ASTRO 6570

Lecture 1Historical Survey

EARLY GREEK ASTRONOMY:

Earth-centered universe - Some radical suggestions for a sun-centered model…

Shape of the Earth - Aristotle (4th century BCE) made the first known reference:

- Spherical shape of Earth’s shadow during a lunar eclipse.

- Stars rise to a different “altitude” depending on where

you are on Earth.

Obliquity of Earth - Angle between plane of the Sun’s motion in the sky (the

ecliptic) and the plane of Earth’s equator.

- Known in the 6th century BCE – measured angle differences for

shadows at the summer solstice and the winter solstice ≈ 470.- Tropic of Cancer is at +23.50; tropic of Capricorn is at -23.50

- Eratosthenes (276 – 194 BCE) measured a difference of 11/83

of a circle = 470 43’

- Real value NOW = 460 26’ – has decreased by ~15’ since antiquity.

Horizontalsundial– tracksofshadowwithtimeofdayandseason

Credit : Jean-Pol GRANDMONT

Meridian Line at the Church of Santa Maria degli Angeli, Rome (~1700 AD).

ECLIPTIC and the ZODIAC:

Looking from Earth, the Sun moves in the Ecliptic plane – defined by solar eclipses since you can’t see the stars around the Sun.

Ecliptic plane corresponds to the Zodiac – the constellations through which the Sun and planets pass during a year.

Babylonian astronomers knew about the Zodiac in the 6th century BC; Greeks in the 5th century.

Object Axial tilt (°)Mercury ~0.01

Venus 177.4

Earth 23.439

Moon 1.542

Mars 25.19

Ceres ~4

Jupiter 3.13

Saturn 26.73

Uranus 97.77

Neptune 28.32

Pluto 119.61

OBLIQUITY- angle between the plane of the planet’s orbit about the Sun and the plane of the planet’s equator

Variations:

Earth: from 22.10 to 24.50 with a period of 42,000 yrs

Mars: from ~110 to 590 (huge!)

Earth’s obliquity is stabilized by the Moon; this may change in about 1.5 billion years as the Moon moves away from the Earth.

FromDr JohnSmetankaStVincentCollege

In2500years,at50”peryear,precessionamountsto35deg,orjustover1“sign”oftheZodiac(360/12).

SothenodewasinAriesintheGreekperiod.

ECLIPTICandtheZODIAC(cont’d.):TheGreekastronomerHipparcos (130BCE)discoveredprecessionoftheequinoxes.

Astronomicalcoordinates:

RightAscensionandDeclination

(analogoustoLongitudeandLatitudeonEarth)

Needtospecifythedate(epoch)duetoprecessionoftheEarth’sequatorialplane,whichslowlymovestheVernalequinox.

ModernstarcatalogsgivepositionsattheEpochJ2000=2000Jan0.5UT.

SIZES and DISTANCES:1. Size of the Earth

Eratosthenes (276-194 BCE – librarian of Alexandria)

When the Sun was right overhead at Syene – near Aswan on the Nile river – as determined using a well, he measured the shadow angle at Alexandria on the Mediterranean coast of Egypt, using a Gnomen which measures angles as a fraction of a circle.

He found an angle of 1/50 of a circle. The distance was estimated at 5,040 stadia (I stadium thought to be about 157.5 m)

=> 250,000 stadia for the circumference of the Earth.

=> R = 6,270 km, which is VERY CLOSE to the true value of 6,370 km, but possibly somewhat accidental given the difficulty of the measurement.

Arclength=Rxθ (radians)

Relative sizes of the MOON & SUN:Aristarchus (~310 – 230 BCE)

From solar eclipses Aristarchus knew that the angular size of the Moon is approximately the same as that of the Sun.

Therefore: Sun ≈ 19 x size of the Moon

He also estimated the size of the Moon relative to that of Earth at ~1/4 using lunar eclipses, and thus concluded that the Sun is ~5 times larger than Earth.

Quartermoon– EMS=900

PLANETARY ORBITSMotion of the Sun: The working assumption was that the Sun moved at uniform

speed on a circle centered on Earth but inclined to Earth’s equator by 23.50.

=> Equal periods for all seasons.

But early Greeks realized that the lengths of the seasons are not the same!

Hipparcos (~130 BCE) measured:

Spring = 94 ½ days; Summer = 92 ½ days

Autumn = 88 1/8 days; Winter = 90 1/8 days

[We know now that this is because the orbit of Earth is an ellipse and its velocity varies with its orbital location.]

Greeks did not know this, so they had to

sacrifice one assumption è

They kept circles & constant speed, but

gave up on Earth at center of circle.

(Note that precession has since moved the

Equinox back by ~35 deg wrt perihelion.)

Gothere,25Jan

Copernicus (1543) showed that retrograde loops were a natural consequence of a Sun-centered solar system.

RETROGRADE LOOPS

Question faced by Greek astronomers: If the planets are also in circular orbits about Earth then why, at opposition (opposite the Sun) do the outer planets appear to go backwards in the sky?In a heliocentric model of the solar system this is due to the relative orbital motions of Earth and the outer planet.

Consider Earth and Mars:

Periods = 1.0 yr and 1.9 yr.

As Earth passes Mars, Mars appears to go “backwards” with respect to the stars.

EPICYCLES

Greeks solved the problem differently – they made the planets move around the Earth on epicycles!

First suggested by Apollonius but did not fully account for the observations.

PTOLEMY (1st half of 2nd century AD in Alexandria) refined previous models, to reachthe culmination of Greek astronomy:

Epicycle center moves at uniform angular speed on a circle – the Deferent – about the Equantthat is a point off-center from the circle, opposite the Earth.

Mars, Jupiter and Saturn’s epicycles are aligned with one another & with the Earth-Sun line.

Complicated but provided very accurate predictions of the orbits of the planets.

Ptolemaic theory held sway for ~1,400 years until the Copernican “revolution” in 1543.

Tycho Brahe – 1546-1601

Johannes Kepler – 1571-1630

Used Tycho Brahe’s measurements to determine orbital “laws”.

Very accurate positional measurements of the planets

Johannes Kepler (1571-1630) - THE THREE LAWS

(based on the very precise observations of Tycho Brahe)

1. Planetary orbits are ellipses with the Sun at one focus (1610).

2. The radius vector from the Sun to the planet sweeps out equal areas in equal times - i.e. r2 dθ/dt = constant (1610).

3. The orbital period squared is proportional to the semi-major axis of the ellipse cubed (1619).

i.e. a3/P2 = C = constant

N.B. If a – the semi-major axis - is in units of AU

and P – the orbital period - is in years,

Then C = 1 REMEMBER THIS!

If a and P are in physical units then C = G (Msun + Mplanet)/4π2 – Newton

G = Gravitational constant

CONCEPTS of the UNIVERSE

Plato & Aristotle: “crystal spheres” around EarthHipparchus & Ptolemy: Circular orbits and epicycles

- good predictions but very complicated

- by 1,500 AD there were 79 variables fitted

Copernicus: Heliocentric system; circular orbits. (On the Revolutions of the Heavenly Spheres, 1543)

Kepler: Heliocentric system with elliptical orbits. (The New Astronomy, 1610)

Galileo Galilei (1564 (?) – 1642

Galileo’s telescope –about 2 cm effective aperture

Jupiter and its moons (1609)

2009 – 400 years since the first telescope –International Year of Astronomy

GiordanoBruno1600

ORBITS: Confirmation of the heliocentric model of the solar system

1. Galileo (1609 and 1610)

- Observed that Venus showed “phases” just like the Moon.

- not correct with the epicycle model (Venus is never fully lit)

- Discovered the Jovian (Galilean) satellites.

- clearly in orbit about Jupiter – a mini-solar system

2. Bradley (1783)

- Detected stellar aberration – a shift in apparent

position of a star due to velocity of Earth in its orbit

- Position shift is vEarth/c = 10-4 rad = 20 arcsec.

3. Bessel (1830)

- Observed stellar parallax – shift in apparent nearby star position when

observed from Earth at different locations in its orbit.

- Position shift is ~ aEarth/D = 1 arcsec at D = 1 pc = 206,265 AU.

Handy numbers (approximate only!):One AU = Earth – Sun distance = 150 x 106 km

Lunar orbit semi-major axis ≈ 60 Earth radii

Earth radius ≈ 6,400 km ≈ 4 lunar radii

Jupiter radius ≈ 10 Earth radii

Solar radius ≈ 10 Jupiter radii ≈ 100 Earth radii

Angular size of Moon and Sun ≈ 0.50 or ~0.01 radians

Planetary symbols:

MostlyInheritedfromtheGreeks.Stillusedbymodernplanetaryscientists.

ASTRONOMICAL DISTANCE SCALE:

Astronomical Unit (AU): Mean distance from Earth to the Sun

(1 AU = 149.598 x 106 km)

Light year: Distance light travels in one year (= 9.46065 x 1012 km)

Parsec: Distance at which 1.0 AU subtends 1 arc sec, or ~ 206,265 AU

(in physical units, 1 pc = 3.08568 x 1013 km ~ 3.26 light years)

- common unit for distances in our galaxy and the universe

Kiloparsec (kpc), megaparsec (Mpc) and gigaparsec (Gpc) are used on galactic and extragalactic scales.

Velocity of light: = 2.99792458 x 108 m s-1 = 300 m per microsec

Some“Modern”discoveries• UranusdiscoveredbyHerschelin1781.• CeresandPallasdiscoveredbyPiazziin~1801.• Neptune“discovered”byAdams,Leverrier andGallein

1846.• SatellitesofMarsseenbyHall,1877.• PlutodiscoveredbyTombaugh,1930.• RingsofUranus(1977),Jupiter(1979) &Neptune(1986).• SatelliteofPlutodiscoveredbyChristie,1978.• FirstKuiperbeltobject(QB1)discoveredin1992.• Firstextrasolar planetsdiscovered,1992,1995(51Pegb).

Weareprobablynearingthelimitofallwecanknowaboutastronomy.- SimonNewcomb,leadingUSastronomer,1888