Astro 101Fall 2013 -- Lecture #2

Ancient Observers Noticed the “Wandering Stars” (e.g., planets) …

They saw that sometimes they had “retrograde” motion. But they thought thatEverything orbited the Earth. How could this be?

(example)

The hash marksshow the positionof Mars relative tothe fixed stars atFive-day intervals

The “Geocentric Model”

Aristotle vs. Aristarchus (3rd century B.C.):

Aristotle: Sun, Moon, Planets and Stars rotate around fixed Earth.

Ancient Greek astronomers knew of Sun, Moon, Mercury, Venus, Mars, Jupiter and Saturn.

Aristotle: But there's no wind or parallax.

Difficulty with Aristotle's "Geocentric" model: "Retrograde motion of the planets".

Aristarchus: Used geometry of eclipses to show Sun bigger than Earth (and Moon smaller), so guessed Earth orbits Sun. Also guessed Earth spins on axis once a day => apparent motion of stars.

But if you support geocentric model, you must attribute retrograde motion to actual motions of planets, leading to loops called “epicycles”.

Ptolemy's geocentric model (A.D. 140)

Retrograde Motion – Correct Explanation

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"Heliocentric" Model

● Rediscovered by Copernicus in 16th century.

● Put Sun at the center of everything.

● Much simpler. Almost got rid of retrograde motion.

● But orbits circular in his model. In reality, they’re elliptical, so it didn’t fit the data well.

● Not generally accepted then.

Copernicus 1473-1543

Galileo (1564-1642)

Built his own telescope in 1609.400 years ago.

Discovered four moons orbiting Jupiter => Earth is not center of all things!

Co-discovered sunspots. Deduced Sun rotated on its axis.

Discovered phases of Venus, inconsistent with geocentric model.

Johannes Kepler• (1571 - 1630)• Born near Stuttgart• Studied philosophy and theology at Tubingen• Developed love for astronomy as a child• Showed high level of mathematical skill• Had a reputation as a skilled astrologer• Wanted to be a minister; became instead a

teacher of astronomy and math in Graz, Austria

• Became assistant to Tycho Brahe in 1601

• Developed Laws of Planetary Motion

Orbits of Planets – Heliocentric Model

All orbit in same direction.

Most orbit in same plane.

Elliptical orbits, but low eccentricity for most, so nearly circular.

Retrograde Motion – Correct Explanation

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Earth

Jupiter(for example)

Kepler's First Law

The orbits of the planets are elliptical (not circular) with the Sun at one focus of the ellipse.

Ellipses

eccentricity =

(flatness of ellipse)

distance between foci major axis length

Kepler's Second Law

A line connecting the Sun and a planet sweeps out equal areas in equal times.

Translation: planets move fasterwhen closer to the Sun.

slower faster

Kepler's Third Law

The square of a planet's orbital period, P, is proportional to the cube of its semi-major axis, a.

P2 α a3

(for circular orbits, a=radius).

Translation: the larger a planet's orbit,the longer the period.

So compare Earth and Pluto:

Object a (AU) P (Earth years)

Earth 1.0 1.0Pluto 39.53 248.6

With the scale of the Solar System determined, can rewrite Kepler’s Third Law as:

P2 = a3

as long as P is in years and a in AU.

Newton (1642-1727)

Kepler was playing with mathematical shapes and equations and seeing what worked.

Newton's work based on experiments of how objects interact.

His three laws of motion and law of gravity described how all objects interact with each other.

Newton's Correction to Kepler's First Law

The orbit of a planet around the Sun has the common center of mass (instead of the Sun) at one focus.

Timelines of the Big Names

Copernicus

Galileo

Brahe

Kepler

Newton1473-1543 1546-16011473-1543

1564-1642

1571-1630

1642-1727

At this time, actual distances of planets from Sun were unknown, but were later measured. One technique uses parallax.

“Earth-baseline parallax” uses telescopes on either side of Earth to measure planet distances.

The Celestial Sphere

Features:- Does not rotate with Earth- Poles, Equator- Coordinate System

An ancient concept, as if all objects at same distance.

But to find things on sky, don't need to know their distance, so still useful today.

Celestial Coordinates:

Right Ascension – parallel to lines of longitude, i.e., run from North to South

-- in units of Hours, Minutes, Seconds-- why? Correspondence with sidereal

rotation of the sky in 23 hr 56 min solar time

Declination – parallel to lines of latitude, i.e., parallel to Equator

N Pole

S Pole

S CelestialPole

N CelestialPole

Equator

Lines of R.A. (Right Ascension)

Lines of Decl. (Declination)+ = Northern hemisphere- = Southern hemisphere

A typical celestialcoordinate would looklike this:

21h 34m 13.3 sec+28.6 deg.

Earth

Earth sphere“projected” outwardsto the sky, except, itdoesn’t rotate with the Earth

Inclined view of the Earth’s orbit

The Year

The Earth revolves around the Sun in 365.256 days (“sidereal year”).

The "Solar Day" and the "Sidereal Day"

Solar Day

How long it takes for the Sun to return to the same position in the sky (24 hours).

Sidereal Day

How long it takes for the Earth to rotate 360o on its axis.

These are not the same!

One solar day later, the Earth has rotated slightly more than 360o .A solar day is longer than a sidereal day by 3.9 minutes(24 hours vs. 23 hours 56 minutes 4.091 seconds).

Inclined view of the Earth’s orbit

ScorpiusOrion

The Year

The Earth revolves around the Sun in 365.256 days (“sidereal year”). But the year we use is 365.242 days (“tropical year”). Why?

Precession

The Earth has a bulge. The Moon "pulls down" on the side of the bulge closest to it, causing the Earth to wobble on its axis (how do we know this?)

Spin axis**Vega Polaris

Precession Period 26,000 years!

Precessionanimation

Scorpius

Scorpius

Winter: July or January?

Winter: January

DayNight Day Night

Night

DayNight Day

Summer: January or July?

Summer: July

Now

13,000 years from now

We choose to keep July a summer month, but then in 13,000 years, summer occurs on other side of orbit!

Orion

Orion

The Motion of the Moon

The Moon has a cycle of "phases", which lasts about 29 days.

Half of the Moon's surface is lit by the Sun.

During this cycle, we see different fractions of the sunlit side.

Which way is the Sun in each case?

Q: What is a “Blue Moon” ?A: The second Full Moon occuring within a single calendar month. Occur, on average, once every 2.7 years.

Some American Full MoonsSeptember: Harvest Moon (Colonial American)October: Corn Ripe Moon (Taos)November: Sassafras Moon (Choctaw)December: Big Freezing Moon (Cheyenne)

… there are many others (names for every month) …

Cycle of phases slightly longer than time it takes Moon to do a complete orbit around Earth.

Cycle of phases or "synodic month"

Orbit time or "sidereal month"

29.5 days 27.3 days

Eclipses

Lunar Eclipse

When the Earth passes directly between the Sun and the Moon.Sun Earth Moon

Solar Eclipse

When the Moon passes directly between the Sun and the Earth.

Sun EarthMoon

Solar Eclipses

Total

Diamond ring effect - just before or after total

Partial Annular - why do these occur?

Lunar Eclipse

Why don't we get eclipses every month?

How can there beboth total and annular eclipses?

Moon's orbit tilted compared to Earth-Sun orbital plane:Sun

EarthMoon

Moon's orbit slightly elliptical:

Earth

Moon

Side view

Top view, exaggerated ellipse

Distance varies by ~12%

5.2o

Types of Solar Eclipses Explained

Certain seasons are favorable for eclipses. Solar “eclipse season” lasts about 38 days. Likely to get at least a partial eclipse somewhere.

It's worse than this! The plane of the Moon's orbit precesses, so that the eclipse season occurs about 20 days earlier each year.

Next total solar eclipse in N. America = August 2017

Rocket Science 101

Rocket Science 101• The same laws that govern the motion of the planets

around the sun (Kepler’s Laws) also govern:

-- Motion of satellites (“moons”) around planets-- Motion of artificial satellites and spacecraft around the Earth-- Motion of spacecraft on their way through the Solar System

• What are the differences?

-- The body creating the gravity that governs the orbit (the “central

body”) is not necessarily the same-- This determines the period of each orbit (time for

orbit)-- Orbits may be highly elliptical, or inclined-- This also affects the period-- The velocity (“speed”) of something moving in an

elliptical orbit will be different than the velocity of something moving in a circular orbit at the same distance from the central body

Example

CentralBody

CircularOrbit 1

CircularOrbit 2

EllipticalOrbit 3

Central Body could beEarth, Sun, Jupiter, …

P1 P2

Orbits 1 and 2 are circular, so the velocity of the satellite/moon/spacecraft is the same everywhere in each orbit, BUT Because the orbits have different radii (sizes = distances from the body), the velocities in the two orbits are not the same ! Velocity at P1 for Orbit 1 and Orbit 3 are also NOT the same (because they aren’t the same orbit!)

Some terminology

CentralBody

EllipticalOrbit 3

“peri” –Point of closestapproach =fastest speed inthe orbit

“Apo” –Point of furthestdistance =slowest speed inthe orbit

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Central body = Earth (satellites, Moon), we say “Perigee” and “Apogee”

Central body = Sun (planets, comets, asteroids, interplanetary spacecraft) we say “Perihelion” and “Aphelion”

We can use Kepler to our advantage …How to get from Orbit 1 to Orbit 2:

CircularOrbit 1

CircularOrbit 2

Elliptical (“transfer”)Orbit 3

Burn 1

Burn 2

Burn 1 =Add velocity so thatthe moving object hasthe proper velocity for the”transfer” orbit

It moves in the ellipseOut to point 2, then

Burn 2 = Add velocity so that themoving object has theproper velocity forOrbit 2

All of these velocitiescan be calculated fromKepler’s Laws

You can see satellites sometimes…http://www.heavens-above.com

ISS Pass20 Oct 2011Albuquerque

Sky Path