introduction to astronomy - iniciotpuzia/puc/2014b-ia-lectureexercises_files/... · diurnal...

Introduction to Astronomy !AST0111-3 (Astronomía)

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Semester 2014B

Prof. Thomas H. Puzia

1. Celestial Sphere

2. Diurnal Movement

3. Annual Movement

4. Lunar Movement

5. The Seasons

6. Eclipses

Theme Our Sky

Precession

• The axis of the Earth (and of the celestial sphere) precesses like the axis of rotation of a top (trompo). The period of this movement is very long: P = 26000 yr.

• The Earth is not perfectly spherical, it is wider at the Equator by ~43 km. The inclination of the rotational axis and the asymmetric gravitational pull of the Sun and the Moon produce a change (“torque”) in the axis direction.

• Thus the Earth's equatorial plane changes position gradually. This precession of the equinoxes was discovered by Hipparchus in the second century BC.

• Example: Today, the spring equinox is in Pisces, but in the year 2600 it will be in Aquarius.

• Nutation: a small oscillatory motion superimposed on the Earth's axis precession.

The Nutation of Equinoxes

Nutation (discovered by James Bradley in 1748) is generally described as the sum of higher-order terms of Earth’s polar motion due to some time-variable nature of tidal forces that act on Earth’s body (“Precise Geoid”). !Nutation is generally:

split into vector terms parallel and perpendicular to the direction of precession split into short- and long-period terms due to various effects, such as time-dependent distances of moon, sun, jupiter et al., variable tilt of orbits e.g. moon vs. earth orbit, ocean currents, location of Earth crust relative to her NiFe core, etc. largest nutation component (17x9 arcsec) has a period 6798 days or 18.6 years, while the second-largest (1.3x0.6 arcsec) has a period of 183 days. For unknown reasons nutation terms appear to avoid periods in the range of 34.8 to 91 days.

Sun

View of Earth from Mars

Mean distance: 385000 km Mass ratio: 81:1 !Double planet? No: Barycenter is 1750 km under Earth’s surface

Lunar Movement! We observe that the Moon also changes position with

respect to the “fixed” background stars. " This is the result of the Moon’s orbit around the Earth.

! Additionally, we observe that the Moon has phases: new(nueva), 1st quarter (creciente), full (llena), 3rd quarter (menguante). " This is the result of the relative position of the Sun, which

illuminates the Moon, as seen from the Earth. ! The Moon always shows the same “face” to the Earth: thus

its period of rotation = its period of revolution. " This is a result of the tidal forces (of the sea) between the

Earth and the Moon. Note: this does not mean that the opposite “face” of the Moon

is always dark (just that we cannot see it).

Phases of the Moon

! Sidereal month = 27.3d is the time that takes the Moon to orbit once around the Earth. ! Sinodic Month = 29.5d is time it takes lunar phases to repeat themselves

Phases of the Moon

Eclipses! The plane of the lunar orbit is inclined ~5 degrees with respect to the ecliptic plane

Eclipses

Eclipses of the Moon! Eclipses of the Moon are more frequent that those of the Sun ! Additionally, the time duration is longer than those of the Sun ! This demonstrates that the Earth > Moon in size.

Eclipses of the Sun

! Depending on the type of occultation, eclipses of the Sun can be total, partial, or annular.

Eclipse of the Sun! Solar Eclipse: as seen from the Earth and the Moon.

simulation!

Eclipses Solares

Solar Eclipses

Saros Cycle

every ~18 yrs eclipse geometry repeats (but not same as viewed from Earth)

Moon Affects TidesCaused by slight differential gravitational forces on near and far side of Earth facing the Moon. !Daily effect relatively small: 0.1% change in gravity force between near and far sides. !During course of 1 day, Earth rotates through 2 high and 2 low tides. !Compare height of typical high/low tides to pole and equator radius difference due to rotation.

“effective” net force

The Sun also produces tides (~5x weaker than Moon). These can add or cancel with those of the Moon.

“Spring”

“Neap”strong

weak

Sun Also Affect Tides

Why does the Moon look dramatically larger sometimes and smaller others?

A. In its orbit around the Earth, it occasionally gets really close or really far B. It expands and contracts due to tidal forces C. The atmosphere acts as a magnifying glass so it is bigger sometimes D. It is an optical illusion

Why does the Moon look dramatically larger sometimes and smaller others?

A. In its orbit around the Earth, it occasionally gets really close or really far B. It expands and contracts due to tidal forces C. The atmosphere acts as a magnifying glass so it is bigger sometimes D. It is an optical illusion

Can the Moon’s distance change much in 6 hrs?

“Movements” of the Moon

Moon distance varies +/- 5% from apogee to perigee over ~7 yrs ➠ ~20% gravitational force variation (causes perigean tides)

“Movements” of the Moon

Key Concepts:

Celestial Sphere + coordinates (more later)

Times (days, months, years). Sidereal vs. Solar/Synodic (more later)

Seasons.

Phases of the Moon.

Eclipses.

Tides.

Theme

Coordinate Systems

Different types

How to use

Coordinate System Fundamental Plane

Poles Coordinates Zero Point

Geographic (Earth) Equator Poles latitude longitude

Greenwich, UK

Local = Horizontal (also Alt/Az or Az/El)

Horizon zenith/nadir elevation (or altitude) azimuth

Your meridian

Equatorial celestial equator celestial poles declination right ascension/hour angle

Vernal Equinox Epoch (J2000)

Ecliptic ecliptic ecliptic poles ecliptic latitude ecliptic longitude

Sun + VE Epoch (J2000)

Galactic galactic plane galactic poles galactic latitude galactic longitude

Galactic Center

Supergalactic supergalactic plane

supergalactic poles

supergalactic latitude supergalactic longitude

Intersection of Galaxy plane and supercluster plane

Coordinate Systems

Coordinate Systems

Coordinate Systems

Equatorial Coordinates

R.A. = right ascension!Dec. = declination

Coordinate Systems

GalacticHorizontal

Equatorial

The arc of C-Υ-R-D is the curve of the of Celestial Equator

R-S corresponds to a segment of the great meridian circle N-Z-R-S Υ is the vernal equinox or “first point of constellation Aries” (actually in Pisces now). The direction of Υ is nominally “fixed” relative to the stars (but precesses slowly).

!X position of the star: arc between X-C is star’s declination δ (+90°,-90°) arc between Υ-C is star’s right ascension α (0-24h)

α increases to the East of Υ.

!Hour angle, H, time since the object crosses the meridian. !If H = 0, object on the meridian (N-Z-R-S), transit, ⇒ ST = α (object passes meridian)

Equatorial Coordinates

WestEast S

HRD

Motion!of Y

Y

X

Motion!of X

Cα

δ Υ

Horizon

Equator

With respect to object X, object Y will

A. Transit before object X. B. Transit after object X. C. Transit at the same time. D. None of the above

A. Appear to move faster on the sky B. Appear to move slower on the sky C. Appear to move at the same speed D. None of the above, since stars do not move

What are the highest/lowest declinations which are visible from Santiago?

WestEast S

HRD

Motion!of Y

Y

X

Motion!of X

Cα

δ Υ

Horizon

Equator

http://www.physics.sfasu.edu/astro/Planets/planetchart.htmlCheck out animation of this at:

0h 1h 2h 3h 4h 5h 6h 7h 8h 9h 10h 11h 12h 13h 14h 15h 16h 17h 18h 19h 20h 21h 22h 23h 24hRight Ascension

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0h 1h 2h 3h 4h 5h 6h 7h 8h 9h 10h 11h 12h 13h 14h 15h 16h 17h 18h 19h 20h 21h 22h 23h 24h

Locations of visible planetsD

eclin

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Locations of visible planets

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