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

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

How ancient astronomers attempted to How ancient astronomers attempted to explain the motions of the planetsexplain the motions of the planets

What led Copernicus to a Sun-centered What led Copernicus to a Sun-centered model of planetary motionmodel of planetary motion

How Tycho’s naked-eye observations of the How Tycho’s naked-eye observations of the sky revolutionized ideas about the heavenssky revolutionized ideas about the heavens

How Kepler deduced the shapes of the How Kepler deduced the shapes of the orbits of the planetsorbits of the planets

What you will learn…

How Galileo’s pioneering observations with a How Galileo’s pioneering observations with a telescope supported a Sun-centered modeltelescope supported a Sun-centered model

The ideas behind Newton’s laws, which The ideas behind Newton’s laws, which govern the motion of all physical objects, govern the motion of all physical objects, including the planetsincluding the planets

Why planets stay in their orbits and don’t fall Why planets stay in their orbits and don’t fall into the Suninto the Sun

What causes ocean tides on EarthWhat causes ocean tides on Earth

What you will learn…

Nicolaus Copernicus (1473-1543)

The Geometry The Geometry of Parallaxof 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 BraheTycho Brahe(1546-1601) (1546-1601)

Johannes Kepler Johannes Kepler (1571-1630)(1571-1630)

Kepler’s 1Kepler’s 1stst Law of Planetary Motion 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 2Kepler’s 2ndnd Law of Planetary Law of Planetary MotionMotion

Planets move faster at perihelion than at aphelion.

1 Month1 Month

Kepler’s 3Kepler’s 3rdrd Law of Planetary Law of Planetary MotionMotion

Period is related to average distance

P2 = a3

• 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 Galileo Galilei (1564-1642) (1564-1642)

• 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(1642-1727)

Newton’s 1Newton’s 1stst Law of Motion 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 2Newton’s 2ndnd Law of Motion Law of Motion

The acceleration of an object The acceleration of an object depends on the force(s) exerted depends on the force(s) exerted

on it and the object’s masson it and the object’s mass

Force = Mass * AccelerationF = m*a

(unit of force is the Newton or N…1 kg accelerated at 1 m/s2)

Newton’s 3Newton’s 3rdrd Law of Motion 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 GravitationNewton’s Universal Law of Gravitation

1 22

GM MF

R

F force of gravity (measured in Newtons)

G universal gravitational constant (6.67 x 10-11 Nm2/kg2)

M1, M2 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 1st 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 2nd Law was…

GRAVITY !!!

Newton’s Revisions to Kepler’s Laws of Planetary Motion

•Newton used Kepler’s 3rd Law to find the mass of the Sun…• 1 980 000 000 000 000 000 000 000 000 000 kg

(1.98 x 1030 kg)2 3

22 3

1 2

became...

4

( )

P ka

P aG M M

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

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

Key Ideas

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

In a heliocentric system, the Earth is one of the planets In a heliocentric system, the Earth is one of the planets orbiting the Sun.orbiting the Sun.

A planet undergoes retrograde motion as seen from A planet undergoes retrograde motion as seen from Earth when the Earth and the planet pass each other.Earth when the Earth and the planet pass each other.

Key Ideas

Kepler’s Improved Heliocentric Model and Elliptical Kepler’s Improved Heliocentric Model and Elliptical Orbits:Orbits: Copernicus thought that the orbits of the planets Copernicus thought that the orbits of the planets were combinations of circles. Using data collected by were combinations of circles. Using data collected by Tycho Brahe, Kepler deduced three laws of planetary Tycho Brahe, Kepler deduced three laws of planetary motion.motion.

(1) the orbits are ellipses(1) the orbits are ellipses (2) a planet’s speed varies as it moves around its (2) a planet’s speed varies as it moves around its

elliptical orbit (i.e. fastest at perihelion; slowest at elliptical orbit (i.e. fastest at perihelion; slowest at aphelion)aphelion)

(3) the orbital period of a planet is related to the size of (3) the orbital period of a planet is related to the size of its orbit.its orbit.

Key Ideas

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

Newton’s Laws of Motion:Newton’s Laws of Motion: Isaac Newton developed Isaac Newton developed three principles, called the laws of motion, that apply to three principles, called the laws of motion, that apply to the motions of objects on Earth as well as in space. the motions of objects on Earth as well as in space.

Key Ideas

(1) the tendency of an object to maintain a constant (1) the tendency of an object to maintain a constant velocity,velocity,

(2) the relationship between the net outside force on an (2) the relationship between the net outside force on an object and the object’s acceleration,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 These laws and Newton’s law of universal gravitation Newton’s law of universal gravitation

can be used to deduce Kepler’s laws. They lead to can be used to deduce Kepler’s laws. They lead to extremely accurate descriptions of planetary motions.extremely accurate descriptions of planetary motions.

The mass of an object is a measure of the amount of The mass of an object is a measure of the amount of matter in the object. Its weight is a measure of the force matter in the object. Its weight is a measure of the force with which the gravity of some other object pulls on it.with which the gravity of some other object pulls on it.

Key Ideas In general, the path of one object about another, such as In general, the path of one object about another, such as

that of a planet or comet about the Sun, is one of the that of a planet or comet about the Sun, is one of the curves called conic sections: circle, ellipse, parabola, or curves called conic sections: circle, ellipse, parabola, or hyperbola.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.