ASTRO 6570 Lecture 1

Transcription

1 ASTRO 6570 Lecture 1 Historical Survey

2 EARLY GREEK ASTRONOMY: Earth-centered universe - Some radical suggestions for a sun-centered model Shape of the Earth - Aristotle (4 th 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 6 th century BCE measured angle differences for shadows at the summer solstice and the winter solstice Tropic of Cancer is at ; tropic of Capricorn is at Eratosthenes ( BCE) measured a difference of 11/83 of a circle = Real value NOW = has decreased by ~15 since antiquity.

3 Horizontal sundial tracks of shadow with time of day and season

4 Credit : Jean-Pol GRANDMONT Meridian Line at the Church of Santa Maria degli Angeli, Rome (~1700 AD).

5 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 6 th century BC; Greeks in the 5 th century.

6 OBLIQUITY- angle between the plane of the planet s orbit about the Sun and the plane of the planet s equator Object Axial tilt ( ) Mercury ~0.01 Venus Earth Moon Mars Ceres ~4 Jupiter 3.13 Saturn Uranus Neptune Pluto Variations: Earth: from to with a period of 42,000 yrs Mars: from ~11 0 to 59 0 (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.

7 ECLIPTIC and the ZODIAC (cont d.): The Greek astronomer Hipparcos (130 BCE) discovered precession of the equinoxes. In 2500 years, at 50 per year, precession amounts to 35 deg, or just over 1 sign of the Zodiac (360/12). From Dr John Smetanka St Vincent College So the node was in Aries in the Greek period.

8 Astronomical coordinates: Right Ascension and Declination (analogous to Longitude and Latitude on Earth) Need to specify the date (epoch) due to precession of the Earth s equatorial plane, which slowly moves the Vernal equinox. Modern star catalogs give positions at the Epoch J2000 = 2000 Jan 0.5 UT.

9 SIZES and DISTANCES: 1. Size of the Earth Eratosthenes ( BCE librarian of Alexandria) Arc length = R x θ (radians) 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 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.

10 Relative sizes of the MOON & SUN: Aristarchus (~ BCE) Quarter moon EMS = 90 0 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.

11 PLANETARY ORBITS Motion 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 => 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; Autumn = 88 1/8 days; Summer = 92 ½ 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.)

12 Got here, 25 Jan

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

14 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 (1 st half of 2 nd century AD in Alexandria) refined previous models, to reach the culmination of Greek astronomy: Epicycle center moves at uniform angular speed on a circle the Deferent about the Equant that 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.

15 Tycho Brahe Very accurate positional measurements of the planets Johannes Kepler Used Tycho Brahe s measurements to determine orbital laws.

16 Johannes Kepler ( ) - 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. r 2 dθ/dt = constant (1610). 3. The orbital period squared is proportional to the semi-major axis of the ellipse cubed (1619). i.e. a 3 /P 2 = 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 (M sun + M planet )/4π 2 G = Gravitational constant Newton

17 CONCEPTS of the UNIVERSE Plato & Aristotle: crystal spheres around Earth Hipparchus & 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)

18 Galileo Galilei (1564 (?) 1642 Giordano Bruno 1600 Galileo s telescope about 2 cm effective aperture Jupiter and its moons (1609) years since the first telescope International Year of Astronomy

19 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 v Earth /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 ~ a Earth /D = 1 arcsec at D = 1 pc = 206,265 AU.

20 Planetary symbols: Mostly Inherited from the Greeks. Still used by modern planetary scientists. Handy numbers (approximate only!): One AU = Earth Sun distance = 150 x 10 6 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 or ~0.01 radians

21 ASTRONOMICAL DISTANCE SCALE: Astronomical Unit (AU): Mean distance from Earth to the Sun (1 AU = x 10 6 km) Light year: Distance light travels in one year (= x km) Parsec: Distance at which 1.0 AU subtends 1 arc sec, or ~ 206,265 AU (in physical units, 1 pc = x 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: = x 10 8 m s -1 = 300 m per microsec

22 Some Modern discoveries Uranus discovered by Herschel in Ceres and Pallas discovered by Piazzi in ~1801. Neptune discovered by Adams, Leverrier and Galle in Satellites of Mars seen by Hall, Pluto discovered by Tombaugh, Rings of Uranus (1977), Jupiter (1979) & Neptune (1986). Satellite of Pluto discovered by Christie, First Kuiper belt object (QB1) discovered in First extrasolar planets discovered, 1992, 1995 (51Peg b).

23 We are probably nearing the limit of all we can know about astronomy. - Simon Newcomb, leading US astronomer, 1888