Early Astronomy

← Astro210

Greek

• Aristotle
• earth is spherical
• partial lunar eclipses
• some stars visible from southern locations but not northern and vice versa
• had ideas regarding perfect geo influenced by Pythagoras and Plato

\item Aristarchus (310-230 BC):

• unpreceded heliocentric framework
• trig distances earth-moon-sun system
• angular diameters ${\theta }_{sun}\approx {\theta }_{moon}\therefore \frac{A}{C}=\frac{D_{moon}}{D_{moon}}$
• diameters from lunar eclipses $D_{moon}<D_{earth}$

\item Eratoshs (176-195 BC):

• Determined radius of spherical earth $R_E$
• Sun at zenith at noon on summer solstice at Aswan
• But further north in Alexandria, Egypt, the sun is south of the zenith by angle $\alpha$

\item Hipparchus (190-120 BC):

• Discover precession of the equinoxes from examination of star catalogs over centuries
• established the magnitude system

\item Copernicus (1473-1543):

• heliocentric
• earth rotates
• still assumed uniform circular celestial motion
• inferior planets: orbit smaller than earths
• superior planets: orbits larger than earths

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Emergence of modern Astro

\large Inferior planets

• B/C = sin ${\theta }_E$
• B=C Sin ${\theta }_E$
• C is AU
• Early astronomers didnt know C, so they could only infer rations of B/C. Ie. Orbital radii measured in AU

\large Superior Planets

• Measure time between opposition and eastern quadrature
• want angle $\theta$ between opp and east quad
• $\theta =({\omega }_E-{\omega }_p)$ and $C/B=cos\theta$
• measure $\tau$ and synodic period, calculate sidereal period and ${\omega }_p$; know ${\omega }_E$ and infer $C/B$

\large Galilean Revolution

• Galileo Galilei (1564 -1642)
• \begin{list}{-}{}
• improved and used a basic refracting telescoping

\item def publication of early results 1610 “starry messenger” \item - Moon is cratered; not a perfect Sphere

• milkyway is made out of stars
• Jupiter has moons (or as he thought, stars)
• measured phases of Venus

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\large Phases of Venus

• direct confrontation with Ptolemaic geocentric models
• in Ptolemaic models you only see crescent phases

\large Tycho Brahe (1546-1601)

• Denmark, later Prague
• Given island by king Fredrick (and staff)
• made a accurate and vast database of celestial motion
• had a lead nose?
• Threw giant ragers
• supernova named after him

\large Johannes Kepler (1571–1630, Prague)

• ‘Inherited’ (maybe stole) Brahe’s data
• also has a SN
• Kepler fit a new empirical model of heliocentric orbits, abandoning perfect circles \begin{list}{-}{}
• “It was as if I awoke from sleep and saw a new light” (Kepler, New astronomy)

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\large Kepler’s Laws

First law

• The planets travel on elliptical orbits with the sun at one focus
• Semimajor axis, half the major axis
• eccentricity: how elliptical (stretched) an orbit is - distance between foci divided by major axis.

**second law **

• A line drawn from the sun to a planet sweeps out equal areas in equal time intervals’
• perihelion: orbital point closet to the sun
• aphelion: furthest orbital point from the sun

**third law **

Def: The square of the sidereal orbital periods of the planets are prop to the cubes of the Semimajor axis of their orbits $p^2=K{a}^3$ \begin{center} P = planets sidereal period

a= length of semimajor axis

K = constant

\end{center}

\large Consequences of heliocentric model

• retrograde motion of outer planets
• positions of outer and inner planets wrt sun
• annual parallax
• aberration of starlight
• Coriolis effect

\large Parallax

• annual parallax: change in the apparent position when seen from two diff locations due to earth revolving around the sun. First measured by Bessel in 1838

\large Aberration of starlight

• deflection of apparent stellar positions in the direction of the observers motion
• analog: running throw rain and getting wet in the front and not in the back
• detected (Picard, 1680); explained (Bradley, 1729)
• telescope is moving along orbital vector around the sun; translation along orbit cannot exceed transit time of light through telescope

\large Coriolis effect: evidence of earth rotation

• Coriolis acceleration is perp to the direction of motion
• $\overrightarrow{a_{cor}}=s\vec{v}\times \vec{\omega }$
• can be deduced from a pendulum
• and in hurricanes!