CHAPTER 4 Gravitation and the Waltz of the Planets CHAPTER 4 Gravitation and the Waltz of the Planets

How ancient astronomers attempted to explain the motions of the planets How ancient astronomers attempted to explain the motions of the planets What led Copernicus to a Sun-centered model of planetary motion What led Copernicus to a Sun-centered model of planetary motion How Tycho’s naked-eye observations of the sky revolutionized ideas about the heavens How Tycho’s naked-eye observations of the sky revolutionized ideas about the heavens How Kepler deduced the shapes of the orbits of the planets How Kepler deduced the shapes of the orbits of the planets What you will learn…

How Galileo’s pioneering observations with a telescope supported a Sun-centered model How Galileo’s pioneering observations with a telescope supported a Sun-centered model The ideas behind Newton’s laws, which govern the motion of all physical objects, including the planets The ideas behind Newton’s laws, which govern the motion of all physical objects, including the planets Why planets stay in their orbits and don’t fall into the Sun Why planets stay in their orbits and don’t fall into the Sun What causes ocean tides on Earth What causes ocean tides on Earth What you will learn…

Nicolaus Copernicus ( )

The Geometry of Parallax d (in Parsecs) = 1 (AU) p (in arcseconds) p 1 parsec (pc) = 3.26 ly

Comet – beyond the Moon Supernova – far away Naked eye observations of planets Accuracy through repetition Best observations of planetary positions Tycho Brahe ( )

Johannes Kepler ( )

Kepler’s 1 st Law of Planetary Motion Kepler’s 1 st Law of Planetary Motion Planets move in elliptical orbits with the Sun at one foci Sun Foci (sing. Focus) Perihelion Aphelion Average distance from the Sun = 1 Astronomical Unit (1 A.U.)

Kepler’s 2 nd Law of Planetary Motion Kepler’s 2 nd Law of Planetary Motion Planets move faster at perihelion than at aphelion. 1 Month

Kepler’s 3 rd Law of Planetary Motion Kepler’s 3 rd Law of Planetary Motion Period is related to average distance P 2 = a 3 P  period of the planet around the Sun in years a  semi-major axis (or orbital distance) of the planet from the Sun in AU Can be used for anything orbiting anything else in space!

Galileo Galilei ( ) Knew of Copernicus’s & Kepler’s work Used a telescope to look at the sky

The Moon was an imperfect object, i.e. craters, landscape

Saturn is imperfect, i.e. rings

And so is the Sun, i.e. sunspots

Sir Isaac Newton ( )

Newton’s 1 st Law of Motion Newton’s 1 st Law of Motion Objects at rest (or in motion) tend to stay at rest (or in motion) Inertia  the tendency of an object to stay at rest (or motion) An object’s mass is the measure of its inertia The more mass, the more inertia!

Newton’s 2 nd Law of Motion The acceleration of an object depends on the force(s) exerted on it and the object’s mass Force = Mass * Acceleration F = m*a (unit of force is the Newton or N… 1 kg accelerated at 1 m/s 2 )

Newton’s 3 rd Law of Motion Newton’s 3 rd Law of Motion For every action there is an equal and opposite reaction. The three laws of motion form the basis for the most important law of all (astronomically speaking)…

Newton’s Universal Law of Gravitation F  force of gravity (measured in Newtons) G  universal gravitational constant ( 6.67 x Nm 2 /kg 2 ) M 1, M 2  masses that attract each other gravitationally R  distance from “centers” Gravity is the most important force in the Universe

Newton’s Revisions to Kepler’s Laws of Planetary Motion Newton agreed with Kepler’s 1 st Law…all objects the orbit the Sun are either in bound (i.e. elliptical or circular) orbits OR unbound (i.e. parabolic or hyperbolic) orbits

Newton’s Revisions to Kepler’s Laws of Planetary Motion Newton explained the cause of Kepler’s 2 nd Law was… GRAVITY !!!

Newton’s Revisions to Kepler’s Laws of Planetary Motion Newton used Kepler’s 3 rd Law to find the mass of the Sun… kg (1.98 x kg) Importance: if you know period and average distance of a planet, you can find mass of the Sun, any planet or any mass that orbits around another object!!! This is very important in astronomy!

Key Ideas Apparent Motions of the Planets: Like the Sun and 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 or prograde motion, in the same direction as the Sun and the Moon, but from time to time it moves westward in retrograde motion. Apparent Motions of the Planets: Like the Sun and 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 or prograde 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 the 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. The Ancient Geocentric Model: Ancient astronomers believed the 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.

Key Ideas Copernicus’s Heliocentric Model: Copernicus’s heliocentric (Sun-centered) theory simplified the general explanation of planetary motions. Copernicus’s Heliocentric Model: Copernicus’s heliocentric (Sun-centered) theory simplified the general explanation of planetary motions. In a heliocentric system, the Earth is one of the planets orbiting the Sun. In a heliocentric system, the Earth is one of the planets orbiting the Sun. A planet undergoes retrograde motion as seen from Earth when the Earth and the planet pass each other. A planet undergoes retrograde motion as seen from Earth when the Earth and the planet pass each other.

Key Ideas 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. 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 ellipses (1) the orbits are ellipses (2) a planet’s speed varies as it moves around its elliptical orbit (i.e. fastest at perihelion; slowest at aphelion) (2) a planet’s speed varies as it moves around its elliptical orbit (i.e. fastest at perihelion; slowest at aphelion) (3) the orbital period of a planet is related to the size of its orbit. (3) the orbital period of a planet is related to the size of its orbit.

Key Ideas 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, motions of four moons around Jupiter, rings of Saturn, lunar geography & sunspots 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, motions of four moons around Jupiter, rings of Saturn, lunar geography & sunspots 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. 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.

Key Ideas (1) the tendency of an object to maintain a constant velocity, (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, (2) the relationship between the net outside force on an object and the object’s acceleration, and (3) the principle of action and reaction. 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. 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. 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.

Key Ideas 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. 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. 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 Sun produce tides in the Earth’s oceans (i.e spring and neap tides). The tidal forces of the Earth have locked the Moon into synchronous rotation.