ASTR 330: The Solar System Lecture 2: Finding Our Place in Space ~ and ~ A Historical Perspective on Astronomy Dr Conor Nixon Fall 2006

ASTR 330: The Solar System

Lecture 2:

Finding Our Place in Space

~ and ~

A Historical Perspective on Astronomy

Dr Conor Nixon Fall 2006


The Night Sky…

Dr Conor Nixon Fall 2006Picture credit: Wally Pacholka AMS

…what sorts of

things do we see?

“An', as it blowed an' blowed, I often looked up at the sky an' assed meself the question -- what is the stars, what is the stars?”

from Juno and the Paycock, by Sean O’ Casey


Constellations


• What do we mean by the term ‘constellation’?

• A constellation (meaning ‘stars together’) is a pattern of stars on the sky, popularly recognized to form the shape of a person, animal or object: e.g. Orion the hunter, Ursa Major the Great Bear, Libra the scales, etc.

• The stars comprising a constellation are only apparently clustered together in one place: they may actually be at greatly varying distances from us.


Orion: The

Hunter

Dr Conor Nixon Fall 2006Figure credit: wikipedi.org

ASTR 330: The Solar System The Orion Nebulae



Nebulae In Orion


M43 Horsehead Nebula(picture: Angle-Australian Telescope)

“Pillars of Creation” in M42, The Great Orion Nebula (picture: Hubble Space Telescope)


Apparent Motion of The Sun and Stars


(Circumpolar Stars Movie)

(Sirius Diurnal Motion Movie)

Movie credit: Rick Pogge, Ohio State

C:\Documents and Settings\nixon\My Documents\Solar System Lectures\Movies\circumpolar.mov

C:\Documents and Settings\nixon\My Documents\Solar System Lectures\Movies\SiriusDiurnalMotion.mov


Solar ‘motions’


• The Sun appears to travel from east to west across the sky each day.

• The path the sun takes across the sky changes during the year:

• Higher in the summer → longer days.• Lower in the winter → shorter days.



• apparent solar path on sky:

The Ecliptic

Figure credit: David P. Stern, Code 695, NASA GSFC


Seasonal Changes


• Some important dates:

• 21st June = northern summer solstice: longest day (northern hemisphere) shortest day (southern hemisphere)

• 21st December = northern winter solstice: shortest day (northern hemisphere) longest day (southern hemisphere)

• 21st September & 21st March … what? equal length day and night:

spring and fall equinoxes.


Extremes of Day and Night


• The extremes of solar motion occur at the poles:

• 24 hours daylight in mid-summer.• 24 hours darkness in mid-winter.

• What sort of seasonal variation in the length of day would we expect at the equator?


The Zodiac


• The Sun appeared to pass through 12 of the original constellations in the sky over the course of one year, hence your ‘sun-sign’ depending on which day you were born.

• The 12 signs were mostly animals, hence the ‘zodiac’ from the same Greek etymology as ‘zoo’.

• Actually, the Sun now passes through 13 constellations, and at different dates from the ‘official’ astrological ones!

Picture credit: [email protected]


Phases Of The Moon


• The Moon is observed to change in appearance over the course of about 30 days:

Why?


Lunar Phases: Explanation

Dr Conor Nixon Fall 2006Picture credit: wikipedia.org

• The position of the Moon, relative to the Sun (lighting) and Earth (viewer) determines whether we see the sunlit side, shadow side, or somewhere in between.


Eclipses


• The Sun, Moon and Earth all lie nearly in the same plane.

• Also, by coincidence, the apparent size, or angular diameter of the Moon and Sun as seen from the Earth are about the same.

• As the Moon goes round the Earth, what happens when:

• The Moon comes between the Earth and Sun?• The Earth comes between the Moon and Sun?


Solar Eclipse



Total Solar Eclipse



Views Of Solar Eclipses...


Below shows a sequence of shots as the eclipse unfolds…

The solar corona (‘crown’) – the outer part of the sun’s atmosphere, and normally invisible – is spectacularly revealed at totality. Many solar astronomers use this opportunity to study the corona.


“Bailey’s Beads”


What could be causing the ‘beading’ effect?


Lunar Eclipse



Lunar Eclipse Views…


Why does the moon not disappear completely at totality?


Announcements 9/5/06


• Revised Office hours:

Conor Nixon: 11-12 Tuesdays and 2-3 Thursdays Room CSS 0225

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Room CSS 0224

• Yellow forms & enrollment.

• Textbooks.

• Homework #1 out today. Due back 9/12/06.


The Moon and the Calendar


• The near 30-day cycle of lunar phases gives us the basic period of one ‘monath’, or month.

• We can then simply divide the year (solar cycle) into 12 months (lunar cycles), with some extra days being added to some of the months.

• We already know where the idea of ‘day’ comes from…

… but where does the 7-day week come from??


Wandering Stars


• In the night sky, there are five points of light visible to the naked eye, which move, like the Sun and Moon, and unlike the stars in the fixed constellations.

• The Greeks used the term ‘wanderer’ from which we get the word ‘planet’.

• These acquired the names of different gods in different cultures: we use the Roman names:swift Mercury the messenger god, bright Venus goddess of love, red Mars god of war, kingly Jupiter, and slow-moving Saturn, god of time.


Planets, Astrology, Alchemy


• Over time, the seven ‘heavenly bodies’ became associated with more than just deities:

Planet Symbol Metal Weekday (latin)

Sun Gold Sunday

Moon Silver Monday

Mercury Mercury Wednesday

Venus Copper Friday

Mars Iron Tuesday

Jupiter Tin Thursday

Saturn Lead Saturday

Symbol graphics from astro.uvic.ca


Motions of the planets


• The planets wandered through the same 12 constellations of the zodiac as the Sun and Moon.

• Mercury and Venus stayed close to the Sun and so were always seen at dawn or dusk (hence the ‘Evening Star’). The others could be seen during the night as well.

• However, unlike the Sun and Moon, these planets exhibited curious ‘retrograde motion’ – periodic reversals of direction.


Retrograde Motion


Picture: www.mhhe.com

The apparent motion of Mars, Jupiter and Saturn was erratic, showing retrograde loops in their forward motion.

(Mars Retrograde Movie)Movie credit: Rick Pogge, Ohio State

C:\Documents and Settings\nixon\My Documents\Solar System Lectures\Movies\marsretro95.mov


Geocentric System


• To the ancient Greeks, the circle was the most perfect geometric figure. The Sun, Moon and planets were thought to be perfect, unchanging bodies circling a stationary Earth – a geocentric universe. There was little reason to doubt this hypothesis.

• However, an explanation for retrograde motion and also the periodic variations in brightness of the planets was needed. This was provided by a system of circles within circles: known as epicycles.

• The triumph of ancient astronomy was the Ptolemaic system of epicycles (after Claudius Ptolemy, right, 2nd century AD) which endured for over 1000 years!


Aristotle’s Geocentric Universe

Dr Conor Nixon Fall 2006Picture credit: phys.utk.edu


Ptolemy’s Epicycles


Picture and animation credit: phys.utk.edu


Nicholaus Copernicus (1473-1543)


• Copernicus was the reluctant revolutionary who overthrew the geocentric universe.

• In a book published at the end of his life, he proposed that a much simpler model of the universe was possible, if we assume that the Sun is at the center and the Earth and other planets circled around it.

• This heliocentric model was a heretical view in the 16th century!

• In fact, Aristarchus of Samos had proposed a heliocentric model around 200 BC, but Aristotle’s view won (back then)! What were the objections?

Picture: Univ. St. Andrews


Copernican Heliocentric Universe


Picture credit: phys.utk.edu


Retrograde motion in the Copernican system

Dr Conor Nixon Fall 2006Animation credit: phys.utk.edu

Much fewer epicycles were needed.



• the Earth’s view of the Sun changes over the year:

The Ecliptic: revisited

Figure credit: David P. Stern, Code 695, NASA GSFC

• definition: 1 astronomical unit (AU) is the average distance from the Earth to the Sun (150 million km, 93 million miles).


Johannes Kepler (1571-1630)


• Kepler took Copernicanism a step further. By analyzing very precise astronomical observations made by his mentor, Tycho Brahe (1546-1601), he realized that circles were hopeless for fitting the data.

• Kepler’s genius was to fit the motions of Mars using an elliptical orbit, with the Sun at one focus:

Picture credit: phys.utk.edu



Kepler’s Laws (1)


1. Law of Orbits: Each planet moves in an elliptical orbit about the sun, with the Sun at one focus of the ellipse.

Picture credit: gsu.edu

a = semi-major axise = eccentricityRa = aphelion distanceRp = perihelion distance


Kepler’s Laws (2)


2. Law of Areas: An imaginary line connecting the Sun with a planet sweeps out equal areas in equal times as the planet moves about the sun.



Kepler’s Laws (3)


3. The Law of Periods: The square of the period of any planet is proportional to the cube of the semi-major axis of orbit.


T2 = K a3


Galileo Galilei (1564-1642)


• Galileo provided the first crucial evidence that the Copernican solar system was physical reality, not just a useful aid to calculation.

• Galileo enthusiastically took to the new tool of science: the telescope, and turned it on the sky. He soon found:

1. The four large moons of Jupiter, a mini-solar system, in itself.

2. The phases of the planet Venus, similar to the moon.

3. The rings of Saturn.



Isaac Newton (1642-1727)


• Newton was a temperamental genius who founded multiple areas of classical physics: including optics, gravitation, and mechanics.

• His three laws of motion (see textbook) form the basis of mechanics.

• Newton crucially realized that the force which holds the Moon in its orbit about the Earth is the same force causing an apple to fall to the ground.

• Newton was hence able to deduce the famous inverse-square law of gravity, and prove Kepler’s laws.


Newton’s Law of Universal Gravitation


221

R

MGMF =

“The gravitational force between two objects is proportional to product of their masses and inversely proportional to the square of the distance between them”.

• This centrally-acting force opposes the tendency of the planets to continue in straight line motion, and holds them in orbit about the sun.


Newton’s Cannon and orbits


• Newton proposed a ‘thought experiment’ in which a cannon was fired from a mountaintop, at progressively greater and greater speeds.

• The ball falls further and further from the mountain, and eventually ‘misses’ the Earth altogether!

• Today, we know it is possible to do as Newton imagined and to send objects into orbit…


Blast-Off!


Picture and movie credit: NASA KSC

(STS 108 Launch Movie)

C:\Documents and Settings\nixon\My Documents\Solar System Lectures\Movies\sts-108_launch.mov


Escape Velocity


• Orbital velocity depends on the altitude of the orbit:

• LEO – Low Earth Orbit (200 km) requires 8 km/s• GEO – Geo-stationary Earth Orbit requires about 10 km/s

• At a velocity of 11.2 km/s, known as escape velocity, the spacecraft can escape the Earth’s gravity and go into solar orbit.

• This is the minimum velocity required for spacecraft to reach other planets.


Numerical Examples from Chapter 1


• Question 2: What is the revolution period of a hypothetical planet that orbits the Sun at half the distance of Mercury?

Kepler’s third law states that T2 = Ka3, where T is the orbital period and a is the semi-major axis of orbit. If T is in years and a in AU (distance from Sun to Earth) then K=1. So T2 = a3.

Now, Mercury orbits the Sun at a=0.39 AU. So, a for the proposed planet is 0.195, and a3 = (0.195)3 = 7.41 x 10-3.

Finally, T = √(7.41 x 10-3) = 0.086 years.

• Of one that has twice the distance from the Sun as Pluto? (distance of Pluto = 39.48 AU). You do it!

Answer: 702 years!

Quick method: rearrange formula to T=√(a3)=a1.5


Numerical Examples from Chapter 1


• Question 5: A spacecraft on a trajectory from the Earth to Saturn follows an ellipse with perihelion at the Earth’s orbit (1 AU) and aphelion at Saturn’s orbit (9 AU). If the semi-major axis of the ellipse is 5 AU what is the time required for the trip from the Earth to Saturn?

The key here is to realize that the spacecraft is in an orbit about the Sun, although an elliptical one. Kepler’s third law is applied again, to calculate the period, T = √(a3) = √(53) = 11.2 years.

But, this is the time for one complete orbit. We only need the time from perihelion to aphelion, or half the total time, = 5.6 years.

• Using similar reasoning, find the trip time to Mars (1.5 AU).

Answer: ½ T = ½ √(a3) = ½ √(1.253) = 0.7 years.


Quiz - Summary


1. What is a constellation?

2. Define ecliptic and zodiac, and explain the relation between them.

3. What causes a solar eclipse? A lunar eclipse?

4. What is meant by a geocentric universe? A heliocentric one?

5. Which is the odd one out: 1 day, 1 week, 1 month, 1 year?

6. Give a major contribution to astronomy by each of the following: Aristotle, Ptolemy, Copernicus, Kepler, Galileo, Newton.

7. What are Kepler’s three laws of planetary motion?