PHYS 190 Study Guide - Midterm Guide: Planetary System, Sidereal Year, Radio Astronomy
10 May 2018
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Chapter 0: Charting the Heavens
- Thee’s o ight stas i the “outh elestial pole o southe Pole “ta
- Brightest stars are named by Greek letters alpha, beta (2nd brightest), etc.
o Limited use, best used for naked-eye astronomy
Celestial Coordinates
- More precise measurements, use celestial coordinates on the sky
- Just as Eath’s sufae is usig longitude and latitude, celestial analogs of those are: declination and right ascension
o These are fixed on celestial sphere (remain constant sphere)
o Declination: measured in degrees north or south of celestial equator
▪ Celestial equator is at 0 degrees. North: +90 | South: -90
o Right ascension (RA): measured in angular units hours, minutes and seconds; increases eastward direction
Diurnal motion: daily progress of the “u ad othe stas aoss the sk due to Eath’s otatio
Sidereal day: a day measured of the shift of stars each day (differs in length from a solar day)
Our planet takes 365 days to orbit the Sun, so the additional angle is 360ᵒ/365=0.986ᵒ.
- Because Earth take ~3.9minutes to rotate through this angle. Solar day is 3.9minutes longer than sidereal day
Ecliptic: apparent motion of the Sun on the sky traces out a path on the celestial sphere
Zodiac: 12 constellations on celestial sphere through which the Sun appears to pass during the course of the year
Summer solstice: point on the ecliptic where the Sun is at its northernmost point above the celestial equator
Winter solstice: southeost poit elo elestial euato Eath’s Noth Pole is oieted farthest from the Sun)
- “hotest da: Eath’s Nothe Heisphee | Logest da: “outhe Heisphee
- Summer: when Sun is highest above horizon and days are longest; much warmer than winter when Sun is low and days are short
- Earth is closest to Sun in early January (Northern Hemisphere). Distance from Sun cannot be main factor controlling our climate
Equinoxes: Earth rotation axis is perpendicular to line joining Earth to the Sun; days and nights are of equal duration
Tropical year: interval of time from 1 vernal equinox to the next (265.242 solar days)
Sidereal year: time required for Earth to complete 1 orbit around Sun
- 1 sidereal year: 265.256 solar days long (about 20mins longer than tropical year)
Precession: reason for slight difference between sidereal and tropical year
- Eath’s ais hages dietios oe tie, although agle etee ais ad lie pepediula to plae of elipti is always close to
23.5ᵒ (caused by combined gravitational pulls of Moon and Sun)
- During complete cycle of peessio takes ~6,s, Eath ais taes out oe. Beause of slo shift i oietatio of Eath’s
rotation axis, vernal equinox (tropical year) drifts slowly around ecliptic over course of precession cycle
Lunar Phases: Moo’s appeaae undergoes regular cycle of changes taking little more than 29 days to complete
- Full moon rises in east, Sun sets in West. 1st quarter Moon rises at noon, often becomes visible later i da as “u’s light fades
- Whe Moo is full, e see the etie da lit face because Sun and Moon are in opposite directions from Earth in sky
- Sun’s light is not blocked by Earth at the full phase because Moon’s orbit is inclined at angle of 5.2ᵒ to the plane of the ecliptic
Synchronous rotation: Moon always keep same face towards Earth
1 sidereal month (27.3d): Moon completes 1 revolution and returns to starting point on celestial sphere
1 synodic month (29.5d): time required for Moon to complete full cycle of phases
- Beause of Eath’s otio aoud “u, Moo ust oplete slightly more than 1 full revolution to return to same phase in orbit
Lunar eclipse: when Sun and Moon are in exactly opposite directions as seen from Earth
- Eath shado seeps aoss Moo, tepoail lokig “u’s light ad dakeig Moo
Partial eclipse: alignment of Sun, Earth and Moon is imperfect often casting deep red coloration
- sall aout of light eig efated et Eath’s atosphee onto lunar surface
Solar eclipse: Moon passes directly in front of Sun, turning day into night
Umbra: part of shadow where all light from the course is blocked
Penumbra: portion of shadow cast by eclipsing object which eclipse is seen as partial
Annular eclipse: thin ring of sunlight that can still be seen surrounding Moon
Small parallax implies large distance; large parallax implies small distance
Theory: framework of ideas and assumptions used to explain some set of observation and make predictions about real world
- must be continuously tested
Theoretical model: physical object or phenomenon accounting for its known properties. Model then makes further predictions about
ojet’s popeties o ho it ight ehae/hage ude e iustaes
- If experiments and observations favour predictions, theory can be further developed and refined
o If not: theory must be reformulated or rejected
find more resources at oneclass.com
find more resources at oneclass.com
- Theo a e ialidated sigle og peditio ut o aout of oseatio/epeietatio a ee poe it oet
- If theory cannot explain experimental result/observation or prediction are untrue, it must be discarded or amended
Scientific theories: must be testable | must be continually tested | should be simple and some sense elegant
Chapter 1: The Copernican Revolution
The Geocentric Universe
- Earliest models of solar system followed teachings of Greek philosopher Aristotle and were geocentric: Earth lay at center of universe
and all other bodies move around it (a better model was needed to describe the planets)
1st step toward new model: each planet was taken to move uniformly around small circle (epicycle), whose center moved uniformly around
Earth on 2nd and larger circle (deferent)
- Motio as oposed of sepaate iula oits, eatig possiilit that soe ties plat’s appaet otio could be retrograde
(backward loop)
- As number and quality of observations increased, astronomers had introduced small corrections into simple epicyclic model to bring
it into line with new observations
- Center of deferent had to be shifted slightly from Earth’s ete ad otio of epiles had to e iagied uifo ith espet
not to Earth but to another point in space
- Greek astronomer Claudius Ptolemaeus (Ptolemy) constructed best geocentric model of all time: Ptolemaic model (had 80 circles)
o Major errors lay in assuming of geocentric universe, compounded by insistence on uniform circular motion, the basis of which
was mainly philosophical than scientific
Aristarchus of Samos proposed that all planets revolved around the Sun and that Earth rotates on its axis once each day
- He as oet ut as ejeted i his lifetie eause Aistotle’s ifluee is too stog ad his itigs ee too opehensive
- Aristotelian school did present some simple and compelling argument in favour of their views
1. Eath does’t feel as if it’s oig
2. If Eath as oig, ould’t thee e stog id/foe as e oe high speed aoud “u?
3. The atage poit fo hih e ie stas hages oe ouse of a ea, h do’t e see stella paalla?
o we now know there is stellar parallax as Earth orbits the Sun
The Heliocentric Model of the Solar System
- 16thc Polish cleric Nicholas Copernicus rediscovered Atistahu’s Heliocentric (Sun-centered) model
- Said that Earth spins on its axis and like all other planets orbiting the Sun
Copernican revolution: realization toward end of 16thc that Earth is not center of universe
- Was iflueed Geek thikig, lug to idea of iles to odel plaets’ otio, foed to etai idea of epili otio, through
with the deferent centered on Sun rather than on Earth and with smaller epicycles than in Ptolemaic
o By saying Earth is not center, etc. it went against Roman Catholic Church
- On the Revolution of the Celestial Spheres: not published until 1543, year that he died
Galileo’s Historic Observations
- Was an Italian mathematician and philosopher
Using his telescope he made, Galileo discovered:
- Moon has mountains, valleys and craters, terrain much like Earth
- Sun has imperfections (dark blemishes): sunspots. Saw that these sunspots moved and concluded Sun rotates ~every month around
axis roughly perpendicular to ecliptic plane
- 4 small points of light, invisible to naked eye, orbit planet Jupiter; realized they were moons circling that planet
o Concluded that Earth is not center of the universe because of this
- Venus shows complete cycle of phases much like the familiar monthly changes like our Moon
- 1610 Galileo published his observations supporting Copernican theory, 1616 ideas were banned by Church, Galileo was told to
abandon astronomical pursuits, refused, published more findings, 1633 remained in house arrest till he died
Johannes Kepler, German mathematician and astronomer announced discovery of simple empirical laws describing motions of planets
- Tycho was educated as some best universities in Europe where he studied astrology, alchemy and medicine
- Kepler joined Tycho in Prague in 1600, as put to ok tig to fid theo that ould eplai Bahe’s plaeta data
- Tycho died yr later, Kepler inherits position: Imperial Mathematician of Holy Roman Empire & decades of observations of planets
o Tho’s oseatios ee ade ith aked ee
- Keple deteied shapes ad elatie sizes of eah plaet’s oit tiagulatio ot fo diffeet poits o Eath ut fom
diffeet poits o Eath’s oit usig oseatios ade at diffeet ties of the ea
o Succeeded in summarizing the motions, created laws of planetary motion
Keple’s “iple Las
1. The orbital paths of planets are elliptical not circular with the Sun at one focus
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
The(cid:396)e"s (cid:374)o (cid:271)(cid:396)ight sta(cid:396)s i(cid:374) the outh (cid:272)elestial pole (cid:894)(cid:374)o (cid:862)southe(cid:396)(cid:374) pole ta(cid:396)(cid:863)(cid:895) Brightest stars are named by greek letters alpha, beta (2nd brightest), etc. More precise measurements, use celestial coordinates on the sky. Just as ea(cid:396)th"s su(cid:396)fa(cid:272)e is usi(cid:374)g longitude and latitude, celestial analogs of those are: declination and right ascension. These are fixed on celestial sphere (remain constant sphere: declination: measured in degrees north or south of celestial equator. North: +90 | south: -90: right ascension (ra): measured in angular units hours, minutes and seconds; increases eastward direction. Diurnal motion: daily progress of the u(cid:374) a(cid:374)d othe(cid:396) sta(cid:396)s a(cid:272)(cid:396)oss the sk(cid:455) (cid:894)due to ea(cid:396)th"s (cid:396)otatio(cid:374)(cid:895) Sidereal day: a day measured of the shift of stars each day (differs in length from a solar day) Our planet takes 365 days to orbit the sun, so the additional angle is 360 /365=0. 986 . Because earth take ~3. 9minutes to rotate through this angle. Solar day is 3. 9minutes longer than sidereal day.
