Astronomy 101Astronomy 101Section 020Section 020

LectureLecture 4 4

Gravitation and Gravitation and the Waltz of the the Waltz of the

PlanetsPlanets

John T. McGraw, John T. McGraw, ProfessorProfessor

Laurel Ladwig, Laurel Ladwig, Planetarium ManagerPlanetarium Manager

How How EclipsesEclipses Can Occur Can Occur

Three Types of Three Types of Lunar EclipsesLunar Eclipses

A Total Lunar EclipseA Total Lunar Eclipse

The Geometry of a The Geometry of a Total Solar EclipseTotal Solar Eclipse

Solar EclipsesSolar Eclipses

Total (1991, La Paz) and annular (1973, Total (1991, La Paz) and annular (1973, Costa Rica) solar eclipses.Costa Rica) solar eclipses.

Eclipse Paths for Total Solar Eclipses:Eclipse Paths for Total Solar Eclipses:1997 - 20201997 - 2020

Ancient astronomers invented geocentric Ancient astronomers invented geocentric models to explain planetary motionsmodels to explain planetary motions

Like the Sun and Moon, the planets move on the celestial Like the Sun and Moon, the planets move on the celestial sphere with respect to the background of starssphere with respect to the background of stars

Most of the time a planet moves eastward in direct motion, Most of the time a planet moves eastward in direct motion, in the same direction as the Sun and the Moon, but from in the same direction as the Sun and the Moon, but from time to time it moves westward in retrograde motiontime to time it moves westward in retrograde motion

Ancient astronomers believed the Earth to be at the center of the universe.Ancient astronomers believed the Earth to be at the center of the universe.

They invented a complex system of They invented a complex system of deferentsdeferents and and epicyclesepicycles,,each of which is a “perfect circle,” to describe retrograde motion.each of which is a “perfect circle,” to describe retrograde motion.

The Scientific MethodThe Scientific Method(or “how to be correct every single time”)(or “how to be correct every single time”)

1.1. Observe some aspect of the Observe some aspect of the universe.universe.

2.2. Invent a tentative Invent a tentative description, called a description, called a hypothesishypothesis, , that is consistent with what you that is consistent with what you have observed.have observed.

3.3. Use the hypothesis to make Use the hypothesis to make predictions.predictions.

4.4. Test those predictions by Test those predictions by experiments or further experiments or further observations and modify the observations and modify the hypothesis in the light of your hypothesis in the light of your results.results.

5.5. Repeat steps 3 and 4 until Repeat steps 3 and 4 until there are no discrepancies there are no discrepancies between theory and experiment between theory and experiment and/or observation. and/or observation.

Nicolaus Copernicus devised the first Nicolaus Copernicus devised the first comprehensive heliocentric modelcomprehensive heliocentric model

Copernicus’s heliocentric Copernicus’s heliocentric (Sun-centered) theory (Sun-centered) theory simplified the general simplified the general explanation of planetary explanation of planetary motionsmotions

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

The sidereal period of a The sidereal period of a planet, its true orbital planet, its true orbital period, is measured with period, is measured with respect to the starsrespect to the stars

A planet undergoes retrograde motion as A planet undergoes retrograde motion as seen from Earth when the Earth and the seen from Earth when the Earth and the

planet pass each otherplanet pass each other

(The Galles and Unser families know all about this!)

A planet’s synodic period is measured with A planet’s synodic period is measured with respect to the Earth and the Sun (for respect to the Earth and the Sun (for

example, from one opposition to the next)example, from one opposition to the next)

Tycho Brahe’s astronomical observations Tycho Brahe’s astronomical observations disproved ancient ideas about the heavensdisproved ancient ideas about the heavens

Diurnal (daily) Diurnal (daily) parallaxparallax of a star of a star

(Or, why you havetwo eyes to keep the other drivers fromcrashing into you, andother useful stuff.)

(Or, how to dotrigonometry in yourhead without reallyknowing it.)

Johannes Kepler proposed elliptical pathsJohannes Kepler proposed elliptical pathsfor the planets about the Sunfor the planets about the Sun

Using data collected by Using data collected by Tycho Brahe, Kepler Tycho Brahe, Kepler deduced three laws of deduced three laws of planetary motion:planetary motion:

1.1. the orbits are the orbits are

ellipsesellipses2.2. a planet’s speed a planet’s speed

varies as it moves varies as it moves around its elliptical around its elliptical orbit orbit

3.3. the orbital period of the orbital period of a planet is related to a planet is related to the size of its orbitthe size of its orbit

Kepler’s First LawKepler’s First Law

Kepler’s Second LawKepler’s Second Law

Kepler’s Third LawKepler’s Third Law

PP22 = a = a33

P P = planet’s sidereal period, in years= planet’s sidereal period, in yearsa a = planet’s semimajor axis, in AU= planet’s semimajor axis, in AU

Galileo’s discoveries with a telescope Galileo’s discoveries with a telescope strongly supported a heliocentric modelstrongly supported a heliocentric model

The invention of the The invention of the telescope led Galileo telescope led Galileo to new discoveries to new discoveries that supported a that supported a heliocentric modelheliocentric model

These included his These included his observations of the observations of the phases of Venus and phases of Venus and of the motions of four of the motions of four moons around Jupitermoons around Jupiter

Application of the Application of the scientific methodscientific method

One of Galileo’s most important discoveries with the One of Galileo’s most important discoveries with the telescope was that Venus exhibits phases like those of the telescope was that Venus exhibits phases like those of the MoonMoon

Galileo also noticed that the apparent size of Venus as seen Galileo also noticed that the apparent size of Venus as seen through his telescope was related to the planet’s phasethrough his telescope was related to the planet’s phase

Venus appears small at gibbous phase and largest at Venus appears small at gibbous phase and largest at crescent phasecrescent phase

There is a correlation between the phases of Venus There is a correlation between the phases of Venus and the planet’s angular distance from the Sunand the planet’s angular distance from the Sun

Geocentric Model of the Solar SystemGeocentric Model of the Solar System

To explain why Venus is To explain why Venus is never seen very far from never seen very far from the Sun, the Ptolemaic the Sun, the Ptolemaic model had to assume that model had to assume that the deferents of Venus and the deferents of Venus and of the Sun move together of the Sun move together in lockstep, with the in lockstep, with the epicycle of Venus centered epicycle of Venus centered on a straight line between on a straight line between the Earth and the Sunthe Earth and the Sun

In this model, Venus was In this model, Venus was never on the opposite side never on the opposite side of the Sun from the Earth, of the Sun from the Earth, and so it could never have and so it could never have shown the gibbous phases shown the gibbous phases that Galileo observedthat Galileo observed

In 1610 Galileo In 1610 Galileo discovered four discovered four moons, now moons, now called the called the Galilean Galilean satellites, satellites, orbiting Jupiterorbiting Jupiter

Galileo’s mini-solar systemled to the immense fame of Ole Roemer!

Isaac Newton formulated three laws that describe Isaac Newton formulated three laws that describe fundamental properties of physical realityfundamental properties of physical reality

Isaac Newton developed three Isaac Newton developed three principles, called the laws of principles, called the laws of motion, that apply to the motion, that apply to the motions of objects on Earth as motions of objects on Earth as well as in spacewell as in space

These areThese are1.1. the law of inertia: a body the law of inertia: a body

remains at rest, or moves in a remains at rest, or moves in a straight line at a constant straight line at a constant speed, unless acted upon by a speed, unless acted upon by a net outside forcenet outside force

2.2. F = m F = m xx a (the force on an a (the force on an object is directly proportional to object is directly proportional to its mass and acceleration)its mass and acceleration)

3.3. the principle of action and the principle of action and reaction: whenever one body reaction: whenever one body exerts a force on a second exerts a force on a second body, the second body exerts body, the second body exerts an equal and opposite force on an equal and opposite force on the first bodythe first body

Newton’s Law of Universal GravitationNewton’s Law of Universal Gravitation

F F = gravitational force between two objects= gravitational force between two objectsmm = mass of first object = mass of first object

M = mass of second objectM = mass of second objectr r = distance between objects= distance between objects

G G = universal constant of gravitation= universal constant of gravitation

If the masses are measured in kilograms and the distance If the masses are measured in kilograms and the distance between them in meters, then the force is measured in between them in meters, then the force is measured in newtonsnewtons

Laboratory experiments have yielded a value for Laboratory experiments have yielded a value for G G of of G G = 6.67 × 10–11 newton • m= 6.67 × 10–11 newton • m22/kg/kg22

mar

mMGF

2

Newton’s description of gravity accounts for Newton’s description of gravity accounts for Kepler’s laws and explains the motions of the Kepler’s laws and explains the motions of the

planets and other orbiting bodies planets and other orbiting bodies

OrbitsOrbits

The law of universal The law of universal gravitation accounts for gravitation accounts for planets not falling into the planets not falling into the Sun nor the Moon crashing Sun nor the Moon crashing into the Earthinto the Earth

Paths A, B, and C do not Paths A, B, and C do not have enough horizontal have enough horizontal velocity to escape Earth’s velocity to escape Earth’s surface whereas Paths D, surface whereas Paths D, E, and F do.E, and F do.

Path E is where the Path E is where the horizontal velocity is horizontal velocity is exactly what is needed so exactly what is needed so its orbit matches the its orbit matches the circular curve of the Earthcircular curve of the Earth

Orbits may be any of a family of curves Orbits may be any of a family of curves called conic sectionscalled conic sections

Gravitational forces between two objects Gravitational forces between two objects produce tidesproduce tides

The origin of tidal forcesThe origin of tidal forces

The origin of Earth tidesThe origin of Earth tides

The origin of Earth tidesThe origin of Earth tides

The origin of Earth tidesThe origin of Earth tides

The origin of Earth tidesThe origin of Earth tides

The origin of deadly tides!The origin of deadly tides!