of the following statements CORRECTLY states the significance of Galileo's observation that Jupiter has satellites (moons)? A) It showed that Jupiter must be four times the size of the Earth (because Jupiter has four moons and the Earth has one). B) It showed that bodies can orbit an object other than the Earth. C) It was interesting but had no other particular significance. D) It showed that Jupiter must orbit the Sun, not the Earth. Isaac Newton formulated three laws to describe the fundamental properties of physical reality. NEWTON’S THREE LAWS OF MOTION LAW #1: A body remains at rest or moves in a straight line at constant speed unless acted upon by a net outside force. LAW #2: The acceleration of an object is proportional to the force acting on it. LAW #3: Whenever one body exerts a force on a second body, the second body exerts an equal and opposite force on the first body. 1642-1727 According to Newton's first law, A) if no net force is acting upon an object, then both the object's speed and direction of travel will be constant. B) the larger the rate of change of speed of an object, the larger the force acting upon the object. C) an applied force always causes a change in the speed of an object. D) an applied force always causes a change in the direction of travel of an object. The acceleration of an object is defined as A) the rate of changes of its speed. B) the rate of change of its velocity. C) the rate of change of its direction of travel. D) the rate of change of its position. Which of the following four objects or persons is NOT accelerating? A) A bicyclist gradually slowing down on a straight road while coasting toward a stop sign B) A motorcyclist traveling around a circular racetrack at a constant speed C) An apple falling to the ground from an apple tree D) An Olympic swimmer exerting considerable force to maintain a constant speed in a straight line through the water Two spaceships that have different masses but rocket engines of identical force are at rest in space. If they fire their rockets at the same time, which ship will speed up faster? A) The one with the lower mass B) The one with the higher mass C) They will increase speed at the same rate because they have identical rocket engines. D) They will not speed up at all, but move at a constant speed because they are in space and the rocket has nothing against which to push. An unbalanced force acting on an object will ALWAYS cause it to A) change its direction of travel. B) change its speed or its direction of travel or both. C) change its acceleration. D) change its speed. Which of the following statements is a CORRECT version of Newton's third law? A) Whenever some object A exerts a force on some other object B, B must exert a force of equal magnitude on A in the same direction. B) Whenever some object A exerts a force on some other object B, B must exert a force of equal magnitude on A in the opposite direction. C) Whenever two forces act, they must be equal in magnitude and opposite in direction. D) Whenever any object feels some force, it must also feel another force of equal magnitude in the opposite direction from some other source. Newton also discovered that gravity, the force that causes objects to fall to the ground on Earth, is the same force that keeps the Moon in its orbit around the Earth. NEWTON’S LAW OF UNIVERSAL GRAVITATION Two objects attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. With his laws, Newton was able to derive Kepler’s three laws, as well as predict other possible orbits. The force of gravity between two objects is proportional to A) the sum of their masses. B) the difference of their masses. C) the ratio of their masses. D) the product of their masses. Newton’s laws were applied to other objects in our solar system. Using Newton’s methods, Edmund Halley worked out the details of a comet’s orbit and predicted its return. Deviations from Newton’s Laws in the orbit of the planet Uranus led to the discovery of the eighth planet, Neptune. How was the planet Neptune discovered? A) It was discovered by mathematical prediction using Newton's laws. B) It happened to pass close to Jupiter in the sky and was discovered by an astronomer studying Jupiter. C) It was discovered accidentally during a telescopic survey of the sky. D) No one knows—it has been known since ancient times. Key Terms acceleration angular momentum aphelion astronomical unit configuration (of a planet) conjunction conservation of angular momentum cosmology ellipse elongation focus (of an ellipse) force Galilean moons (satellites) gravity heliocentric cosmology hyperbola inferior conjunction Kepler’s laws kinetic energy law of equal areas law of inertia light-year mass model momentum Newton’s laws of motion Occam’s razor opposition parabola parallax parsec perihelion physics potential energy retrograde motion scientific method scientific theory semimajor axis (of an ellipse) sidereal period superior conjunction synodic period universal constant of gravitation universal law of gravitation velocity weight work