astro 101 – 001 summer 2013 -- lecture #2

Astro 101 – 001 Summer 2013 -- Lecture #2

Ancient Observers Noticed the “Wandering Stars” (e.g., planets) … They saw that sometimes they had “retrograde” motion. But they thought that Everything orbited the Earth. How could this be?

(example) The hash marks show the position of Mars relative to the fixed stars at Five-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 faster when 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 1.0 Pluto 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

Newton 1473-1543 1546-1601 1473-1543

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 Celestial Pole

N Celestial Pole

Lines of R.A. (Right Ascension)

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

A typical celestial coordinate would look like this: 21h 34m 13.3 sec +28.6 deg.

Earth

Earth sphere “projected” outwards to the sky, except, it doesn’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

Scorpius Orion

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!

Precession animation

Scorpius

Scorpius

Winter: July or January?

Winter: January

Day Night Day Night

Night

Day Night 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 Moons September: 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 Earth Moon

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 be both total and annular eclipses?

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

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

Central Body

Circular Orbit 1

Circular Orbit 2

Elliptical Orbit 3

Central Body could be Earth, 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

Central Body

Elliptical Orbit 3

“peri” – Point of closest approach = fastest speed in the orbit

“Apo” – Point of furthest distance = slowest speed in the orbit

x x

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:

Circular Orbit 1

Circular Orbit 2

Elliptical (“transfer”) Orbit 3

Burn 1

Burn 2

Burn 1 = Add velocity so that the moving object has the proper velocity for the”transfer” orbit It moves in the ellipse Out to point 2, then Burn 2 = Add velocity so that the moving object has the proper velocity for Orbit 2 All of these velocities can be calculated from Kepler’s Laws

10/20/11 11:40 AMISS - Visible Passes

Page 1 of 1http://www.heavens-above.com/PassSummary.aspx?satid=25544&lat=35.084&lng=-106.651&loc=Albuquerque&alt=1510&tz=MST

ISS - Visible Passes | Home | Info. | Orbit | Prev. | Next | Help |

Search period start: 00:00 Thursday, 20 October, 2011

Search period end: 00:00 Sunday, 30 October, 2011

Observer's location: Albuquerque, 35.0840°N, 106.6510°W

Local time zone: Mountain Daylight Time (UTC - 6:00)

Orbit: 374 x 396 km, 51.6° (Epoch Oct 18)

Type of passes to include: Visible only All

Click on the date to get a star chart and other pass details.

Date MagStarts Max. altitude Ends

Time Alt. Az. Time Alt. Az. Time Alt. Az.

20 Oct -0.9 19:05:32 10 WNW 19:07:36 16 NNW 19:09:41 10 NNE

22 Oct -0.5 18:45:38 10 NW 18:46:30 11 NNW 18:47:23 10 N

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10/20/11 11:40 AMISS - Visible Passes


ISS - Visible Passes | Home | Info. | Orbit | Prev. | Next | Help |










20 Oct -0.9 19:05:32 10 WNW 19:07:36 16 NNW 19:09:41 10 NNE

22 Oct -0.5 18:45:38 10 NW 18:46:30 11 NNW 18:47:23 10 N


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You can see satellites sometimes…

http://www.heavens-above.com

ISS Pass 20 Oct 2011 Albuquerque Sky Path

10/20/11 11:43 AMHST - Visible Passes


HST - Visible Passes | Home | Info. | Orbit | Prev. | Next | Help |










20 Oct 3.4 20:06:10 10 S 20:06:15 10 S 20:06:15 10 S

21 Oct 3.0 20:01:59 10 SSW 20:03:44 14 S 20:03:44 14 S

22 Oct 2.7 19:58:23 10 SSW 20:01:10 18 SSE 20:01:10 18 SSE

23 Oct 2.4 19:55:02 10 SW 19:58:22 22 SSE 19:58:32 22 SSE

24 Oct 2.2 19:51:49 10 SW 19:55:23 26 SSE 19:55:52 26 SSE

25 Oct 2.1 19:48:42 10 SW 19:52:25 30 S 19:53:11 28 SSE

26 Oct 2.0 19:45:40 10 WSW 19:49:28 32 S 19:50:27 28 SSE

27 Oct 2.0 19:42:40 10 WSW 19:46:30 33 S 19:47:44 28 SE

28 Oct 2.0 19:39:43 10 WSW 19:43:33 33 S 19:45:01 26 SE

29 Oct 2.1 19:36:48 10 WSW 19:40:35 31 S 19:42:20 23 SE


astro 101 – 001 summer 2013 -- lecture #2

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